What is the primary purpose of chi-square tests in statistics?

Chi-square tests analyze categorical data patterns.

• Assessing data significance.

• Comparing observed vs expected.

• Identifying meaningful relationships.

Chi-square tests require that all expected frequencies be at least ___ to produce valid results.

5

In conducting a chi-square goodness-of-fit test, what are the two hypotheses you must state?

Null and Alternative Hypotheses

• Null hypothesis states fit.

• Alternative hypothesis states no fit.

• Key for chi-square testing.

True or False: Chi-square tests can be applied to numerical data.

False. Chi-square tests are designed specifically for categorical data, not numerical data.

Fill in the blank: The formula for the chi-square statistic is χ² = ___, where O represents observed frequency and E represents expected frequency.

Σ((O - E)² / E)

Riddle: I measure how far observed frequencies differ from what you expect. What am I?

The chi-square statistic.

What does a small p-value (typically ≤ 0.05) indicate in the context of chi-square tests?

A small p-value indicates strong evidence against the null hypothesis, leading to its rejection.

What distinguishes the chi-square test of independence from the chi-square test for homogeneity?

Chi-square tests have distinct purposes.

• Independence tests variable association.

• Homogeneity checks distribution equality.

• Different contexts for usage exist.