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📊 How Chi-Square Tests Read Categorical Counts

Learn how chi-square tests compare observed and expected category counts, choose the right test, check its assumptions, and explain what a p-value does and does not show.

lessons

~20 min

to learn

🔬 Science

subject

Adults

level

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What you’ll learn

Frame the questionChoose and organize the appropriate chi-square question for categorical counts.Test purpose and table structure make the comparison explicit.
Build the null comparisonSet hypotheses and calculate the expected-count comparison.The null, expected counts, statistic, and degrees of freedom define the reference calculation.
Judge the approximationAssess conditions and interpret the chi-square right-tail p-value.Design and expected counts determine whether the reference p-value is credible.
Interpret the resultUse alpha to report a chi-square result with effect and context.A useful conclusion separates evidence, cell pattern, practical size, and limits.

Questions this course answers

What does a goodness-of-fit chi-square test compare?

Goodness of fit asks whether categorical counts match a specified null distribution.

For an independence table, how is an expected cell count found?

That formula gives the count predicted by independence for each cell.

Why is the chi-square p-value taken from the right tail?

The statistic is a sum of nonnegative discrepancy contributions, and unusually large values challenge the null.

What should you say when the p-value is larger than alpha?

A larger p-value means the observed departures are not sufficiently unusual under the chosen threshold.

Why inspect expected counts before using a chi-square approximation?

The approximation needs adequate expected frequencies, with exact guidance depending on the design.

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