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How is a chi-square test used and interpreted?

09/26/2023 | by Patrick Fischer, M.Sc., Founder & Data Scientist: FDS

The chi-square test is a statistical procedure used to test for independence or association between two categorical variables. It compares the observed frequencies in a sample with the expected frequencies that would be obtained if the two variables were independent of each other.

The general procedure of the chi-square test consists of several steps:

Formulation of hypotheses:

Null hypothesis (H0): There is no association between the variables.

Alternative hypothesis (H1): There is an association between the variables.

Collecting data: Collecting data on the two categorical variables.

Constructing a contingency table: creating a table that contains the frequencies of the combinations of the two variables.

Calculating the chi-square value: the chi-square value is calculated by comparing the observed frequencies with the expected frequencies. The expected frequencies are calculated using the assumption of independence.

Determining the degrees of freedom: The degrees of freedom are calculated based on the size of the contingency table. For a 2x2 table, the number of degrees of freedom is (number of rows - 1) * (number of columns - 1).

Determination of Significance: The chi-square value is compared with a chi-square distribution and the degrees of freedom to determine statistical significance. This can be done using a significance threshold (e.g., p < 0.05).

Interpretation of results: If the calculated chi-squared value is statistically significant (i.e., p value below the specified significance threshold), the null hypothesis is rejected. This indicates that there is an association between the variables. If the calculated chi-squared value is not significant, the null hypothesis can be retained, indicating that there is insufficient evidence of an association.

It is important to note that the chi-square test shows association between variables but does not indicate causality. There are also several variations of the chi-square test, such as the goodness-of-fit test or the test for independence, that can be used depending on the question and the nature of the data.

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