Data Analysis

Probability

2010-02-03T08:39:00.000-08:00

Probability is a value that specifies whether or not an event is likely to happen. The value of probability generally lies between zero to one. If the probability of a happening of an event comes out to be zero, then that event would be considered successful. If the probability of a happening of an event comes out to be one, then that event would be considered a failure.
There are certain definitions of probability.

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A sample space S in probability is a non empty set whose elements are called outcomes. The events in the probability are nothing but the subsets of the sample space.

A probability space consists of the sample space and the probability function, which involves the mapping of the events to the real numbers in an interval of zero in such a way that the probability of the sample space is one. If A0 ,A1, ….. is the sequence of disjointed events, then the probability of the union of the sequence will be equal to the sum of the probability of all the disjointed events.

Conditional probability is that type of probability that denotes the probability of a particular event when it is given that another particular event has occurred, provided that the probability of the occurrence of the other particular event is not equal to zero.

There is a product rule in probability that states that the probability of the intersection of any two particular events is equal to the product between the probability of the second event and the conditional probability of the events.

The theorem of total probability states that if the sample space is the disjointed union of events, for example B1, B2, …. then for all events of A, then the probability of A will be equal to the sum of the probability of the intersection between the event A and the disjointed events Bi.

Suppose the two events, A and B, have a positive probability. In this case, the event A would be independent of B if and only if the conditional probability of A given the events B is equal to the probability of A. It is important to remember that this independence probability would be applicable only when the probability of the event B would not be equal to zero.

There is also an independence product rule in probability that states that the probability of the intersection of the two events is equal to the product of the probability of the event A and the probability of the event B. It is important to remember that in the theory of probability, the disjointed events are not the same as that of the independent events.

The theory of probability is the logic of science. According to James Clerk Maxwell (1850), the true logic involves the calculus of probability, which takes into consideration the magnitude of the probability that is supposed to be reasonable.

The theory of probability can be described with a popular example— the tossing of a coin with possible outcomes of “heads” or “tails.” Suppose “heads” is considered a success and “tails” is considered a failure. Thus, the probability of a success (“heads”) will be the probability of the value one, and the probability of failure (“tails”) is the value of zero. Similarly, rolling dice is another popular example based on the theory of probability.

F-test

2010-02-01T08:36:00.000-08:00

An F-test is conducted by the researcher on the basis of the F statistic. The F statistic in the F-test is defined as the ratio between the two independent chi square variates that are divided by their respective degree of freedom. The F-test follows the Snedecor’s F- distribution.

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The F-test contains some applications that are used in statistical theory. This document will detail the applications of the F-test.

The F-test is used by a researcher in order to carry out the test for the equality of the two population variances. If a researcher wants to test whether or not two independent samples have been drawn from a normal population with the same variability, then he generally employs the F-test.

The F-test is also used by the researcher to determine whether or not the two independent estimates of the population variances are homogeneous in nature.

An example depicting the above case in which the F-test is applied is, for example, if two sets of pumpkins are grown under two different experimental conditions. In this case, the researcher would select a random sample of size 9 and 11. The standard deviations of their weights are 0.6 and 0.8 respectively. After making an assumption that the distribution of their weights is normal, the researcher conducts an F-test to test the hypothesis on whether or not the true variances are equal.

The researcher uses the F-test to test the significance of an observed multiple correlation coefficient. The F-test is also used by the researcher to test the significance of an observed sample correlation ratio. The sample correlation ratio is defined as a measure of association as the statistical dispersion in the categories within the sample as a whole. Its significance is tested by the researcher using the F-test.

The researcher should note that there is some association between the t and F distributions of the F-test. According to this association, if a statistic t follows a student’s t distribution with ‘n’ degrees of freedom, then the square of this statistic will follow Snedecor’s F distribution, as in the F-test, with 1 and n degrees of freedom.

The F-test also has some other associations, like the association between the F-test and chi square distribution.

Due to such relationships, the F-test has many properties, like chi square. The F-values in the F-test are all non negative. The F-distribution in the F-test is always non-symmetrically distributed. The mean in F-distribution in the F-test is approximately one. There are two independent degrees of freedom in F distribution, one in the numerator and the other in the denominator. There are many different F distributions in the F-test, one for every pair of degree of freedom.

The F-test is a parametric test that helps the researcher draw out an inference about the data that is drawn from a particular population. The F-test is called a parametric test because of the presence of parameters in the F- test. These parameters in the F-test are the mean and variance. The mode of the F-test is the value that is most frequently in a data set and it is always less than unity. According to Karl Pearson’s coefficient of skewness, the F-test is highly positively skewed. The probability distribution of F increases steadily before reaching the peak, and then it starts decreasing in order to become tangential at infinity. Thus, we can say that the axis of F is asymptote to the right tail.

Autocorrelation

2009-12-17T08:25:00.000-08:00

Autocorrelation occurs due to the chance correlation of the error term of a particular household with some other household or firm. Autocorrelation is also named chance correlation. Autocorrelation is also applied in the case of time series analysis.

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The process of autocorrelation is defined as the correlation that exists between the members of the series of the observations that are planned with respect to time.

If two types of data are considered – a cross sectional type of data and a time series type of data—then for the cross sectional type of data, if the change in the income of a particular person affects the consumption expenditure of another household other than his, then autocorrelation is present in the data. Similarly, for the time series type of data, if an output is low in one quarter due to a labor strike, and if the data showing low output continues in the next quarter as well, then autocorrelation is supposed to be present in the data.

The process of autocorrelation is defined as the type of lag correlation for a given type of series with itself, which is lagged by several numbers of time units. On the other hand, serial autocorrelation is that type of autocorrelation that is defined as the process of lag correlation between two series in time series data.

There are certain patterns that are exhibited by autocorrelation.

Autocorrelation exhibits patterns among the residual errors. Autocorrelation also occurs in cases when the error shows a cyclical kind of pattern, etc.

The major reason why autocorrelation occurs is because of the inertia or sluggishness that is present in time series data.

The occurrence of the non stationary property in time series data also gives rise to the phenomenon of autocorrelation. Thus, to make the time series almost free of the problem of autocorrelation, the researcher should always make the data stationary.

The researcher should know that autocorrelation can be positive as well as negative. Economic time series generally exhibits positive autocorrelation as the series moves in an upward or downward pattern. If the series moves in a constant upward and downward movement, then autocorrelation is negative.

The major consequence of using ordinary least square (OLS) in the presence of autocorrelation is that it will simply make the estimator inefficient. As a result, the hypothesis testing procedures will give inaccurate results due to the presence of autocorrelation.

There is a popular test called the Durbin Watson test that detects the presence of autocorrelation. This test is conducted under the null hypothesis that there is no autocorrelation in the data. A test statistic called ‘d’ is computed, which is defined as the ratio between the sum of the square of the difference in the residuals with ith and (i-1) time and the square of the residual in ith time. If the upper critical value of the test comes out to be less than the value of ‘d,’ then there is no autocorrelation. If the lower critical value of the test is more than the value of ‘d,’ then there is autocorrelation.

If one detects autocorrelation in the data, then the first thing a researcher should do is that he should try to find whether or not the autocorrelation is pure. If it is pure autocorrelation, then one can transform it into the original model, which is free from pure autocorrelation.

Canonical Correlation

2009-12-16T13:03:00.000-08:00

A canonical correlation is a correlation between two canonical or latent types of variables. In canonical correlation, one variable is an independent variable and the other variable is a dependent variable. It is important for the researcher to know that unlike regression analysis, in canonical correlation, the researcher can find a relationship between many dependent and independent variables. A statistic called the Wilk’s Lamda is used for testing the significance of the canonical correlation. The work of the canonical correlation is the same as in simple correlation. In both of these, the point is to provide the percentage of the variances in the dependent variable that are explained by the independent variable. So, canonical correlation is defined as the tool that measures the degree of the relationship between the two variates.

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The process of canonical correlation is considered the member of the multiple general linear hypotheses, and therefore the assumptions of multiple regressions are also assumed in canonical correlation as well.

There are concepts and terms associated with canonical correlation. These concepts and terms will help a researcher better understand canonical correlation. They are as follows:

1. Canonical variable or variate: A canonical variable in canonical correlation is defined as the linear combination of the set of original variables. These variables in canonical correlation are a form of latent variables.

2. Eigen values: The value of the Eigen values in canonical correlation are considered as approximately being equal to the square of the value of the canonical correlation. The Eigen values basically reflect the proportion of the variance in the canonical variate, which is explained by the canonical correlation that relates to the two sets of variables.

3. Canonical Weight: The other name for canonical weight is the canonical coefficient. The canonical weight in canonical correlation must first be standardized. It is then used to assess the relative importance of the contribution of the individual’s variable.

4. Canonical communality coefficient: This coefficient in canonical correlation is defined as the sum of the squared structure coefficients for the given type of variable.

5. Redundancy coefficient, d: This coefficient in canonical correlation basically measures the percent of the variance of the original variables of one set that is predicted from the other set through canonical variables.

6. Likelihood ratio test: This significance test in canonical correlation is used to carry out the significance test of all the sources of the linear relationship between the two canonical variables.

There are certain assumptions that are made by the researcher for conducting canonical correlation. They are as follows:

1. It is assumed that the interval type of data is used to carry out canonical correlation.

2. It is assumed in canonical correlation that the relationships should be linear in nature.

3. It is assumed that there should be low multicollinearity in the data while performing canonical correlation. If the two sets of data are highly inter-correlated, then the coefficient of the canonical correlation is unstable.

4. There should be unrestricted variance in canonical correlation. If the variance is not unrestricted, then this might make the canonical correlation look unstable.

Most researchers think that canonical correlation is computed in SPSS. However, canonical correlation is obtained while computing MANOVA in SPSS. In MANOVA, canonical correlation is used in data sets where one refers to the one set of variables as the dependent and the other as the covariates.

Chi Square test

2009-12-15T13:12:00.000-08:00

Parametric tests are those kinds of tests that involve the use of parameters, and the chi square test is a parametric tests.

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There are varieties of chi square tests that are used by the researcher. They are cross tabulation, chi square test for the goodness of fit, likelihood ratio test, chi square test, etc.

The task of the chi square test is to test the statistical significance of the observed relationship with respect to the expected relationship. The chi square statistic is used by the researcher for determining whether or not a relationship exists.

In the chi square test, the null hypothesis is assumed as there not being an association between the two variables that are observed in the study. The chi square test is calculated by evaluating the cell frequencies that involve the expected frequencies in those types of cases when there is no association between the variables. The comparison between the expected type of frequency and the actual observed frequency is then made in the chi square test. The computation of the expected frequency in the chi square test is calculated as the product of the total number of observations in the row and the column, which is divided by the total size of the sample.

The calculation of the chi square type of statistic in the chi square test is done by computing the sum of the square of the deviation between the observed and the expected frequency, which is divided by the expected frequency.

The researcher should know that the greater the difference between the observed and expected cell frequency, the larger the value of the chi square statistic in the chi square test.

In order to determine if the association between the two variables exists, the probability of obtaining a value of chi square should be larger than the one obtained from the chi square test of cross tabulation.

There is one more popular test called the chi square test for goodness of fit.

This type of chi square test called the chi square test for goodness of fit helps the researcher to understand whether or not the sample drawn from a certain population has a specific distribution and whether or not it actually belongs to that specified distribution. This type of chi square test can be applicable to only discrete types of distribution, like Poisson, binomial, etc. This type of chi square test is an alternative test for the non parametric test called the Kolmogorov Smrinov goodness of fit test.

The null hypothesis assumed by the researcher in this type of chi square test is that the data drawn from the population follows the specified distribution. The chi square statistic in this chi square test is defined in a similar manner to the definition in the above type of test. One of the important points to be noted by the researcher is that the expected number of frequencies in this type of chi square test should be at least five. This means that the chi square test will not be valid for those whose expected cell frequency is less than five.

There are certain assumptions in the chi square test.

The random sampling of data is assumed in the chi square test.

In the chi square test, a sample with a sufficiently large size is assumed. If the chi square test is conducted on a sample with a smaller size, then the chi square test will yield inaccurate inferences. The researcher, by using the chi square test on small samples, might end up committing a Type II error.

In the chi square test, the observations are always assumed to be independent of each other.

In the chi square test, the observations must have the same fundamental distribution.

Analysis Of Variance (ANOVA)

2009-11-24T08:31:00.000-08:00

The question that one usually asks about Analysis of Variance (ANOVA) is about the definition of Analysis of Variance (ANOVA). Analysis of Variance (ANOVA) is defined as the process of examining the differences among the means for two or more populations. The next question that arises in the researcher’s mind is what null hypothesis is assumed in the Analysis of Variance (ANOVA). The answer is that the null hypothesis is assumed as the following: “there exists no significant difference in the means of all the populations that are being examined in the Analysis of Variance (ANOVA).”

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The type of variable on which the Analysis of Variance (ANOVA) is applicable is also an important issue. Analysis of Variance (ANOVA) is applicable in cases where the interval or a ratio type of the dependent variable and one or more categorical type of independent variable is involved. The researchers should also note that the categorical type of variables is considered as the factors in the Analysis of Variance (ANOVA). The combination of the factor levels or the categories in the Analysis of Variance (ANOVA) is generally termed as the treatments.

The Analysis of Variance (ANOVA) technique, which consists of only one categorical type of independent variable, or in other words a single factor, is called one way Analysis of Variance (ANOVA). On the other hand, if the Analysis of Variance (ANOVA) technique consists of two or more than two factors or categorical types of variables or independent variables, then it is called n way Analysis of Variance (ANOVA). In this, the term ‘n’ refers to the number of factors in the Analysis of Variance (ANOVA).

Like regression analysis, the process of Analysis of Variance (ANOVA) also requires the calculation of multiple sums of squares for evaluating the test statistic that is used for testing the null and alternative hypothesis. There is also one difference in Analysis of Variance (ANOVA) and regression analysis, and that is that Analysis of Variance (ANOVA) uses separate and combined means and variances for the samples while evaluating the values that are applicable for the sum of the squares.

Often, the researcher questions what type of test statistic is used for testing the significant difference. The test statistic is nothing but the F statistic that is used in Analysis of Variance (ANOVA). The F test statistic is defined as the ratio between the sample variances. The task of the F test in Analysis of Variance (ANOVA) is to carry out the test of significance of the variability of the components existing in the study.

The most important question is about the assumptions in Analysis of Variance (ANOVA).

The first assumption of Analysis of Variance (ANOVA) is that each sample has been drawn from the population by the process of random sampling.

The second assumption of Analysis of Variance (ANOVA) is that the population from which each sample is randomly drawn should follow normal distribution. In other words, this means that in Analysis of Variance (ANOVA), it is assumed that the error term is normally distributed having its mean as zero and the variance as σ2e.

The third assumption of Analysis of Variance (ANOVA) is that there is homogeneity within the variances of the populations from which the sample has been drawn.

The fourth assumption of Analysis of Variance (ANOVA) is that the population that consists of the random effects (A) is normally distributed having ‘0’ as the mean and σ2a as the variance.

Validity

2009-11-19T08:39:00.000-08:00

Validity refers to the state in which the researcher or the investigator can get assurance that the inferences drawn from the data are error free or accurate. If there is validity in the sample, then there is validity in the population from where that sample has been drawn.

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There are basically four major types of Validity. These types are Internal Validity, External Validity, Statistically Conclusive Validity and Construct Validity.

Internal Validity refers to that type of validity where there is a causal relationship between the variables. Internal Validity signifies the causal relationship between the dependent and the independent type of variable. Internal Validity refers to those factors that are the reason for affecting the dependent variable. This type of validity is used in the case of the design of experiments where the treatments are randomly assigned.

External Validity refers to that type of validity where there is a causal relationship between the cause and the effect. The cause and effect in this type of validity are those that are generalized or transferred either to different people or different treatment variables and the measurement variable.

Statistically conclusive validity refers to that type of validity in which the researcher is interested about the inference on the degree of association between the two variables. For instance, in the study of the association between the two variables, the researcher reaches statistically conclusive Validity only if he has performed statistical significance tests upon the hypotheses predicted by him. This type of validity is violated when the researcher reaches two types of errors, namely type I error and type II error.

Type I error causes violation of this type of validity because in this type of error, the researcher rejects the hypothesis which was indeed true.

Type II error causes violation of this type of validity because in this type of error, the researcher accepts the hypothesis which was indeed false.

Construct Validity refers to that type of validity in which the construct of the test is involved in predicting the relationship for the dependent type of variable. For example, construct validity can be drawn with the help of Cronbach’s alpha. In Cronbach’s alpha, it is assumed that if its value is 0.80, then it is considered good for confirmation, and if its value is 0.70, then it is adequate. So, if the construct satisfies such conditions, then the validity holds. Otherwise, it does not.

Convergent/divergent validation and factor analysis is also used to test this type of validity.
There is a strong relationship between validity and reliability. A test is said to be unreliable if it does not hold the conditions of validity. Reliability is a necessary property of the test, but is not the sufficient condition for validity.

Thus, validity plays the significant role in making an accurate inference about the data.
There are certain things that act as a threat to validity. These are as follows:

If the researcher collects insufficient data to attain validity in the inference, this is not feasible because insufficient data will not represent the population as a whole.

If the researcher measures the sample of the population with too few measurement variables, then he also cannot achieve validity of that sample.

If the researcher selects the wrong type of sample, then he too cannot achieve validity in the inference about the population.

If the researcher selects an inaccurate measurement method during analysis, then the researcher would not be able to achieve validity.

Kaplan-Meier survival analysis (KMSA)

2009-11-17T07:14:00.000-08:00

Kaplan-Meier survival analysis (KMSA) is a method that involves generating tables and plots of the survival or the hazard function for the event history data. Kaplan-Meier survival analysis (KMSA) does not determine the effect of the covariates on either function. Kaplan-Meier survival analysis (KMSA) is a kind of explanatory method for the time to event, where the time is considered as the most prominent variable.

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Kaplan-Meier survival analysis (KMSA) consists of certain terms that are very important to know and understand, as these terms form the basis of a strong understanding of Kaplan-Meier survival analysis (KMSA).

The censored cases in Kaplan-Meier survival analysis (KMSA) indicate those cases in which the event has not yet occurred. In this case of Kaplan-Meier survival analysis (KMSA), the event is considered as the variable of interest for the researcher. Kaplan-Meier survival analysis (KMSA) can efficiently compute the survival functions in those cases that are censored in nature.
The time is considered as the continuous variable in Kaplan-Meier survival analysis (KMSA). However, the researcher should note that in Kaplan-Meier survival analysis (KMSA), the initial time of the occurrence of the event must be clearly defined.

There is a variable called a status variable in Kaplan-Meier survival analysis (KMSA). This variable in Kaplan-Meier survival analysis (KMSA) defines the terminal event. This variable in Kaplan-Meier survival analysis (KMSA) should always be continuous in nature and should always be a categorical type of variable.

There is a variable called the stratification variable in Kaplan-Meier survival analysis (KMSA). As the name suggests, the stratification variable in Kaplan-Meier survival analysis (KMSA) should be a categorical type of variable. This variable in Kaplan-Meier survival analysis (KMSA) represents the grouping effect. In the medical field, the stratification variable in Kaplan-Meier survival analysis (KMSA) can be types of cancer, like lung cancer, blood cancer, etc.
The researcher should note that Kaplan-Meier survival analysis (KMSA) provides incorrect results when covariates other than the time are considered as the prominent aspect in obtaining the extent of a certain consequence.

There is a variable called a factor variable in Kaplan-Meier survival analysis (KMSA). The factor variable in Kaplan-Meier survival analysis (KMSA) should be of categorical type. This type of variable in Kaplan-Meier survival analysis (KMSA) is used by the researcher to indicate the causal effect of a particular consequence. For example, in the case of the previous example, the treatment applied to decrease the effect of the cancer in the body is considered to be the factor variable in Kaplan-Meier survival analysis (KMSA).

The factor variable in Kaplan-Meier survival analysis (KMSA) is the main grouping variable, whereas the stratification variable is the sub grouping variable in Kaplan-Meier survival analysis (KMSA).

Kaplan-Meier survival analysis (KMSA) can be carried out by the researcher with the help of SPSS software.

The log rank test in Kaplan-Meier survival analysis (KMSA) provided in SPSS allows the investigator to examine whether or not the survival functions are equivalent to each other, by measuring their individual time points.

There are certain assumptions that are made in Kaplan-Meier survival analysis (KMSA). For one, it is assumed in Kaplan-Meier survival analysis (KMSA) that the events that occur in the survival function are the dependent variables that depend only upon the time. This is due to the fact that it has been assumed in Kaplan-Meier survival analysis (KMSA) that survival is always based upon time. Thus, this implies that in Kaplan-Meier survival analysis (KMSA), both the censored and uncensored cases perform in similar manners.

Hierarchical Linear Modeling

2009-11-16T08:03:00.000-08:00

Suppose that a researcher wants to conduct Hierarchical Linear Modeling on educational data. Hierarchical linear modeling is a kind of regression technique that is designed to take the hierarchical structure of educational data into account.

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Hierarchical Linear Modeling is generally used to monitor the determination of the relationship among a dependent variable (like test scores) and one or more independent variables (like a student’s background, his previous academic record, etc).

In Hierarchical Linear Modeling, the assumption of the classical regression theory that the observations of any one individual are not systematically related to the observations related to any other individual is violated. This assumption is violated in Hierarchical Linear Modeling because this yields biased estimates by applying this assumption in classical regression theory.

Hierarchical Linear Modeling is also called the method of multi level modeling. Hierarchical Linear Modeling allows the researcher working on educational data to systematically ask questions about how policies can affect a student’s test scores.

The advantage of Hierarchical Linear Modeling is that Hierarchical Linear Modeling allows the researcher to openly examine the effects on student test scores when the policy relevant variables are used on it (like the class size, or the introduction of a particular reform etc.).

Hierarchical Linear Modeling is conducted by the researcher in two steps.

In the first step of Hierarchical Linear Modeling, the researcher must conduct the analyses individually for every school (in the case of educational data) or some other unit in the system.

The first step of Hierarchical Linear Modeling can be very well explained with the help of the following example. In the first step of Hierarchical Linear Modeling, the student’s academic scores in science are regressed on a set of student level predictor variables like a student’s background and a binary variable representing the student’s sex.

In the first step of Hierarchical Linear Modeling, the equation would be expressed mathematically as the following:

(Science)ij=β0j+β1j(SBG)ij+β2j(Male)ij+eij. In this first step of Hierarchical Linear Modeling, β0 would signify the level of performance for each school under consideration after controlling the SBG (student’s background) and sex. In this first step of Hierarchical Linear Modeling, β1 and β2 indicate the extent to which inequalities exist among the student with respect to the two different variables taken under consideration.

In the second step of Hierarchical Linear Modeling, the regression parameters that are obtained from the first step of Hierarchical Linear Modeling become the outcome variables of interest.

The second step of Hierarchical Linear Modeling can be very well explained with the help of the following example. In the second step of Hierarchical Linear Modeling, the outcome variables mean the estimate of the magnitude of consequence of the policy variable. In the second step of Hierarchical Linear Modeling, the β0j is given by the following formula:

β0j = Y00 + Y01(class size)j + Y02 (Discipline)j + U01.

In the second step of Hierarchical Linear Modeling, Y01 indicates the expected gain (or loss) in the test score of science due to an average reduction in the size of the class. In the second step of Hierarchical Linear Modeling, Y02 signifies the effect of the policy of the discipline implemented in the school.

According to Goldstein in 1995 and Raudenbush and Bryk in 1986, Hierarchical Linear Modeling’s statistical and computing techniques involve the incorporation of a multi level model into a single one. This is where regression analyses is performed (it has been already explained in the above two steps of Hierarchical Linear Modeling). Hierarchical Linear Modeling estimates the parameters specified in the model with the help of iterative procedures.

Fisher Exact test

2009-11-13T11:16:00.000-08:00

The Fisher Exact test is a test of significance that is used in the place of chi square test in 2 by 2 tables, especially in cases of small samples.

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The Fisher Exact test tests the probability of getting a table that is as strong due to the chance of sampling. In the case of the Fisher Exact test, the word ‘strong’ is defined as the proportion of the cases that are diagonal with the most cases.

The Fisher Exact test is generally used in one tailed tests. However, the Fisher Exact test can also be used as a two tailed test as well. The Fisher Exact test is sometimes called a Fisher Irwin test. The Fisher Exact test is called by this name because the Fisher Exact test was developed at the same time by Fisher, Irwin and Yates in 1930.

In SPSS, the Fisher Exact test is computed in addition to the chi square test for a 2X2 table when the table consists of a cell where the expected number of frequencies is fewer than 5.

There are certain terminologies that help in understanding the theory of Fisher Exact test.

The Fisher Exact test uses the following formula:

p= ( ( a + b ) ! ( c + d ) ! ( a + c ) ! ( b + d ) ! ) / a ! b ! c ! d ! N !

In this formula of the Fisher Exact test, the ‘a,’ ‘b,’ ‘c’ and ‘d’ are the individual frequencies of the 2X2 contingency table, and ‘N’ is the total frequency.

The Fisher Exact test uses this formula to obtain the probability of the combination of the frequencies that are actually obtained. The Fisher Exact test also involves the finding of the probability of every possible combination which indicates more evidence of association.

There are certain assumptions on which the Fisher Exact test is based.

In the Fisher Exact test, it is assumed that the sample that has been drawn from the population is done by the process of random sampling. This assumption of the Fisher Exact test is also assumed in general in all the significance tests.

In the Fisher Exact test, a directional hypothesis is assumed. The directional hypothesis assumed in the Fisher Exact test is nothing but the hypothesis based on the one tailed test. In other words, the directional hypothesis assumed in the Fisher Exact test is that type of hypothesis which predicts either a positive association or a negative association, but not both.
In the Fisher Exact test, it is assumed that the value of the first person or the unit of items that are being sampled do not get affected by the value of the second person or the other unit of item being sampled. This assumption of the Fisher Exact test would be violated if the data is pooled or united.

In the Fisher Exact test, mutual exclusivity within the observations is assumed. In other words, in the Fisher Exact test, the given case should fall in only one cell in the table.
In the Fisher Exact test, the dichotomous level of measurement of the variables is assumed.

t-test

2009-11-12T06:26:00.001-08:00

The parametric test called the t-test provides a statistical inference about the population by testing the sample that has been drawn from that population in such a manner that it represents the population as a whole.

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This parametric test, called the t-test, is based on the student’s t statistic. This statistic in the t-test is based upon the assumption that the samples are drawn from a normal population. It is assumed in the t-test that the mean of the normal population exists. The shape of the distribution of the t-test is a bell shaped appearance.

The t-test is applicable in those cases where the size of the sample is less than 30. If the sample size is more than 30 and the t-test is carried out on it, then the inference drawn would not be valid as the distribution of the t-test and the normal distribution would not be noticeable.
The parametric test called the t-test is called parametric because it consists of the parameters called the mean and the variance. There are chiefly three types of t-tests: one sample t-test, two independent sample t-tests, and paired sample t-test.

The first type of t-test is applicable in those cases where the testing of one sample is done. For example, if the researcher wants to test whether or not at least 65 % of the students of a particular school would pass their 10 standard board exam, he could use this test. To conduct this type of t-test, a suitable null and alternative hypothesis is created by the researcher. The next step for the researcher is to construct the test statistic. In this case, the test statistic would be t-test. An appropriate level of significance would be selected by the researcher to conduct the t-test of the null hypothesis. The appropriate level of significance for conducting t-test is generally 0.05(which is the same in other significant tests as well). The level of significance refers to the probability that there would be a false rejection of the null hypothesis on which the t-test would be carried out.

Now, the comparison of the tabulated value of the t-test and the calculated value of the t-test is done by the researcher. If the calculated value of the t-test is more than the tabulated value, then the null hypothesis is rejected at that level of significance. In the opposite case of t-test, the null hypothesis is accepted.

Similarly, in the case of the second type of t-test, two independent samples are tested by comparing their significances with the help of the t-test. So, all the steps carried out in the previous step would remain the same, except that the hypothesis assumed by the researcher in this case would be for two independent samples.

Similarly, in the case of the paired sample t-test, the paired type of categories are tested and all the steps would remain the same, except that the hypothesis on which the t-test would be conducted will now be formulated according to the third type of t-test.

Null hypothesis and Alternative Hypothesis

2009-11-09T07:43:00.000-08:00

Hypothesis is an approximate explanation that relates to the set of facts that can be tested by certain further investigations. There are basically two types of hypothesis, namely null hypothesis and alternative hypothesis. A research generally starts with a problem. Next a hypotheses like null hypothesis and alternative hypothesis provide the researcher with some specific restatements and clarifications of the research problem.

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The criteria of the research problem in the form of null hypothesis and alternative hypothesis should be expressed as a relationship between two or more variables. The criteria of the null hypothesis and alternative hypothesis is that the statements should be the one that expresses the relationship between the two or more measurable variables. The null hypothesis and alternative hypothesis should carry clear implications for testing and stating relations.

The major differences between the null hypothesis and alternative hypothesis and the research problems are that the research problems are simple questions that cannot be tested. The null hypothesis and alternative hypothesis, however, can be tested.

The null hypothesis and alternative hypothesis are required to be fragmented properly before the data collection and interpretation phase in the research. A well fragmented null hypothesis and alternative hypothesis indicates that the researcher has adequate knowledge in that particular area and is thus able to take the investigation further because they can use a much more systematic system. The null hypothesis and alternative hypothesis give direction to the researcher on his/her collection and interpretation of data.

The null hypothesis and alternative hypothesis are useful only if the null hypothesis and alternative hypothesis state the expected relationship between the variables or if the null hypothesis and alternative hypothesis are consistent with the existing body of knowledge. The null hypothesis and alternative hypothesis should be expressed as simply and concisely as possible. The null hypothesis and alternative hypothesis are useful if the null hypothesis and alternative hypothesis have explanatory power.

The purpose and importance of the null hypothesis and alternative hypothesis are that the null hypothesis and alternative hypothesis provide an approximate description of the phenomena. The purpose of the null hypothesis and alternative hypothesis is to provide the researcher or an investigator with a relational statement that is directly tested in a research study. The purpose of the null hypothesis and alternative hypothesis is to provide the framework for reporting the inferences of the study. The purpose of the null hypothesis and alternative hypothesis is to behave as a working instrument of the theory. The purpose of the null hypothesis and alternative hypothesis is to prove whether or not the test is supported, which is separated from the investigator’s own values and decisions. The null hypothesis and alternative hypothesis also provide direction to the research.

The null hypothesis is generally denoted as H0. The null hypothesis states the exact opposite of what an investigator or an experimenter predicts or expects. The null hypothesis basically defines the statement which states that there is no exact or actual relationship between the variables.

The alternative hypothesis is generally denoted as H1. The alternative hypothesis makes a statement that suggests or advises a potential result or an outcome that an investigator or the researcher may expect. The alternative hypothesis has been categorized into two categories: directional alternative hypothesis and non directional alternative hypothesis.

The directional hypothesis is a kind of alternative hypothesis that explains the direction of the expected findings. Sometimes this type of alternative hypothesis is developed to examine the relationship among the variables rather than a comparison between the groups.

The non directional hypothesis is a kind of alternative hypothesis that has no definite direction of the expected findings being specified.

LISREL

2009-11-06T12:55:00.000-08:00

LISREL stands for linear structural relation. The methodology of LISREL was first developed by Karl Joreskog in 1970. LISREL is statistical software that is used for structural regression modeling. Structural equation models are the system of linear equations. LISREL is the simultaneous estimation of the structural model and measurement model. Structural model assumes that all variables are measured without error. Factor analysis is the technique that deals with the measurement model. Factor analysis is of two types: one is the exploratory factor analysis, (where the computer determines the underlining factor) and the second type of factor analysis is confirmatory factor analysis (where the researcher determines the factor structure). LISREL makes it possible to combine the structural equation and factor analysis. LISREL can also generate path diagrams for structural equations. LISREL 8.8 is the latest version available. LISREL is not only used for structural equation modeling, but it also has several other program applications. In LISREL, the PRELIS (Lisrel pre-processor) option is used for data manipulation and basic statistics. In LISREL, the SURVEYGLIM option is used for generalized linear modeling. For categorical response variables, formative interface modeling is used in LIRSEL. For continuous response variables, the COMFIRM option is used. For multivariate data, the MAPGLIM option is used for generalized linear modeling. In business, psychology and medical research, most researchers use LISREL for structural equation modeling. LISREL was the first software that was used for structural equation modeling. Competing software for LISREL include AMOS, SAS, and EQS, etc. However, LISREL has its own importance due to unique features.

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The following are some basic features of LISREL:

Starting of LISREL: Select “LISREL” from the start menu or create a shortcut and start from the short cut.
Importing data in to LISREL: To enter data into LISREL, select “import options” from the file menu.

Opening a new window: In LISREL file, the “new “option is used to open a new window. From the new option we can open syntax, output, path diagram or data window as required.

Data manipulation: In the “data” option of LISREL, there are options like the variable properties, select variable, sort case, insert variable, delete variable, assign weight, etc.
Transform option: Like SPSS, LISREL also has an option to record or compute a new variable by using the “transform” option.

Statistics option: In LISREL, by using the statistics option, we can perform all the statistical models. LISREL can handle a number of models that include measurement models, no recursive models, hierarchical linear models, confirmatory factor analysis models, ordinal regression models, multiple group comparisons model, etc.

Graph option: Like many other statistical software, LISREL also has the option for graphs. By using the “graph” option in LISREL, we can produce high quality univariate, bivariate and multivariate charts.

Advance modeling: In LISREL, the multilevel option provides the flexibility to perform advance level modeling. By using the multilevel option, we can perform advance level linear and non-linear statistical methods.

View and Window option: Like any other statistical software, LISREL also has the view and window option. View option has the basic features like the tool bar, status bar, etc. By using the window option, we can arrange the window in a horizontal or vertical manner.

Advantages of LISREL:
1. This software provides the full information about the model coefficient which increases the power of the model.
2. It provides good treatment to the missing value.
3. It provides significance testing for all the coefficients.
4. It imposes restrictions on models if that is what is wanted.
Drawbacks of LISREL:
1. It is complicated to handle when someone is a novice.
2. The interaction effects are hard to handle.
3. Correlation matrix is used in SEM and it is assumed that these correlations are derived from the multivariate normality distribution. This assumption does not look valid.

Kolmogorov Smrinov’s one sample test

2009-11-06T12:45:00.000-08:00

The Kolmogorov Smrinov’s one sample test is a test for goodness of fit. The Kolmogorov Smrinov’s one sample test is concerned with the degree of agreement between the distribution of the observed sample values and some specified theoretical distribution. The Kolmogorov Smrinov’s one sample test determines whether or not the values in a sample can reasonably be thought to have come from a population having a theoretical distribution.

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In Kolmogorov Smrinov’s one sample test, it is assumed that the distribution of the underlying variables being tested is continuous in nature. The Kolmogorov Smrinov’s one sample test is appropriate for those types of variables that are tested at least on an ordinal scale.
One usually conducts Kolmogorov Smrinov’s one sample test in order to test the normality assumption in analysis of variances.

Suppose, for example, F0(x) has a completely specified cumulative relative frequency distribution function in Kolmogorov Smrinov’s one sample test. In this case in Kolmogorov Smrinov’s one sample test, the theoretical distribution under the null hypothesis for any value of F0(x) is the proportion of the cases that are expected to have values which are equal to or are less than the value of x.

Suppose Sn(x) is the observed cumulative relative frequency distribution function of a random sample of ‘n’ observations in Kolmogorov Smrinov’s one sample test. If xi is any possible value in Kolmogorov Smrinov’s one sample test, then Sn(xi) = Fi/n , where Fi is nothing but the number of expected proportions of observations which are less than or equal to xi.

Now, according to the null hypothesis in Kolmogorov Smrinov’s one sample test, it is expected that for every value of xi, Sn(xi) should be fairly close to F0(xi). In other words, in Kolmogorov Smrinov’s one sample test, if the null hypothesis is true, then the difference between Sn(xi) and F0(xi) is small and should be within the limits of the random error.

The Kolmogorov Smrinov’s one sample test focuses on the largest of the deviations. The largest deviation in Kolmogorov Smrinov’s one sample test is called the maximum deviation. The maximum deviation in Kolmogorov Smrinov’s one sample test is the largest absolute difference between the cumulative observed proportion and the cumulative proportion expected on the basis of the hypothesized distribution. The sampling distribution of the maximum deviation in Kolmogorov Smrinov’s one sample test under the null hypothesis is generally known.

There are certain assumptions that are made in Kolmogorov Smrinov’s one sample test.

It is assumed that in Kolmogorov Smrinov’s one sample test, the sample is drawn from the population by the process of random sampling.

It is assumed in Kolmogorov Smrinov’s one sample test that the level of data variables should be continuous interval or ratio types in order to get the exact results. If approximate results are required by the researcher through Kolmogorov Smrinov’s one sample test, then the researcher can use ordinal data or grouped interval level of data.

Kolmogorov Smrinov’s one sample test is also used for ordinal scale of data when the large-sample assumptions of the chi-square goodness-of-fit test are not met.

The hypothetical distribution is specified in advance in Kolmogorov Smrinov’s one sample test.
In the case of the normal distribution in Kolmogorov Smrinov’s one sample test, the expected sample mean and sample standard deviation should always be specified in advance.

In the case of Poisson distribution and in the case of exponential distribution in Kolmogorov Smrinov’s one sample test, the expected sample mean should always be specified in advance.

In the case of uniform distribution in Kolmogorov Smrinov’s one sample test, the expected range which consists of the minimum and maximum values, should always be specified in advance.

Descriptive measure

2009-10-29T06:25:00.000-07:00

Descriptive measure is that kind of measure that deals with the quantitative data in a mass which exhibits certain general characteristics. The descriptive measure is of different types for different characteristics of data. This document will discuss different descriptive measures for different types of data.

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There is a tendency for data to cause variation about the descriptive measure of central tendency. This descriptive measure of deviation is also called the descriptive measure of variation or dispersion.

The descriptive measure of deviation is a descriptive measure of the extent to which an individual item may vary. This descriptive measure of deviation of the data should satisfy certain properties which have been laid down by Prof. Yule. These properties are as follows:

The descriptive measure of deviation should be rigidly defined. This descriptive measure should be flexible in calculation and should be easy to understand. This descriptive measure should be based on all the observations. This descriptive measure should be open to further mathematical treatment. This descriptive measure should not be affected by the fluctuations of the sampling.

The descriptive measure of dispersion has been classified into two broad categories.

The descriptive measure of dispersion involves expressing the spread of observations in terms of distance. Such categories of descriptive measure of deviations include range and inters quartile range (or quartile deviation).

The descriptive measure of deviation called range is defined as the difference between the two extreme observations of the distribution. Suppose A and B are the greatest and the smallest observations respectively. In this case, the descriptive measure of deviation (i.e. range) is Range= A-B.

The descriptive measure of deviation called inter quartile range or quartile deviation is also called semi inter quartile range. This descriptive measure is defined mathematically as: Q= (Q3 – Q1)/ 2, where Q3 is the third quartiles and Q1 is the first quartiles. This descriptive measure is definitely a better measure than the previous descriptive measure, as this descriptive measure makes use of 50% of the data. However, this descriptive measure ignores the other 50 % of the data, therefore, this descriptive measure cannot be regarded as a reliable descriptive measure.

The descriptive measure expresses the spread of observations in terms of the average of deviations of the observations from some central value. Such categories of descriptive measure of deviation include mean deviation and standard deviation.

The mean deviation is a descriptive measure of deviation based on all the observations and is a much better type of descriptive measure then other descriptive measure of deviations. However, since in this type of descriptive measure of deviation the sign of the deviation has been ignored, this descriptive measure becomes useless for further mathematical treatment.

The standard deviation is a descriptive measure of deviation that is generally denoted by the Greek letter (σ). This type of descriptive measure is defined as the positive square root of the arithmetic mean of the squares of the deviation of the given values from their arithmetic mean. In this type of descriptive measure, the deviation is being squared. Thus, this descriptive measure overcomes the drawback of the descriptive measure of the mean deviation.

This is the only descriptive measure of deviation which satisfies almost all the ideal properties of the descriptive measure of deviation laid down by Prof. Yule, except for the general nature of extracting the square root which is generally not readily comprehensible for a non-mathematical person. It should be observed that this type of descriptive measure gives greater weight age to the extreme values and is not as popular in terms of being used by economists or businessmen.

Statistics Analysis

2009-10-12T06:20:00.000-07:00

Statistics analysis is by no means easy, and yet, all dissertation writing students are expected to know exactly how to perform statistics analysis. What’s more, most doctoral degree seeking students are not trained properly in statistics and they must complete extremely complex and complicated statistics analysis to complete their dissertation.

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Because statistics analysis can be so difficult, it is important for doctoral degree seeking students to get help on the statistics analysis. And one excellent place to look for help is a student’s advisor. The student’s advisor should be the first step in terms of getting help on the statistics analysis. However, not all advisors can provide the student with the help that the student needs to complete the statistic analysis. This is true for many reasons, the least of which is that the student’s advisor is usually busy and only has a limited amount of time. Additionally, many advisors wait for the students to make mistakes before offering a helping hand—and those mistakes can be incredibly costly in terms of time and energy expended by the degree seeking student.

When a student’s advisor is unable to provide the assistance, support, guidance and aide required for the statistics analysis, the doctoral degree seeking student should turn to experts. Those experts are dissertation consultants and dissertation consultants can provide the student with everything that he or she needs to complete the difficult and lengthy statistics analysis.

Proper statistics analysis first starts with the gathering of data. For one must gather an extensive amount of data in order to obtain statistics on that data! But how does a student know how to gather that data? And how does a student know how many samples he or she should use when gathering that data?

In order for the statistics analysis to be accurate, precise and dependable, the student must follow accurate, precise and laid-out rules of statistics when it comes to gathering data. A dissertation consultant can teach the student these precise rules of statistics—and this, of course, will greatly help the student when it comes to the statistics analysis.

Additionally, there are rules and procedures that must be followed every step of the way when it comes to statistics analysis. Dissertation consultants know the rules, procedures, regulations and methodology of statistics, and thus, with the help of dissertation consultants, the dissertation writing student will know how to accurately perform statistics analysis for his or her dissertation. And when the student learns these methodologies of statistics, he or she will be guaranteed to have proper, accurate, dependable and precise statistics analysis.

Once the student has learned how to do proper statistics analysis, he or she can complete the dissertation on time and with success. Additionally, because the student actually understands the statistics analysis, he or she will be able to accurately defend his or her dissertation. This is extremely important as this oral defense is the very last thing that is standing in between the doctoral degree seeking student and the coveted diploma. With a dissertation consultant guiding a doctoral degree seeking student every single step of the way and with a dissertation consultant making sure that the statistics analysis is done accurately and correctly, the doctoral degree seeking student will finish on time and with the degree confidently attained.

Statistics Analysis

2009-10-06T06:06:00.000-07:00

Statistics analysis plays a crucial role in any dissertation because statistic analysis is what is necessary for a doctoral student to prove his or her thesis. With improper statistics analysis, the dissertation will neither be approved nor accepted.

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Though statistics analysis is necessary for all dissertations and for all PhD candidates to complete, many PhD students have a very difficult time completing the statistic analysis properly and accurately. This struggle with the statistical analysis is quite common and the reason for this struggle is because PhD students have not had enough experience with statistics to know how to complete the complicated statistical procedures and statistical analysis necessary for the dissertation. Granted, PhD students have spent years and years in school—but they have not spent years and years studying statistics, and this is often what is necessary to complete the statistics analysis with ease and success.

It is obviously very important to complete the statistics analysis properly for all PhD students. What is not so obvious, however, is that a student can get help on the statistics analysis and this help can save the student much time and frustration. This help on statistics analysis usually comes in the form of a statistical consultant. A statistical consultant is a trained statistician who can help a PhD student with every single statistical process of the dissertation—including with the statistics analysis. A statistical consultant can guide the student through the statistics methodologies and with this guidance, a PhD student is sure to always be on the right track. And when a PhD student is always on the right track, the statistics analysis will be accurate and the PhD student will no longer have to struggle with the statistics analysis.

A student, then, can make sure that the statistics analysis is completed properly with the help of a statistical consultant. A statistical consultant is also very easily attainable and a statistical consultant can start at any point in the dissertation process. Obviously, a student should not waste time struggling through the statistical procedures and the statistics analysis alone when there is such help available—so a dissertation writing student should seek help on the statistics analysis and the statistical procedures early on. The sooner a PhD student seeks help from a statistical consultant, the more help can be provided.

It is also incredibly important for the PhD student to realize that a statistical consultant providing help on the statistics analysis will be able to instruct the student. In fact, this is often the most valuable part of getting help on the statistics analysis from a statistical consultant. One on one help with statistics and the statistics analysis can be incredibly useful because the statistical consultant can go at the pace of the PhD student. Unlike what happens in a room full of students when the PhD student is enrolled in a class, the instruction between a statistical consultant and a PhD student is one on one. And this can mean all the difference between a student struggling to keep up with a room full of students, or a student no longer feeling intimidated by peers around him/her. Thus, the help provided by a statistical consultant is absolutely unmatched as the statistical consultant is able to give individualized attention to the student and the statistical consultant is able to make sure that the PhD student actually understands the statistical procedures and the statistics analysis.

There is no better way to get help on the dissertation and on the statistics analysis than to seek professional help in the form of a statistical consultant. Once the PhD student does get this much needed help, he or she will see results immediately.

PhD Statistics Analyses

2009-10-02T06:39:00.001-07:00

The time spent working on and thinking about a dissertation is practically immeasurable. This is true because the dissertation is the longest and most difficult aspect of one’s academic career. PhD students spend countless hours working on the dissertation and as such, PhD students are usually frustrated, fed-up, discouraged and burnt out by the time that they get to one of the most challenging parts of the dissertation: the PhD statistics analyses.

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The PhD statistics analyses come after all of the data has been collected by the doctoral degree seeking student. And again, countless hours have already been spent by the doctoral student in the collection of the data, before the PhD statistics analyses have even begun. Thus, when a PhD student gets to the PhD statistics analyses, he or she is worn out and sick of the dissertation.

What’s more, the PhD statistics analyses takes a student even more time than the gathering of data—especially if the PhD student has never performed PhD statistics analyses. PhD statistics analyses require that the doctoral degree seeing student have extensive training in and with statistical and statistical procures and methodologies. Many PhD students do not have this training and experience with statistics, so many students struggle mightily when it comes time to perform the PhD statistics analyses.

Doctoral degree seeking students do not have to struggle on their PhD statistics analyses, however, because doctoral degree seeking students have many options available when it comes to getting help on the PhD statistics analyses. The first place where many doctoral degree seeking students turn, and rightfully so, is to their advisor. The doctoral student’s advisor can indeed help the doctoral student, because that is what an advisor is there for. However, many advisors are not readily available and many advisors are not able to offer the doctoral student help when he or she needs it. Thus, while it is always advisable to go to an advisor, sometimes that advisor is not able to help the doctoral student.

The next place where many PhD students turn when it comes to getting PhD statistics analyses is the internet. This too is an okay place for students to turn as there are many websites dedicated to offering help to PhD students when it comes to the PhD statistics analyses. However, if one were to go online and actually type PhD statistics analyses into the search engine, he or she would find that thousands and thousands of hits come up. Additionally, the information that is provided about the PhD statistics analyses is oftentimes contradictory. This is true because PhD statistics analyses requires extensive knowledge of statistics—and this is not something that can be acquired online. In fact, people spend years and years studying statistics, so it would be impossible to have all of that information summed up on-line. The internet, then, can be somewhat helpful, but it is not the best place to turn when it comes to PhD statistics analyses.

The best place for a struggling doctoral student to turn for help on the PhD statistics analyses is a dissertation consulting firm. A dissertation consulting firm can provide the student with everything that he or she needs to finish the dissertation and to perform the PhD statistics analyses with accuracy and precision. A dissertation consulting firm will offer the PhD candidate valuable instruction when it comes to the PhD statistics analyses and a dissertation consulting firm will make sure that the student is on the right track in terms of the PhD statistics analyses. With the help of a dissertation consulting firm, the doctoral degree seeking student will be well on his or her way to completing the dissertation and will have absolutely no trouble with the complicated and difficult PhD statistics analyses.

Dissertation Data Analysis

2009-10-01T07:19:00.000-07:00

You’ve spent months gathering the data that you need for your dissertation, you’ve been working on your dissertation for what seems like forever, you finally are at the point where you can start making conclusions that will apply to your thesis… and then you realize, “I’m not exactly sure how to make sense of all of this data! I’m not exactly sure how to do the dissertation data analysis!”

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While it takes months and months and months to gather accurate and valid data, that time spent on gathering the data can be wasted if the data is not then used properly—if proper dissertation data analysis is not performed correctly. Dissertation data analysis is very difficult to perform, especially if the doctoral student is working on his or her first dissertation. Dissertation data analysis is especially difficult to perform because it requires that the doctoral student knows all there is to know about statistics, statistical procedures and statistical methodologies. Thus, without the proper expertise and know-how in statistics, doctoral students can flounder through the dissertation data analysis part of the dissertation, and essentially, all the hard work and energy spent on gathering accurate data can be wasted.

This does not have to happen, however, as there are dissertation consultants who can help any doctoral student with the dissertation data analysis. Indeed, dissertation consultants can help the student make sense of the dissertation data analysis and dissertation consultants can provide the knowhow and expertise that the PhD student lacks. This is especially helpful in the dissertation data analysis phase, as a dissertation consultant is trained in all things concerning statistics—including having extensive training in dissertation data analysis.

There is no sense, then, for a PhD student do “go it alone” and attempt to figure out the dissertation data analysis parts of the dissertation all by him/herself. Help on the dissertation data analysis is incredibly easily attainable because dissertation consultants are very easy to contact and to obtain. In fact, a simple internet search will yield thousands of hits for dissertation consultants—mainly because dissertation consultants are that good at helping students on their dissertations and on the dissertation data analysis portions of their dissertations. For help on the dissertation data analysis, there is no better solution than to seek the professional help of a dissertation consultant who can take any PhD student through the lengthy, difficult and challenging aspects of the dissertation data analysis.

Many students hesitate, however, before seeking help on the dissertation data analysis and before contacting a dissertation consultant. PhD students hesitate for several reasons, one of them being the fact that they are so used to doing everything alone. It is always good to get help, however, and this is equally true on the dissertation data analysis. Some students, while ready to get help, wonder if it is ethical to use a dissertation consultant to get help on the dissertation data analysis. While this is definitely worth thinking about, it is absolutely imperative that a PhD student understand that a dissertation consultant simply helps a student—simply offers assistance in the challenging aspects of the dissertation. A dissertation consultant, then, does NOT do the work for the student. Rather, a dissertation consultant instructs the student and provides the student with very valuable teachings. This instruction is perhaps one of the biggest benefits of getting a dissertation consultant—they do not do the work for the PhD student, they instruct the student and guide the student so that the student can do all of the statistical procedures and the dissertation data analysis on his or her own. And truly, there is no better help than this.

How do I do dissertation data analysis?

2009-09-30T11:40:00.000-07:00

How do I do dissertation data analysis?

One of the most challenging and difficult parts of the already very challenging dissertation is to accurately and precisely analyze the data that you have collected for your dissertation. Dissertation data analysis involves compiling, understanding, collecting, and processing thousands of numbers, and this is by no means easy. This is made even more difficult by the fact that many doctoral students are not trained in dissertation data analysis. To do proper dissertation data analysis, a doctoral student must have a good deal of statistical know how, experience, and understanding. With this statistical know how, experience and understanding, a doctoral student can certainly complete the dissertation data analysis on his or her own; but if a student does not have statistical expertise, it is a good decision to get help on the dissertation data analysis.

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Why do I have to do dissertation data analysis?

If you are working on your dissertation and proving something, you have gathered and acquired facts, figures, numbers and statistics to prove your point. It is not enough to simply gather and accumulate these numbers and figures, however, as dissertation data analysis must be done so that you can apply these numbers to your dissertation. In performing proper dissertation data analysis, you will be providing scientific backing to your thesis and conclusion, thus dissertation data analysis must be completed in order for a doctoral student to receive his or her degree and finish the dissertation.

Who can help me with dissertation data analysis?

Usually, students turn to their dissertation advisor for help on all things concerning the dissertation. This can be extremely useful, as a student’s advisor knows how to point the student in the proper direction and an advisor knows what the approval panel will be looking for when the approval panel goes to judge the student’s dissertation. And some advisors provide wonderful on-going support that helps the doctoral student throughout the entire task of the dissertation. Other advisors, however, are not always available when the student needs him or her and this can be extremely frustrating. Still other advisors wait until the student makes a mistake somewhere along the way and then provides information and guidance to the student that would have been helpful before the student actually made the mistake (as mistakes can take weeks and months to fix—depending on where the mistake happens and when the student realizes the mistake). There is no need, however, to be frustrated with advisors who are not always available to a doctoral student when he or she needs him/her. Instead, doctoral students can now seek out help from a dissertation consultant and that dissertation consultant can provide one on one, hands on guidance, assistance and help on al things concerning the dissertation—including on the dissertation data analysis—whenever the doctoral student needs that help. With the help of a dissertation consultant, the student will be able to accurately and precisely perform the dissertation data analysis because dissertation consultants are trained in statistics and can easily “make sense” of both statistical procedures and of thousands and thousands of numbers that are used in those statistical procedures and the dissertation data analysis. Thus, with the help of a dissertation consultant, the dissertation data analysis and every other aspect of the dissertation will be manageable, accurate and relatively easy to complete. It is best, therefore, to get help on the dissertation data analysis. And if a student’s advisor is not available to offer that help on the dissertation data analysis, a dissertation consultant can more than fill in as the advisor, offering invaluable and unmatched help to the student.

What is a Statistical Analysis Consultant?

2009-09-23T11:17:00.000-07:00

What is a statistical analysis consultant?

A statistical analysis consultant is a trained and professional statistician who can be hired to help anyone who is struggling with statistics. A statistical analysis consultant will provide one on one help to anyone who needs to use statistical procedures and gather statistical data and analysis.

Who uses a statistical analysis consultant?

Many people turn to a statistical analysis consultant. In fact, statistical analysis consultants are useful for many different people in many different fields. Doctors and nurses, for example, turn to a statistical analysis consultant when they want to find out the effectiveness of a particular drug or a particular dosage. Additionally, the government uses statistical analysis consultants all the time in order to measure the accuracy and effectiveness of certain government programs. Business owners also turn to a statistical analysis consultant so that they can get an accurate measurement of what works and what does not work in their business or company. And finally, doctoral students often turn to a statistical analysis consultant as doctoral students must use statistics heavily and often in their dissertations.

Why do doctoral students use a statistical analysis consultant?

Many doctoral students hire a statistical analysis consultant because many doctoral students struggle with the statistical aspects of their dissertations. This is true because many doctoral students do not have the training or background in statistics that they need to complete the sophisticated and complicated aspects of their dissertation. The dissertation relies very heavily on statistics because statistics are used to prove whatever it is that the student has set out to prove in his or her dissertation. Thus, doctoral degree seeking students often turn to a statistical analysis consultant so that the doctoral degree seeking student can get the help that he or she needs in order to finish his or her dissertation. With the help of a statistical analysis consultant, the doctoral student will be well on his or her way to obtaining his or her degree, and finishing all of his or her statistical analyses for the dissertation.

How specifically can a statistical analysis consultant help a doctoral degree seeking student?

Specifically, a statistical analysis consultant can help a doctoral student with every single statistical process and procedure of the dissertation. This help provided by a statistical analysis consultant includes giving valuable help to the doctoral student in the following ways:
• A statistical analysis consultant can help the student phrase his or her topic statistically—so that it makes statistical sense
• A statistical analysis consultant can help the student with the proposal phase of the dissertation where the student has to explain what statistical processes and procedures he or she will follow throughout the dissertation
• A statistical analysis consultant can help the student determine the sample sizes for the data collection
• A statistical analysis consultant can help the doctoral student gather the data in a way that the data is neither skewed nor biased
• A statistical analysis consultant can help the doctoral student analyze the data that has been collected
• A statistical analysis consultant can help the student make sense of and interpret all of the data that has been collected
• A statistical analysis consultant can help the student apply the results of the data and the statistics to the student’s dissertation.

Thus, a statistical analysis consultant can prove to be a tremendous help to all degree seeking students as they work through the statistical portions of their dissertations.

t-test

2009-08-21T12:53:00.001-07:00

The t-test involves the single interval dependent variable and a dichotomous independent variable if the researcher wishes to conduct the t-test for the difference of means. The t-test can also be used to compare the means for two dependent samples and two independent samples. Additionally, the t-test can be used to test between a sample mean and a known mean, which is also called the t-test for one sample.

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The t-test is a parametric test that makes a very popular and obvious assumption—that of normal distribution or normal population. The researcher should note that if all the assumptions of the t-test are met, then the t-test becomes the most powerful. It is the most powerful test of any particular two sample non-parametric test.

The t-test is basically employed in those cases where the size of the sample is generally less than 30. If, however, the sample size is larger than 30, then instead of using the t-test, the researcher employs the z test.

The t-test is mainly based upon the student’s t distribution. The calculation of the t-test is different for comparison between the independent and the dependent samples, but the inference drawn from the t-test is the same.

The critical value in the t-test is the value that is found in the table of values of the t distribution for a given level of significance. If the value that has been calculated by using the t-test is more than the critical t value, then the null hypothesis that has been assumed in the t-test is rejected. But, if the value that has been calculated by using the t-test is less than the critical t value, then the null hypothesis that is assumed in the t-test is accepted.

The confidence limits in the t-test basically construct the upper bound and the lower bound on an estimate for a given level of significance. The confidence interval in the t-test is the range within these bounds. Such limits are employed in the t-test because such limits provide additional information on the relative meaningfulness of the estimates.

In SPSS, the t-test is conducted by selecting the “compare means” from the “analyze” menu and then by clicking any option, depending upon the type of t-test to be conducted by the researcher in SPSS. If two samples are involved, then the researcher can either employ an independent sample t-test or a paired sample t-test, depending on the type of data.

The following are some assumptions that have been assumed in the t-test:

The first assumption in the t-test is that the distribution, or the population under consideration, is that of normal distribution or normal population. For satisfying this assumption, there are certain tests for normality. The researcher should note that the t-test can draw invalid conclusions when the two samples come from widely different shaped distributions. Some statisticians suggest that the t-test should be normally distributed for the sample size, which is mainly less than 15.

The second assumption made in the t-test is that of the homogeneity of the variances in the sample. SPSS employs a test for testing the homoscedastic nature of the sample in the t-test. This test is called "Levene's Test for Equality of Variances," with F value and corresponding significance. The researcher should note that the t-test will result in invalid inferences if the two samples are unequal in size and also have unequal variances.

The third assumption is that in the t-test it does not matter whether the sample is a dependent or independent sample. This is because the inference drawn from the t-test will remain the same whether the sample is independent or dependent; only the calculation of the t-test will differ.

Multiple Regression

2009-08-21T12:47:00.000-07:00

Multiple regression involves a single dependent variable and two or more independent variables. Multiple regression is basically a statistical technique that simultaneously develops a mathematical relationship between two or more independent variables and an interval scaled dependent variable.

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Questions like how much of the variations in sales can be explained by advertising expenditures, prices and the level of distribution can be answered by employing the statistical technique called multiple regression.

The general form of multiple regression is given by the multiple regression model and is the following:

Y= ß₀ + ß₁X₁+ ß₂X₂+ …….. + ß_kX_k+ e.

This multiple regression model is estimated using the following equation:

= a + b₁X₁+ b₂X₂+ …….. + b_kX_k.

There are certain statistics that are used while conducting the analysis on multiple regression.

The R² in multiple regression is the coefficient of the multiple determination. This coefficient in multiple regression measures the strength of association.

The F test in multiple regression is used to test the null hypothesis that the coefficient of the multiple determination in the population is equal to zero.

The partial F test in multiple regression is used to test the significance of a partial regression coefficient. This incremental F statistic in multiple regression is based on the increment in the explained sum of squares that results from the addition of the independent variable to the regression equation after all the independent variables have been included.

The partial regression coefficient in multiple regression is denoted by b₁. This denotes the change in the predicted value per unit change in X_1,when the other independent variables are held constant.

In SPSS, multiple regression is conducted by the researcher by selecting “regression” from the “analyze menu.” From regression, the researcher selects the “linear” option. When the linear regression dialogue box appears, then the researcher enters one numeric dependent variable and two or more independent variables and then finally he will carry out multiple regression in SPSS.

The following assumptions are made in multiple regression statistical analysis:

The first assumption of multiple regression involves the proper specification of the model. This assumption is important in multiple regression because if the relevant variables are omitted from the model, then the common variance which they share with variables that are included in the mode is then wrongly characterized with respect to those variables, and hence the error term is inflated.

The second assumption is that the residual errors in multiple regression are normally distributed. In other words, one can say that the residual errors in multiple regression should follow the normal population having zero as mean and a variance as one.

The third assumption in multiple regression is that of unbounded data. The regression line produced by OLS (ordinary least squares) in multiple regression can be extrapolated in both directions, but is meaningful only within the upper and lower natural bounds of the dependent.

Dissertation Data Analysis

2009-08-20T11:26:00.000-07:00

The dissertation is the single most important part of any doctoral student’s career because the dissertation is the last step that a doctoral student must take if he or she is to receive his or her doctoral degree and graduate with the title of “Dr.” The dissertation, then, needs to be completed carefully and meticulously as it will be scrutinized by professors before a student can obtain his or her degree. One of the most difficult aspects of the lengthy and time consuming dissertation is the dissertation data analysis. The dissertation itself revolves around data because the doctoral student must actually prove something new and of interest in the field in which he or she is working. The dissertation data analysis will be that proof and the dissertation data analysis will center the entire dissertation.

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Doctoral students often struggle with the dissertation data analysis because the dissertation data analysis revolves around statistics. In other words, in order to have accurate dissertation data analysis, a doctoral student must be proficient in statistics if he or she is to have valid dissertation data analysis. Dissertation data analysis also takes a lot of time, which is another reason why doctoral students often have a hard time with it. If mistakes are done in the dissertation data analysis phase, then those mistakes from the dissertation data analysis will severely affect the student’s dissertation, conclusion and results. Thus, it is very important that the dissertation data analysis is done in a precise and accurate manner.

Because dissertation data analysis can be so complicated and difficult for doctoral students, there is help available. The first source for help on the dissertation data analysis, of course, is the student’s advisor. The doctoral student’s advisor is not always available to answer questions and provide help on the dissertation data analysis, however, and for that reason, dissertation consultants are the perfect solution to getting help and working on the dissertation data analysis. Dissertation consultants can make sure that the dissertation data analysis is accurate and done correctly because dissertation consultants specialize in dissertation data analysis. The reason why dissertation consultants are a sound solution to acquiring dissertation data analysis help is because dissertation consultants are trained statisticians who specialize in both statistics and in dissertations. Dissertation consultants can look at all of the data that the student has gathered over the course of working on his or her dissertation and dissertation consultants can make sense of that data. Thus, dissertation consultants can be an immense help to students on the dissertation data analysis.

Not only can dissertation consultants help with the dissertation data analysis, however, dissertation consultants can also make sure that the data that has been collected by the doctoral student is valid, accurate and statistically sound. In order to produce accurate dissertation data analysis, one must have valid dissertation statistics and dissertation data. If that data is not valid or accurate, that will of course throw off the dissertation data analysis. Dissertation consultants know this and dissertation consultants will make sure that the data that has been collected has been collected properly, that all of the proper tests were used while collecting the data, that the correct sample sizes were used while collecting the data and that the data is not biased. Once the dissertation consultant has double checked to make sure that the dissertation data is indeed accurate, the dissertation consultants can get to work with the student on the dissertation data analysis. With the help of a dissertation consultant, then, the student will be sure to obtain his or her doctoral degree as every single part of the dissertation data and the dissertation data analysis will be correct, accurate, valid and dependable.

Descriptive Measures

2009-08-20T11:01:00.000-07:00

Quantitative data in statistics exhibits some general characteristics that constitute the ideology of descriptive measures.

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There are four different forms of descriptive measures.

The first form of descriptive measures is the measure of central tendency, which is also called the averages.

The second form of descriptive measures is the measure of variation or dispersion.

The third form of descriptive measures is the measure of skewness.

The fourth form of descriptive measures is the measure of kurtosis.

The first form of descriptive measures consists of five descriptive measures, namely Arithmetic Mean, Median, Mode, Geometric Mean and Harmonic Mean.

There are some characteristics that have been put forth by Professor Yule regarding descriptive measures. They are as follows:

1. Descriptive measures should be rigidly defined.

2. Descriptive measures should be less complicated and easy to calculate.

3. The descriptive measures being calculated must be based upon all the observations under consideration.

4. The descriptive measures must be applicable for further mathematical treatment.

5. The descriptive measures must not get affected by the fluctuations of the sampling.

6. The descriptive measures should not get affected by extreme values.

The descriptive measure called the arithmetic mean is defined as the sum of the set of the observations that is divided by the number of that particular set of observations. This descriptive measure satisfies the first five properties laid down by Professor Yule. The biggest disadvantage of this descriptive measure is that it can’t be used in the case of qualitative data and it is also affected by extreme values.

The descriptive measure called the median is defined as that value of the variable which divides the data under consideration into two equal parts. This descriptive measure satisfies the first two and the sixth property put forth by Professor Yule. This descriptive measure can be used in the case of qualitative data, but this descriptive measure cannot be measured quantitatively.

The descriptive measure called mode is defined as the value that occurs most of the time in a particular set of observations. This descriptive measure satisfies the second and the last property that has been put forth by Professor Yule. It is that type of descriptive measure that is used in obtaining an ideal size in business forecasting, etc.

The descriptive measure called the geometric mean is defined as the nth root of the product of the set of the observations under consideration. The basic disadvantage of this type of descriptive measure is that it can neither be easily understood nor be calculated by the person who does not have a mathematical background. This descriptive measure satisfies the first, third, fourth and fifth property put forth by Professor Yule.

The descriptive measure called the harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of the given values provided that none of the observations are zero. The basic disadvantage of this type of descriptive measure is that it cannot be easily understood or be calculated by a person who does not have a mathematical background. This descriptive measure satisfies the first, third, fourth and fifth property put forth by Professor Yule.

The second form of descriptive measure is classified into two categories.

The first category is used in expressing the spread of the observations with respect to the distance that exists between the values of the selected observations. This includes things like range, inter-quartile range, etc.

The second category is used in expressing the spread of the observations with respect to the average of the deviations of the observations for some central value. This includes things like mean, deviation, standard deviation, etc.

The third form of descriptive measure consists of three coefficients of skewness, namely Professor Karl Pearson’s coefficient of skewness, Professor Bowley’s coefficient of skewness and the coefficient of the skewness that is based on the moments.

The fourth form of descriptive measure gives an idea about the flatness or peakedness of the frequency curve. If the curve is neither flat nor peaked, then the descriptive measure concludes that it is a normal curve or a mesokurtic curve. If the curve is flatter than the normal curve, then the descriptive measure concludes that it is a platykurtic curve. If the curve is more peaked, then the descriptive measure concludes that it is a leptokurtic curve.

Binomial Test of Significance

2009-08-20T10:52:00.000-07:00

The binomial test of significance is a kind of probability test that is based on various rules of probability. The binomial test of significance is used to examine the distribution of a single dichotomous variable in the case of small samples. The binomial test of significance involves the testing of the difference between a sample proportion and a given proportion.

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This document will discuss certain terms used in the binomial test of significance so that the reader can better understand the binomial test of significance.

The calculation of the binomial test of significance is done in the following manner:

Let us assume that p(r) is to be calculated in the binomial test of significance. In the binomial test of significance, p(r) is the probability that the researcher will obtain an ‘r’ observation in one category of a dichotomy and the researcher will obtain an ‘n – r’ observations in the other category, when the sample size is n. In the binomial test of significance, if ‘p’ is the probability that the researcher will obtain the first category, and ‘q’ is equal to ‘1 – p,’ then it denotes the probability that the researcher will obtain the second category. The formula for the calculation of the binomial test of significance is given by the following:

p(r) = _nC_r*p_r*q_n-r= (n!p_rq_n-r)/(r!(n-r)!)

In this formula of the binomial test of significance, _nC_r is denoted as the number of combinations of n things drawn from ‘r’ at a time.

The normal approximation of the binomial test of significance is made in following manner:

When the size of the sample ‘n’ is greater than 25, and the probability ‘p’ of obtaining the first category is around 0.50, then product of the term ‘npq’ in the binomial test of significance is at least 9. In this case, the binomial distribution approximates the normal distribution in the binomial test of significance. Because of this approximation, a normal curve z-test is used as an approximation of the binomial test of significance. This formula of the approximation of the binomial test of significance is given by the following:

z = ((r[+,-].5) - np)/SQRT(npq)

The binomial test of significance can be done in SPSS. This non parametric test is calculated in SPSS by selecting “Non Parametric test” from the “analyze” menu and then selecting “binomial test of significance.”

There are certain assumptions that are made in the binomial test of significance. The assumptions are the following:

A dichotomous kind of a distribution is assumed in the binomial test of significance. In other words, in the binomial test of significance, it is assumed that the variable of interest is considered to be dichotomous in nature where the two values are mutually exclusive and mutually exhaustive in all cases being considered. The word ‘binomial’ in the binomial test of significance suggests that the variables of interest should be dichotomous in nature as the term ‘binomial’ means two.

Since this binomial test of significance does not involve any parameter and therefore is non parametric in nature, the assumption that is made about the distribution in the parametric test is therefore not assumed in the binomial test of significance.

In the binomial test of significance, it is assumed that the sample that has been drawn from some population is done by the process of random sampling. The sample on which the binomial test of significance is conducted by the researcher is therefore a random sample.

Chi square test

2009-08-20T10:47:00.000-07:00

The definition of chi square in the chi square test is defined as the square of the standard normal variable.

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The chi square test is basically a test for approximating the large values of ‘n.’ Here ‘n’ is considered as the number of observations under consideration.

There are different varieties of the chi square test where the chi square statistic finds its application. They are as follows:

A chi square test is used to test the hypothetical value of the population variance.

A chi square test is used to test the goodness of fit.

A chi square test is used to test the independence of attributes.

A chi square test is used to test the homogeneity of independent estimates of the population variance.

A chi square test is used to test the homogeneity of independent estimates of the population correlation coefficient.

The chi square distribution involved in the chi square test is a continuous kind of distribution. The range of the chi square distribution in the chi square test is from zero to infinity. The probability density function (pdf) of the statistic involved in the chi square test is given by the following:

f(x)=(exp-{χ²/2} (χ²)^(n/2)-1)/2^n/2г(n/2); 0<∞

Among these entire chi square tests that are mentioned above, the most popular chi square tests are the chi square test for the goodness of fit and the chi square test for the independence of attributes.

The chi square test for the independence of attributes is conducted on the observations that are assigned in the contingency tables. It should be noted that this type of chi square test is carried out only upon those variables that are of categorical type.

Let us state an example in which the chi square test for the independence of the attributes is carried out. Suppose two sample polls of votes for two candidates A and B for a public office are taken, one from among the residents of rural areas and one from urban areas. In this case, there are two variable votes and two areas that are categorized as A and B, rural and urban respectively. The chi square test is carried out here for examining whether the nature of the area is associated to voting preference in the election in the two areas.

The second popular test is the chi square test for goodness of fit. This is a very powerful chi square test for testing the significance of the discrepancy between theory and experiments. This popular chi square test was introduced by Prof. Karl Pearson. This popular chi square test enables the researcher to find out whether the deviation of the experiment from theory has occurred by chance or due to inadequacy of the theory.

This popular chi square test is considered as an approximate test for testing the large values of ‘n.’

There are certain conditions that must be satisfied while conducting the chi square test. They are as follows:

The sample observations in the chi square test must be independent from each other.

The constraints on the cell frequencies in the chi square test must be linear in nature. In other words, this means that in the chi square test, the sum of the observed frequencies must be equal to the sum of the expected frequencies.

The total frequency in the chi square test, which is ‘N,’ must be reasonably large, which means that it should be greater than 50.

The theoretical cell frequency in the chi square test must not be less than five.

Methodology

2009-08-17T13:10:00.000-07:00

Methodology refers to the way of doing things in every field. This document will detail the statistical methodology used in the field of medicine and nursing. There is a methodology called testing of hypothesis and this methodology is extensively used in the field of medicine and nursing. The testing of hypothesis methodology is a kind of a confirmatory test that helps the researcher understand whether or not the hypothesis he/she made is true. This methodology consists of some terms which are often used by the researcher while making some of the other statistical inferences about the drug being tested.

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There are many terminologies used in this methodology. The term null hypothesis is used in this methodology and represents the theory that states that there is no significant difference in the two products being tested. Thus, the methodology of null hypothesis in this case will be stated in the following way: there is no statistical significant difference in the new drug and the current drug. On the other hand, the methodology behind the alternative hypothesis states that it is the complementary of null hypothesis. So in the field of medicine and nursing, the methodology of the alternative hypothesis will be stated in the following way: there might be some statistical significance in the new drug and the current drug.

The methodology behind Type I error involves the rejection of the correct sample. In the field of medicine and nursing, according to the methodology of Type I error, it will reject the correct sample of the drug. On the other hand, the methodology behind Type II error involves the acceptance of an incorrect sample. In the field of medicine and nursing, according to the methodology of Type II error, it will accept a defective drug assuming it is as an effective drug. According to this methodology, this error is one of the most serious errors in this field.

The methodology behind the test statistic is that it is the value that helps the researcher to decide whether a null hypothesis should be accepted or rejected.

The methodology behind the critical region is that it is the set of values of the test statistic for which the null hypothesis is rejected in tests of hypothesis. The critical region methodology is also called the region of rejection.

The methodology behind the level of significance is that it is the probability that there will be a false rejection of the null hypothesis. Usually, this methodology is chosen by the researcher as 0.05.

The methodology behind the power in tests of hypothesis is that it measures the test’s ability to reject the null hypothesis when the null hypothesis is false. In other words, this methodology helps the researcher in making a correct decision. The maximum value of this methodology should be one and the minimum should be 0.

The methodology behind the one sided test will be discussed with the help of an example. Suppose the researcher wants to test whether or not there is any statistical difference between the current drug and the new drug. According to this methodology, the alternative hypothesis will be that the current drug is more effective than the new drug or the current drug is less effective than the new drug. On the other hand, according to the methodology behind the two sided test, the alternative hypothesis will be that there is some statistical significant difference in the new drug and the current drug to be tested.

Path Analysis

2009-08-06T09:34:00.000-07:00

Path analysis is an extended generalized form of the regression model. Path analysis is used for comparing two or more causal models from the correlation matrix. Path analysis is done diagrammatically in the form of circles and arrows that indicate the causation. The task of path analysis is to predict the regression weight. The regression weight predicted during path analysis is then compared to the observed correlation matrix. In path analysis, the goodness of fit test is done in order to show that the model is the best possible fit.

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While conducting path analysis, a researcher comes across some key terminologies used during path analysis. The following terminologies are used during path analysis:

For researchers, the first thing to tackle is the question that they want answered. The question here is what kind of estimation method is to be used in path analysis. Ordinary least squares (OLS) method and maximum likelihood methods are used to estimate the path.

Additionally, there is a term called path model in path analysis. Path model in path analysis is nothing but a diagram that indicates independent variables, intermediate variables and dependent variables. The arrows with a double head indicate that the covariance is being calculated between the two variables in path analysis.

The exogenous variables in path analysis are those variables with no error pointed towards them, except for the measurement error. The endogenous variables in path analysis can have both approaching and withdrawing arrows.

The path coefficient in path analysis is the same as that of the standardized regression coefficient. This coefficient in path analysis indicates the direct effects of an independent variable on the dependent variable.

Since the estimation method is ordinary least squares (OLS), there is a term called disturbance terms in path analysis. These terms in path analysis are nothing but the residual error terms. These terms in path analysis merely indicate the variances which are unexplained and the errors that occurred during measurement (i.e. the measurement errors).

As discussed, goodness of fit test is used in path analysis, and therefore chi square statistics is also used in path analysis. The values that are not significant in path analysis indicate the model with a good fit.

Path analysis is generally conducted with the help of analysis of a moment structures (AMOS), which is an added module in SPSS. Other than the analysis of a moment structures (AMOS), there is other statistical software like SAS, LISREL, etc. that can be used to conduct path analysis. According to Kline (1998), an adequate sample size should be 10 times the cases of parameters in path analysis. The ideal sample size should be 20 times the cases of parameters in path analysis.

Since path analysis is a statistical method, it has assumptions. The following are the assumptions of path analysis:

In path analysis, the relationship between the variables should be linear in nature. The data used in path analysis should have an interval scale. In order to reduce disturbances in the data, the theory of path analysis assumes that the error terms should not be correlated with the variables.

Path Analysis, however, also has some limitations. Although path analysis can evaluate or test two or more causal hypotheses, path analysis cannot establish the direction of causality.

Path analysis is useful only in cases where a small number of hypotheses (that can be represented by a single path) are being tested.

Methodology in Psychology

2009-07-23T09:46:00.000-07:00

Methodology refers to the theoretical analysis of the methods appropriate to a particular field of study. The purpose of this paper is to discuss statistical methodology in the field of psychology.

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In the field of psychology, statistical methodology (like statistical significance testing) is being done. The methodology consists of statistical significance tests, such as t-tests. The methodology called t-test is used to compare the statistical significance of the two samples under study. Suppose one wants to compare the literacy rate of two regions. In this case, t-test methodology is useful. The null hypothesis in this methodology will be that there is no statistically significant difference between the literacy rate of the two samples drawn from region A and B. Suppose, in this methodology, that the calculated t statistic is more than the tabulated t statistic. The null hypothesis assumed in this methodology will be rejected at a particular level of significance.

A statistical methodology called ANOVA, i.e. Analysis of Variance, is used to examine the differences in the mean values of the dependent variable associated with the effect of the controlled independent variables after taking the influence of the uncontrolled independent variables into account.

ANOVA, or one way methodology, involves only one categorical variable, or a single factor. Similarly, if two or more factors are involved in the methodology, then this methodology can be termed as ANOVA n way methodology. The following two assumptions are assumed in this methodology:

The samples drawn from a population in this methodology should be random in nature.
The variance in this methodology should be homogeneous in nature

A statistical methodology, called partial correlation, is used in the field of psychology. This methodology is the measure of the relationship between two variables while controlling or adjusting the effect of one or more additional variables. In psychology, this methodology is useful in behavioral studies. Since psychology is a branch of social science, quantitative methodology can be done through SPSS, which is a statistical software for social sciences.

There are certain terms used in this methodology that can help in understanding this methodology in a precise manner. The term control variables used in this methodology refers to those variables that draw out variances obtained from the initial correlated variables. The order of correlation in this methodology refers to the correlation with a controlled variable. For example, first order partial correlation methodology is the one that has a single control variable.Other than quantitative methodology, there are two techniques of qualitative methodology that are used in this field. Those two techniques in this methodology are namely Delphi Process and the Nominal Group Technique. The prime objective of Delphi Process methodology is to create a reliable and creative investigation of ideas for enabling suitable information for appropriate decision making. This methodology operates as a useful communication device which in turn facilitates the formation of group judgments, which helps in retrieving the appropriate response. Nominal Group Technique in this methodology is a balanced method involving overall participation. In this methodology, the term “balanced” is used because this methodology encourages equal participation of all the group respondents. It means that this methodology involves ideas and views of a group of people rather than an individual.

The idea behind the theory of Nominal Group Technique methodology is the biggest advantage over Delphi Process methodology. This advantage also cites the major difference between the two methodologies. The difference in these two methodologies is that the information obtained using the Nominal Group methodology is more reliable because the responses were obtained from each and every participant.

Normal Curve Tests of Means and Proportions

2009-06-29T07:21:00.000-07:00

The normal curve tests of means and proportions refer to those tests that are basic methods of testing the possible differences between two samples. The normal curve tests of means and proportions can also be referred to as parametric tests under the assumption that the population follows a normal distribution. Normal curve tests of means and proportions are used when the size of the sample is more than 29.

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There are certain conceptual terms that are helpful to know to better understand the normal curve tests of means and proportions.

The deviation scores in normal curve tests of means and proportions are defined mathematically as the difference between the observed score and the mean for any particular variable. The deviation score in normal curve tests of means and proportions is generally zero, since half of the deviations are above the mean value and the other half are below the mean value.

The standard error in normal curve tests of means and proportions is used to estimate the variability of the sample means. Since there is only one sample in the normal curve tests of means and proportions, the estimated standard error can be computed by the ration between the standard deviation and the square root of the sample size.

The confidence limits in the normal curve tests of means and proportions set the upper and the lower bounds on an estimate for a given level of significance. In the normal curve tests of means and proportions, these limits are regarded by the researchers as they provide additional information about the estimates.

The normal curve tests of proportions in normal curve tests of means and proportions are used to test the difference in the proportions or the percentages rather than the means.

When two independent samples are tested by the researcher in the normal curve tests of means and proportions, then some different formulas are used, although the main aim remains the same. Thus, the comparison of the z values with the critical values in the table is done under the normal curve.

When the correlated two samples test is used by the researcher in the normal curve tests of means and proportions, then the two correlated samples are factored into the formulas for the two sample means and proportions test. The notations that are in these samples of the normal curve tests of means and proportions are similar to the previous samples with an addition of the Pearsonian correlation.

There are also certain assumptions in the normal curve tests of means and proportions.
The first assumption of the normal curve tests of means and proportions is that as the name suggests, the variable of interest should be normally distributed in the population.

The second assumption of the normal curve tests of means and proportions is that the data should be of interval scale.

The third assumption of the normal curve tests of means and proportions is that the size of the sample should not be small.

The fourth assumption of the normal curve tests of means and proportions is that there should be homogeneity within the variances. This assumption of the normal curve tests of means and proportions is used in two sample testing cases.

Reliability Analysis

2009-06-26T07:56:00.000-07:00

In Reliability analysis, the word reliability refers to the fact that a scale should consistently reflect the construct it is measuring. There are certain times and situations where Reliability analysis can be useful.

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An aspect in which the researcher can think about Reliability analysis is when two observations under study that are equivalent to each other in terms of the construct being measured also have the equivalent outcome.

There is a popular technique of Reliability analysis called the split half reliability. This method of Reliability analysis splits the data into two parts. The score for each participant in the Reliability analysis is then computed on the basis of each half of the scale. In that type of Reliability analysis, if the scale is very reliable, then the value of the person’s score on one half of the scale would be equivalent to the score on the other half. In this type of Reliability analysis, the previous fact should remain true for all the participants.

The major problem with this type of Reliability analysis is that there are several ways in which a set of data can be divided into two parts, and therefore the outcome could be numerous.

In order to overcome this problem in this type of Reliability analysis, Cronbach (1951) introduced a measure that is a common measure in Reliability analysis. This measure of Reliability analysis is loosely equivalent to the splitting of the data in two halves in every possible manner and further computing the correlation coefficient for each split. The average of these values is similar to the value of Cronbach’s alpha in Reliability analysis.

There are basically two versions of alpha in Reliability analysis. The first version of alpha in Reliability analysis is the normal version. The second version of alpha in Reliability analysis is the standardized version.

The normal version of alpha in Reliability analysis is applicable when the items on a scale are summed to produce a single score for that scale. The standardized version of alpha in Reliability analysis is applicable when the items on a scale are standardized before they are summed up.
According to Kline (1999), the acceptable value of alpha in Reliability analysis is 0.8 in the case of intelligence tests, and the acceptable value of alpha in Reliability analysis is 0.7 in the case of ability tests.

There are certain assumptions that are assumed in Reliability analysis.

While conducting Reliability analysis in SPSS, the researcher should click on “Tukey’s test of additivity” as additivity is assumed in Reliability analysis.

In Reliability analysis, independence within the observations is assumed. However, it should be noted by the researcher that the test retest type of Reliability analysis involves the correlated data between the observations which do not pose a statistical problem in assessing the reliability in Reliability analysis.

In Reliability analysis, it is assumed that the errors are uncorrelated to each other. This means that in Reliability analysis, there exists no association among the errors and therefore all the errors in Reliability analysis are different.

In Reliability analysis, to attain reliability in the data, the coding done by the researcher should be consistent. This means that in Reliability analysis, the high values must be coded consistently, such that they have the same meaning across the items.

In the split half type of Reliability analysis, the random assignment of the subjects is assumed. Generally, in this type of Reliability analysis, the odd numbered items fall in one category and the even numbered items fall in the other.

Dissertation Statistics Tutoring

2009-06-15T07:46:00.000-07:00

Any student working on a dissertation can benefit from dissertation statistics help. Dissertation statistics help makes the process of writing a dissertation easy, manageable and understandable.

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Dissertation statistics help can provide invaluable help, guidance and assistance to anyone writing a dissertation.The dissertation is the hardest and most challenging part of any student’s academic career. For this reason, it is important to seek dissertation statistics help. Unfortunately, many students do not choose to seek dissertation statistics help until they have reached a ‘stopping point’ or a problem. And while dissertation statistics help can fix that problem, the student has already wasted valuable time as he or she did not seek dissertation statistics help sooner.

Dissertation statistics help provides help throughout the dissertation—from the very beginning, to the very end of the dissertation. Dissertation statistics help is provided by trained professionals who are well versed in all things regarding dissertations and statistics. Dissertation statistics help is also provided by people who have already received their doctoral degrees, and thus dissertation statistics help is provided by people who have gone through every single stress that the student has gone through. This can be important as it is important to be able to understand the needs of the student who is acquiring dissertation statistics help.

Dissertations rely heavily on statistics and unfortunately many students do not know enough about statistics to be successful in their research and design for their project. Here again dissertation statistics help can assist the student. Dissertation statistics help will step in at the very beginning of the project and will help the student design that project properly. Dissertation statistics help will go over every single thing that needs to be done and dissertation statistics help will make sure that the student has the proper tools to complete the project. There will be no “wrong turns’ with dissertation statistics help, as dissertation statistics help will be there assisting the student every single step of the way.

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Dissertation statistics help will make the acquisition of any dissertation easier and more obtainable. While other students who do not seek dissertation statistics help struggle with many aspects of their dissertation, the student who is smart enough to seek dissertation statistics help will finish on-time and with much less stress. Because dissertation statistics help provides guidance, help, and assistance throughout the entire process, the student is sure to finish on-time and with a great amount of success.

Statistical Data Analysis

2009-04-09T07:29:00.000-07:00

Statistics is basically a science that involves data collection, data interpretation and finally, data validation. Statistical data analysis is a procedure of performing various statistical operations. Statistical data analysis is a kind of quantitative research, which seeks to quantify the data, and typically, applies some form of statistical analysis. Quantitative data in statistical data analysis basically involves descriptive data, such as survey data and observational data.

Statistical data analysis generally involves some form of statistical tools, which a layman cannot perform without having any statistical knowledge. There are various software packages to perform statistical data analysis. This software includes Statistical Analysis System (SAS), Statistical Package for the Social Sciences (SPSS), Stat soft, etc.

Data in statistical data analysis consists of variable(s). Sometimes the data in statistical data analysis is univariate or multivariate. Depending upon the number of variables in statistical data analysis, the researcher performs different statistical techniques.

If the data in statistical data analysis is multiple in numbers, then several multivariate statistical data analysis can be performed. The multivariate statistical data analyses are factor statistical data analysis, discriminant statistical data analysis, etc. Similarly, if the data in statistical data analysis is singular in number, then the univariate statistical data analysis is performed. This includes t test for significance, z test, f test, ANOVA one way, etc.

The data in statistical data analysis is basically of 2 types, namely, continuous data and discreet data. The continuous data in statistical data analysis is the one that cannot be counted. For example, intensity of a light can be measured but cannot be counted. The discreet data in statistical data analysis is the one that can be counted. For example, the number of bulbs can be counted.

The continuous data in statistical data analysis is distributed under continuous distribution function, which can also be called the probability density function, or simply pdf.

The discreet data in statistical data analysis is distributed under discreet distribution function, which can also be called the probability mass function or simple pmf.

We use the word ‘density’ in continuous data of statistical data analysis because density cannot be counted, but can be measured. We use the word ‘mass’ in discreet data of statistical data analysis because mass cannot be counted.

There are various pdf’s and pmf’s in statistical data analysis. For example, Poisson distribution is the commonly known pmf, and normal distribution is the commonly known pdf in statistical data analysis.

These distributions in statistical data analysis help us to understand which data falls under which distribution. If the data in statistical data analysis is about the intensity of a bulb, then the data would be falling in Poisson distribution.

There is a major task in statistical data analysis, which comprises of statistical inference. The statistical inference in statistical data analysis is mainly comprised of two parts: estimation and tests of hypothesis.

Estimation in statistical data analysis mainly involves parametric data—the data that consists of parameters. On the other hand, tests of hypothesis in statistical data analysis mainly involve non parametric data— the data that consists of no parameters.

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Data Analysis

2009-04-06T10:59:00.000-07:00

Data analysis is a procedure of collecting and analyzing raw data by interpreting the inference out of raw data. Data analysis is one of the important aspects of the analyst’s work. Data analysis plays a crucial role in deciding whether or not the retrieved data is reliable.

Data analysis is basically a two-step procedure that involves collecting and analyzing data. Data analysis can be explained with the help of the following example:

Suppose a researcher has conducted a survey in order to know if the manufacturing of auto parts in an auto industry is more in Pune or in Chennai. The first step of data analysis is to collect the data through primary or secondary research. The next step of data analysis is to make an inference about the collected data. The second step of data analysis in this case will involve SWOT Analysis. SWOT Analysis stands for Strength, Weakness, Opportunity and Threat of the data under study.

Primary research in data analysis is the one that involves collection of data through questionnaires or telephone interviews. Secondary research in data analysis is the one that involves collection of data using the internet.

There are basically two types of data analysis. These two types are as follows:

Qualitative data analysis: This kind of data analysis is the one that consists of an unstructured, exploratory research methodology based on small samples intended to provide an insight into the problem being solved.

Quantitative data analysis: On the other hand, this kind of data analysis seeks to quantify the data and typically involves some form of statistical data analysis.

Quantitative data analysis can be performed in those cases when one needs to get statistical inferences about the data. In such cases, data analysis is done by using some statistical techniques. These statistical techniques include Factor Analysis, Discriminate Analysis, etc.

A technical analyst performs data analysis by interpreting the charts using a time series technique, and he/she forecasts the price trends of a particular commodity or share. Thus, data analysis can be used to forecast about the data as well.

Data analysis is an integral part of every research work. The validity of data can be known only through data analysis.

In statistics, data analysis is done on quantitative data. Data analysis in relation to quantitative data analysis can be divided into descriptive statistics, exploratory data analysis and confirmatory data analysis.

Descriptive Statistics in data analysis involves techniques like mean, median, mode, variance, standard deviation, etc.

Exploratory data analysis involves the following steps:

· Formulation of a problem in data analysis.
· Identifying alternative courses of action in data analysis.
· Developing hypotheses in data analysis.
· Isolating key variables and relationships for further examination in data analysis.
· Gaining insights for developing an approach to the formulated problem in data analysis.

Sometimes, qualitative data analysis is undertaken to explain the findings obtained from quantitative data analysis. Thus, one can say that both qualitative data analysis and quantitative data analysis are interrelated with each other.

Data analysis is also synonymous to data modeling. Data modeling is a process in which a perfect model (which represents the data as a whole) is being fitted during the data analysis.

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Statistics Help

2009-04-01T13:27:00.001-07:00

Fact and verity go-hand-in-hand in today’s world of constant change and practicality. Statistics has become a necessary facet in daily activity. With statistics as a core subject towards the proper functioning of organizations and firms, help and assistance is made accessible to all those in need. Statistics help has been a compulsory need for businesses as it ensures functionality and efficiency within organizations. Statistical help is used for guiding and assisting clients like students, researchers and members of the business or government communities as it analyzes complicated statistical problems. Backed up by strong statistical facts, organizations with statistical help use these surveys and analyses to create constructive findings and conclusions.

Statistics form a core element in the proper execution of activities and functions of organizations. Statistics form a crucial part in determining business activities and behavior. In the line of business, applications such as risk assessment, data analysis, data mining and decision support can all be carried out through statistics. Statistical help and analysis go a long way at determining business processes. It also helps set a proper course through its research and findings.

Statistics is also applied by students when they write theses, dissertations, reports and term papers. Statistical help and validity may be required for the report or paper. Statistics help also aids organizations at expediting the growth rate and progress. Statistics help should originate from a well-trained work force that is highly skilled at statistics and is experienced and knowledgeable in the field. Such statistics help can be acquired from experts like professors, business consultants, researchers and specialized statistical consultants. The consultants should have good communication skills for interacting with clients, a good scientific and analytical brain, statistical understanding and should be computer proficient. Statisticians should be able to comprehend the needs of the client and fulfill them as per the clients’ requirements. Statistics help is necessarily centered on the needs of the clients, be it analysis, research, survey, etc. Hence, budget should be taken into consideration as quality is emphasized.

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Given that the competition between firms today is on the rise, statistics help assists organizations in achieving more prospects and thus they gain leverage against other contenders. Some organizations, especially the smaller firms who do not have the required skill and ability to perform statistical analyses, rely on statistical help to further their benefits.

Statistics help is a very relevant instrument in today’s world. It warrants efficiency and accuracy and is applicable to almost every sphere of life. The possibilities that statistics help provide goes beyond measure. Putting an end to ball-park figures and estimates, statistics help has taken the world by storm with its precision and exactness and it remains an indispensable part of everyday activities.

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Exploratory Factor Analysis

2009-04-01T10:37:00.000-07:00

Factor Analysis is a general name denoting a class of procedures primarily used for data reduction and summarization. In research, there are a large number of variables which are extensively correlated and must be reduced to a manageable level. Relationships among sets of many interrelated variables are examined and represented in terms of a few underlying factors.
There are basically 2 approaches to Factor Analysis:

· Exploratory Factor Analysis (EFA) seeks to uncover the underlying structure of a relatively large set of variables. The researcher has a priori assumption that any indicator may be associated with any factor. This is the most common form of factor analysis. There is no prior theory and one uses factor loadings to intuit the factor structure of the data.

· Confirmatory Factor Analysis (CFA) seeks to determine if the number of factors and the loadings of measured (indicator) variables on them conform to what is expected on the basis of pre-established theory. Indicator variables are selected on the basis of prior theory, and factor analysis is used to see if they loaded, as predicted, on the expected number of factors.

The basic difference between Exploratory Factor Analysis and CFA is that in CFA, a researcher’s a priori assumption is that each factor (the number and labels of which may be specified a priori) is associated with a specified subset of indicator variables. The major limitation behind Exploratory Factor Analysis is its simplicity. Hence, the researcher will not get a reliable inference. Therefore, Exploratory Factor Analysis is used less as compared to Confirmatory Factor Analysis.

The following techniques are used in both the approaches—both Exploratory Factor Analysis and CFA:

· Principal Component Technique: This technique is used in Exploratory Factor Analysis, where the total variance in the data is considered. The diagonal of the correlation matrix consists of unities, and full variance is brought into the factor matrix. Principal technique is recommended when the primary concern is to determine the minimum number of factors that will account for maximum variance in the data for use in subsequent multivariate analysis.

There are some techniques, in addition to Principal Component Technique, that are used in Exploratory factor analysis and Confirmatory factor analysis and that are complex. These techniques are also called Extraction Methods. These techniques are as follows:

· Image factoring: This technique in Exploratory Factor Analysis is based on the correlation matrix of predicted or dependent variables rather than actual variables. In this, we predict each variable from the others by using multiple regressions.

· Maximum likelihood factoring(MLF): This technique in Exploratory Factor Analysis is based on a linear combination of variables to form factors, where the parameter estimates are such that they are most likely to have resulted in the observed correlation matrix, by using Maximum Likelihood Estimation (MLE) methods and assuming multivariate normality. Correlations are weighted by each variable's uniqueness. Here, uniqueness refers to the difference between the variability of a variable and its communality. MLF generates a chi-square goodness-of-fit test. The researcher can increase the number of factors one at a time until a satisfactory goodness-of-fit is obtained.

· Alpha factoring: This technique in Exploratory Factor Analysis is based on the maximization of the reliability of factors, assuming that the variables are randomly sampled from a very large set of variables. Unlike other methods, this method does not assume sampled cases and fixed variables.

· Unweighted least squares (ULS) factoring: This technique in Exploratory Factor Analysis is based upon minimizing the sum of squared differences between the observed and estimated correlation matrices, without counting the diagonal.

· Generalized least squares (GLS) factoring: This technique in Exploratory Factor Analysis is based on adjusting ULS by measuring the correlations, which are inversely proportional to their uniqueness (more unique variables weight less). Like MLF, GLS also generates a chi-square goodness-of-fit test. The researcher can increase the number of factors one at a time until a satisfactory goodness-of-fit is obtained.

The major disadvantage of using these techniques in Exploratory Factor Analysis is that they are quiet complex and are not recommended for an inexperienced user. Hence, these methods are usually not used in extraction methods. For help with these techniques, click here.

Screening of the Data

2009-03-31T13:11:00.000-07:00

Careful analysis of data applicability after collection and before analysis is probably the most time-consuming part of data analysis (Tabachnick & Fidell, 2001). This step is, however, of utmost importance as it provides the foundation for any subsequent analysis and decision-making which rests on the accuracy of the data. Incorrect analysis of the data during purification, including EFA, and before conducting confirmatory SEM analysis may result in poor fitting models or, worse, models that are inadmissible.

Data screening is important when employing covariance-based techniques such as structural equation modelling where assumptions are stricter than for the standard t-test. Many of the parametric statistical tests (based on probability distribution theory) involved in this study assume that: (a) normally distributed data – the data are from a normally distributed population, (b) homogeneity of variance – the variances in correlational designs should be the same for each level of each variable, (c) interval data – data where the distance between any two points is the same and is assumed in this study for Likert data, and (d) independence – the data from each respondent has no effect on any other respondent’s scores.

Many of the common estimation methods in SEM (such as maximum-likelihood estimation) assume: (a) “all univariate distributions are normal, (b) joint distribution of any pair of the variables is bivariate normal, and (c) all bivariate scatterplots are linear and homoscedastic” (Kline, 2005, p. 49). Unfortunately, SPSS does not offer an assessment of multivariate normality but Field (2005) and others (Kline, 2005; Tabachnick & Fidell, 2001) recommend first assessing univariate normality. The data were checked for plausible ranges and examination was satisfactory. There were no data out of range.

Data Analysis

2009-01-27T09:58:00.000-08:00

Data analysis refers to the larger subject of gathering, transforming, Interpreting and modeling data into meaningful information relevant for business decisions. With the help of data analysis we can compare, support and highlight content based on relevance and context in a business or research setting. It consists of various techniques, approaches and applications which act as aids in producing information for managerial and business decision making. Data analysis can be applied in various fields such as research, medicine, engineering, election polling and gambling to name a few. Some of the more popular data analysis techniques are:

· Data mining

Data mining is the process of obtaining meaningful information from a raw dataset. For instance, a bank may need to know the specific areas wherein bad debts are frequent, from it’s entire database of collections and bad debts. Data mining is an important step in transforming data into information. Industries that implement data mining include retail, financial services, marketing organizations and many more.

· Business Intelligence

This is a technique used in the interpretation of data available to an organization using reports, transaction processing, analytics, scorecards and even includes data mining in its overall context. It encompasses all the tools, skills, applications and strategies in developing meaningful information that can be used and accessed by managers or decision makers. In essence, business intelligence helps present information to those interested in it, in a format that makes it easy to understand the historical context, key metrics, benchmarks and other relevant topics that aid in the analysis and planning of business activities and performance.

· Exploratory Data analysis (EDA)

This method of data analysis refers to the analysis and interpretation of data. Using tools such as charts and diagrams, along with key descriptive statistics such as means, totals, crosstabs and other related methods, exploratory data analysis attempts to provide the information that helps business performance.

· Confirmatory Data analysis (CDA)

The key difference between exploratory and confirmatory data analysis is that while the former aids in navigating the gamut of performance related data, this technique aids in producing information to assess the validity of business decisions. It includes techniques such as hypothesis testing, structured equation modeling and other quantitative techniques.

Data analysis involves a number of steps in its general form. In order to understand the process behind data analysis in depth, one needs to evaluate the context and needs of the data analysis activity. However, the following steps can act as general guidelines for a data analysis project:

1. The First step is the screening or the cleansing of the data to eliminate errors, such as missing and duplicate values. Typically cleansing will also encompass normalizing date in order to make sure that the results can be easily analyzed using major statistical tools and methods.

2. The Second step is to select key indicators which are meant to be produced from the data analysis project, in terms of metrics, reports, benchmarks and formats. This is similar to a design phase where the entire project is planned and laid out.

3. Next, we conduct the actual analysis or data analysis and obtain results. Depending on the specific technique which is used, it could be a dynamic (real time visuals and reports) or static process (wherein reports and other metrics and generated and delivered to be analyzed). In addition, the process could be interactive, wherein a user selects metrics on-the-fly and the screen report is generated. Many business intelligence platforms offer this facility.

4. Reliability testing should be a priority in nearly every data analysis exercise. It ensures that the output received is meaningful, particularly when statistical analyses are involved.

‘Gotchas’ in data analysis: key validation requirements for meaningful data analysis

Data analysis can help create a very useful and valuable information chain in an organization or it can cause the disruption of perfectly good activities, if it is based on nonsensical information founded on invalid data or analysis techniques. It is important therefore, to know:

· Source of data and collection methods: it’s important to know how the data were collected, organized and sourced, in order for the data analysis to be meaningful. Cases of unethical data collection abound, which can lead to serious privacy concerns and consequences for the analyst as well as the reporter. In addition, how the data were collected is critical to know whether or not the underlying assumptions make any sense whatsoever.

· Analytical methods/techniques: based on the characteristics of the data set itself and the needs of the analysis, techniques or methods have to be chosen carefully. This could mean a simple decision such as z-test versus ANOVA or t-test, or a larger research design concern.

· Understand the limitations of quantitative facts: at the end of the day, the purpose of the data analysis is to help make decisions to improve performance. It is very easy to be misled by averages and totals that do not display the whole picture. A background into quantitative statistics and values can reveal facts that would otherwise be ignored.

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