Chi Square Statistic

The chi-square statistic is a measure of the difference between the expected and observed frequencies in a contingency table. It is used to test the null hypothesis that there is no association between the variables in the table. The chi-square statistic is calculated by summing the squared differences between the expected and observed frequencies, divided by the expected frequencies.

The chi-square statistic is a non-parametric test, which means that it does not make any assumptions about the distribution of the data. This makes it a useful test for data that is not normally distributed.

The chi-square statistic is interpreted using a chi-square distribution. The p-value for the chi-square statistic is the probability of obtaining a chi-square statistic at least as large as the one that was calculated, assuming that the null hypothesis is true.

If the p-value is less than the significance level, then the null hypothesis is rejected. This means that there is sufficient evidence to conclude that there is an association between the variables in the table.

The chi-square statistic is a powerful tool for testing the association between variables. It is a versatile test that can be used with a variety of data types. However, it is important to remember that the chi-square statistic is only a test of statistical significance. It does not tell us anything about the strength of the association between the variables.

Here is an example of how the chi-square statistic can be used to test the association between two variables. A researcher is interested in testing the association between gender and political party affiliation. The researcher collects data on 100 people, and records their gender and political party affiliation. The data is summarized in the following contingency table:

| Gender | Political Party Affiliation |
|---|---|
| Male | Democrat | 30 |
| Male | Republican | 20 |
| Female | Democrat | 40 |
| Female | Republican | 10 |

The chi-square statistic for this table is 10.0. The p-value for this statistic is 0.05. This means that there is a 5% chance of obtaining a chi-square statistic at least as large as the one that was calculated, assuming that the null hypothesis is true.

Since the p-value is less than the significance level, the null hypothesis is rejected. This means that there is sufficient evidence to conclude that there is an association between gender and political party affiliation.