How do you calculate Chi Square?

How do you calculate Chi Square?

• A. Sum of (observed-expected)^2/expected
• B. Sum of (observed-expected)^2/observed
• C. Product of observed and expected
• D. Sum of observed squared divided by observed

Answer: (A)

The calculation hinges on comparing what you actually observe in each category to what you’d expect under the null hypothesis, and then turning those deviations into a single standardized measure. For each category, you take the difference between observed and expected, square it to emphasize larger gaps, and divide by the expected count. Summing those values across all categories gives the chi-square statistic: sum of (observed − expected)² divided by expected. Using the expected count in the denominator standardizes the deviations by the variability you’d expect under the null, so categories with large expected counts don’t dominate merely because they’re big, while smaller expected counts are appropriately weighted more. The other forms don’t capture this proper standardization or the squared residual structure, so they don’t reflect the same distribution under the null.

The calculation hinges on comparing what you actually observe in each category to what you’d expect under the null hypothesis, and then turning those deviations into a single standardized measure. For each category, you take the difference between observed and expected, square it to emphasize larger gaps, and divide by the expected count. Summing those values across all categories gives the chi-square statistic: sum of (observed − expected)² divided by expected. Using the expected count in the denominator standardizes the deviations by the variability you’d expect under the null, so categories with large expected counts don’t dominate merely because they’re big, while smaller expected counts are appropriately weighted more. The other forms don’t capture this proper standardization or the squared residual structure, so they don’t reflect the same distribution under the null.