In a chi-square test for independence, observed and expected frequencies must sum across to the same row totals and down to the same column totals.

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This is true because the chi-square test for independence calculates the difference between observed frequencies and expected frequencies for each cell in a contingency table. The expected frequencies are calculated under the assumption that the variables being tested are independent, and they are based on the row and column totals. Therefore, the observed and expected frequencies must add up to the same row and column totals for the test to be valid.

In a Chi-Square Test for Independence, Observed and Expected Frequencies