Categorical data: Chi square test
Categorical data is also known as nominal data, meaning that one uses labels as opposed to numbers; for example, race and gender are categorical variables.
The central tendency of categorical variables is given by its mode, since median and mean can only be computed on numerical data. Therefore, it does not follow a normal bell-curve distribution, and cannot be analyzed with tests that rely on a normal distribution such as the t-test or ANOVA.
The Chi Square test is a statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true. A common usage of the Chi-square test is the Pearson’s chi-square test, also known as the chi-square goodness-of-fit test or chi-square test for independence. The Chi square test is used to compare a group with a value, or to compare two or more groups, always using categorical data.