How to perform a chi-square test?

To perform a chi-square test, first state the null and alternative hypotheses and choose a significance level.

A chi-square test is used to determine if there is a significant difference between observed and expected frequencies in a categorical data set. The first step is to state the null and alternative hypotheses. The null hypothesis states that there is no significant difference between the observed and expected frequencies, while the alternative hypothesis states that there is a significant difference.

Next, choose a significance level, typically 0.05 or 0.01. This represents the probability of rejecting the null hypothesis when it is actually true.

Calculate the expected frequencies for each category based on the total sample size and the expected proportions. Then, calculate the chi-square statistic by summing the squared difference between the observed and expected frequencies for each category, divided by the expected frequency.

Degrees of freedom can be calculated by subtracting 1 from the number of categories. Use a chi-square distribution table or calculator to find the critical value for the chosen significance level and degrees of freedom.

Compare the calculated chi-square statistic to the critical value. If the calculated value is greater than the critical value, reject the null hypothesis and conclude that there is a significant difference between the observed and expected frequencies. If the calculated value is less than the critical value, fail to reject the null hypothesis and conclude that there is no significant difference.

Finally, interpret the results and draw conclusions based on the context of the data set.