In a chi-square calculation, which quantities are compared to compute the statistic?

In a chi-square calculation, which quantities are compared to compute the statistic?

• A. Observed frequencies and expected frequencies
• B. Means and medians
• C. Variances and standard deviations
• D. Ratios and proportions

Answer: (A)

The key idea here is that the chi-square statistic assesses how well the data fit a theoretical distribution by looking at counts in each category. It compares what you actually observe in each category (observed frequencies) with what you would expect if the null hypothesis were true (expected frequencies). The calculation then sums the squared differences between these two quantities, scaled by the expected counts, across all categories. Means and medians describe central tendency, variances and standard deviations describe spread, and ratios or proportions describe relative sizes, but none of these are the quantities used to form the chi-square statistic. Observed versus expected frequencies are the core pair used to test goodness of fit or independence in this test.

The key idea here is that the chi-square statistic assesses how well the data fit a theoretical distribution by looking at counts in each category. It compares what you actually observe in each category (observed frequencies) with what you would expect if the null hypothesis were true (expected frequencies). The calculation then sums the squared differences between these two quantities, scaled by the expected counts, across all categories. Means and medians describe central tendency, variances and standard deviations describe spread, and ratios or proportions describe relative sizes, but none of these are the quantities used to form the chi-square statistic. Observed versus expected frequencies are the core pair used to test goodness of fit or independence in this test.