An F-test compares two variances by calculating their ratio and testing whether that ratio could plausibly be due to chance. Begin with a null hypothesis that the variances are equal, then use the returned p-value to decide whether to reject it. section 13.0 section 20.2
A practical F-test workflow is:
- Calculate or inspect the standard deviations of the two data series; standard deviation is the square root of variance. section 13.8.3
- Run base R's var.test() with the two numeric vectors. section 13.8.3
- Compare the p-value with a predefined threshold, commonly 0.05: reject equal variances below the threshold and otherwise fail to reject the null hypothesis. section 20.2
- Use the variance result to choose an appropriate effect-size interpretation when methods make different assumptions about standard deviations. section 13.8.3
Comparing win-share inequality
For Gini-index values in ws_giniX and ws_giniY, the standard deviations are 0.07 and 0.04. Run `var.test(ws_giniX$gini_index, ws_giniY$gini_index)`. The result is F = 2.6659 with p = 0.003528, so reject equal variances at the 5% threshold. Reversing the effect-size arguments then produces similar Cohen's d, Hedges' g, and Glass's delta conclusions: a small effect. section 13.8.3
var.test(ws_giniX$gini_index, ws_giniY$gini_index) ## ## F test to compare two variances ## ## data: ws_giniX$gini_index and ws_giniY$gini_index ## F = 2.6659, num df = 758, denom df = 26, p-value = 0.003528 ## alternative hypothesis: true ratio of variances is not equal to 1 ## 95 percent confidence interval: ## 1.410118 4.349496 ## sample estimates: ## ratio of variances ## 2.665942
Inspect the complete var.test() output, including the F statistic, degrees of freedom, p-value, confidence interval, and variance ratio. section 13.8.3
