[Influence of group sample size on statistical power of tests for quantitative data with an imbalanced design]

To explore the relationship between sample size in the groups and statistical power of ANOVA and Kruskal-Wallis H test with an imbalanced design.

The sample sizes of the two tests were estimated by SAS program with given parameter settings, and Monte Carlo simulation was used to examine the changes in power when the total sample size varied or remained fixed.

In ANOVA, when the total sample size was fixed, increasing the sample size in the group with a larger mean square error improved the statistical power, but an excessively large difference in the sample sizes between groups led to reduced power. When the total sample size was not fixed, a larger mean square error in the group with increased sample size was associated with a greater increase of the statistical power. In Kruskal-wallis H test, when the total sample size was fixed, increasing the sample size in groups with large mean square errors increased the statistical power irrespective of the sample size difference between the groups; when total sample size was not fixed, a larger mean square error in the group with increased sample size resulted in an increased statistical power, and the increment was similar to that for a fixed total sample size.

The relationship between statistical power and sample size in groups is affected by the mean square error, and increasing the sample size in a group with a large mean square error increases the statistical power. In Kruskal-Wallis H test, increasing the sample size in a group with a large mean square error is more cost- effective than increasing the total sample size to improve the statistical power.