AP Statistics Flashcards: Carrying Out a Chi-Square Test for Homogeneity or Independence
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
How are the degrees of freedom (df) calculated for a chi-square test for homogeneity or independence?
The degrees of freedom are calculated using the formula df = (number of rows - 1) multiplied by (number of columns - 1).
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How are the degrees of freedom (df) calculated for a chi-square test for homogeneity or independence?
The degrees of freedom are calculated using the formula df = (number of rows - 1) multiplied by (number of columns - 1).
What is the purpose of interpreting the p-value from a chi-square test?
Interpreting the p-value helps determine the statistical significance of the test results and the strength of the evidence against the null hypothesis.
What is the relationship between the chi-square test statistic and the p-value?
The p-value is the probability of observing a chi-square test statistic as large or larger than the one calculated, assuming H0 is true.
What is the primary objective when performing calculations for a chi-square test for homogeneity or independence?
The primary objective is to calculate the appropriate chi-square statistic, which measures the discrepancy between observed and expected counts.
If a chi-square test results in a p-value of 0.15 with an alpha of 0.10, what is the appropriate decision?
Since the p-value (0.15) is greater than alpha (0.10), the decision is to fail to reject the null hypothesis (H0).
What does the p-value represent in relation to the chi-square distribution for a two-way table test?
For a two-way table test, the p-value is the proportion of the chi-square distribution that is equal to or larger than the calculated test statistic.
What is the basis for making a decision to reject or fail to reject the null hypothesis (H0)?
The decision to reject or fail to reject H0 is based on a comparison between the calculated p-value and the chosen significance level (alpha).
What is the formula for the chi-square test statistic?
The chi-square test statistic is calculated as the sum of (Observed - Expected)^2 / Expected for all cells in the table.
What action follows the calculation of the chi-square statistic?
After calculating the statistic, the next step is to determine the p-value for the chi-square test for independence or homogeneity.
If a chi-square test yields a p-value of 0.02 and the significance level (alpha) is 0.05, what conclusion is made?
Because the p-value (0.02) is less than alpha (0.05), the decision is to reject the null hypothesis (H0).
Define the p-value in the context of a chi-square test.
The p-value is the probability of obtaining a test statistic as or more extreme than the observed value, assuming the null hypothesis (H0) is true.
How is the p-value for a chi-square test for independence or homogeneity typically found?
The p-value for a chi-square test is found by using a chi-square distribution table or statistical technology.
What is the final step after interpreting the results of a chi-square test?
The final step is to justify a claim about the population based on the results of the chi-square test for homogeneity or independence.
Chi-Square Test Statistic
A measure of how far the observed counts in a two-way table are from the expected counts, calculated as the sum of (O-E)^2/E.