Statistical Consulting Blog

Chi Square Test

Posted December 15, 2009

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 this test. The computation of the expected frequency 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 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 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 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 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.

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