Analysis Of Variance (ANOVA)

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.