# chi-square test

## Definition of chi-square test

The Chi-square Test is a statistical hypothesis test used to determine the significance of the difference between the observed and expected values of a given data set. The chi-square statistic is used to calculate the degree of freedom associated with the given set, and to determine whether the observed values are significantly different from the expected values.

## What is the chi-square test used for?

The chi-square test is a statistical tool used to test whether two or more groups of observations are independent. It is also used to test the relationship or association between two or more categorical variables. The chi-square test measures the amount of deviation from what would be expected on the basis of chance alone. When conducting this analysis, researchers compare observed data with expected data that is based on theoretical expectations and population statistics.

The formula for the chi-square test statistic is calculated by subtracting the expected frequency from the observed frequency, squaring it, then dividing by the expected frequency and summing them all up for each category being tested. If the p-value for a given chi-square statistic is lower than 0.05, then there is significant evidence that at least one of the groups being compared is different from the others in terms of their relative proportion.

Chi-squared tests can be used to assess relationships between variables in both observational studies (where no manipulation occurs) and experimental studies (where some manipulation occurs). Since chi-squared tests are nonparametric (independent from assumptions about population distributions), they can be used even when sample sizes are small. They are commonly employed in research assessment, market research, medical diagnosis and testing for goodness of fit for certain types of models or theories.