Chi-square analysis is a statistical method used to determine whether there is a significant association between two categorical variables. The categorical variables are usually represented in a contingency table, which displays the frequencies or proportions of observations for each category of both variables.
The chi-square test evaluates whether there is a significant difference between the expected frequencies in each cell of the contingency table and the observed frequencies. The null hypothesis is that there is no association between the variables, and the alternative hypothesis is that there is an association. If the chi-square test statistic is large enough to reject the null hypothesis at a certain level of significance (e.g., alpha = 0.05), then we can conclude that there is evidence of an association between the variables.
The calculation of the chi-square test statistic involves comparing the observed frequencies in each cell of the contingency table to the expected frequencies, which are calculated under the assumption of no association between the variables. The expected frequencies are obtained by multiplying the row and column totals for each cell and dividing by the total number of observations. The chi-square test statistic is then calculated by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies.
Chi-square analysis is commonly used in social sciences, marketing research, and other fields where categorical data is collected. It can be used to test hypotheses about the relationship between variables, to evaluate the goodness of fit of a model to the data, and to compare the distributions of two or more samples. However, it is important to note that the chi-square test assumes that the observations are independent and that the expected frequencies are not too small, otherwise the test may not be reliable.