The various tests of are based on the assumption that the samples have been drawn from the normal. In Z-test, t-tests, F-tests, we had to make an assumption about the population values or parameters and so these are known as “parametric tests”.
There are a number of situations in which it is not possible to make any rigid assumption about the nature of the population. In order to study these problems, some tests are developed which are called “Non-parametric Tests”. Chi-square test (Chi is pronounced as ‘ki’ and symbolically written as χ2) is one of the most prominent non parametric tests and it has great importance in statistical analysis. The importance of χ2 test cannot be denied as it is a distribution free test.
Chi-square test measures the extent to which a set of the observed frequencies of a sample deviates from the corresponding set of the theoretical (expected) frequencies. It is a measure of aggregate discrepancy between the actual frequencies and the theoretical frequencies in a sample. Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.
When our data consists of only the frequencies of various events, the most commonly used statistics is the chi square (X2). Chi-Square test tabulates a variable into categories and computes a chi-square statistic based on the differences between observed and expected frequencies
TYPES OF CHI-SQUARE TEST :-