Chi-square test

A categorical variable (sometimes called a nominal variable) is one that has two or more categories, but there is no intrinsic ordering to the categories (example, gender: male/ female). So, categorical variable is one that allows us to assign categories but cannot clearly order the variables in a particular manner. For example, Hair color is a categorical variable having a number of categories (blonde, brown, brunette, red, etc.) but there is no agreed way to order these from highest to lowest. 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.

A chi-squared test is a statistical hypothesis test wherein the sampling distribution of the test statistic is in a chi-square distribution when the null hypothesis is true.Chi-square is used most commonly to compare the incidence (or proportion) of a characteristic in one group to the incidence (or proportion) of a characteristic in other group(s). The Chi-Square (χ2) test is used for categorical variables which determines whether there is a difference in the population proportions between two or more groups.The Chi Square distribution is the distribution of the sum of squared standard normal deviates. The degrees of freedom of the distribution is equal to the number of standard normal deviates being summed.

Types:

1. Pearson's chi-square test
2. Yates's correction for continuity
3. Cochran–Mantel–Haenszel chi-squared test.
4. McNemar's test
5. Tukey's test of additivity
6. The portmanteau test in time-series analysis, testing for the presence of auto-correlation
7. Likelihood-ratio tests

In anaesthesia, Chi square test is commonly used to compare a group with a value, or to compare two or more groups, but with categorical data.