The idea behind the parametric tests that involve parameters is to test the statistical significance of the observations under study. Chi square test is one of the parametric tests.
Chi square test involves different types of chi square tests, like chi square test for cross tabulation, chi square test for goodness of fit, likelihood ratio chi square test, etc.
The statistic in chi square test is used to test the statistical significance of the observed relationship in the cross tabulation of two variables. The statistic used in chi square test helps the researcher to determine whether or not an appropriate relationship exists between the two variables.
The null hypothesis assumed in chi square test assumes that there exists absolutely no correlation between the two variables being observed under the study. The chi square test is conducted by computing the cell frequencies which consist of the expected frequencies, if there is no correlation between the variables. The expected frequency in chi square test is then compared to the actual observed frequencies found in cross tabulation to calculate the chi square statistic in chi square test. The expected frequency in chi square test is calculated as the product of the total number of observations in the row and the column divided by the total size of the sample. The chi square statistic in chi square test is then calculated as 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 chi square test.
In order to determine the association between the two variables, the probability of obtaining a value of chi square should be larger than the one obtained from 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 that actually belongs to that specified distribution. This type of chi square test can be applicable to only discrete types of distributions, like poisson, binomial, etc. This type of chi square test is an alternative test for the non parametric test and it is 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 as defined 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.
As discussed in the above chi square test, the probability of obtaining a value of chi square should be larger than the one obtained from chi square test for goodness of fit.
There are certain assumptions in a chi square test. The assumptions are as follows:
- In a chi square test, random sampling of the data is assumed.
- In a chi square test, a sample with a sufficiently large size is assumed. If a chi square test is conducted on a sample with a smaller size, then the chi square test will yield an inaccurate inference. The researcher, by using chi square test on small samples, might end up committing a Type II error.
- In a chi square test, the observations are always assumed to be independent of each other.
- In a chi square test, the observations must have the same fundamental distribution.
