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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-{χ

^{2}/2} (χ

^{2})

^{(n/2)-1})/2

^{n/2}г(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.