Although some sample size programs are able to estimate unequal sizes, most calculate sample size assuming that the two groups are of equal size. The program in the Unequal Sample Size Adjustments Program Page uses the sample size for equal size groups to estimate sample sizes for unequal size groups that have the same power. Two calculations are offered.

• Adjustment of sample sizes by ratio. This converts sample size per group of two equal size groups to two samples sizes that has a nominated ratio, retaining the same statistical power. The data required are the original sample size (assuming equal size groups), and the nominated ratio.

  An example We wish to compare the prevalence of depression between male and female residents in retirement communities. We anticipate that about 10% of men (proportion = 0.1) and 5% (proportion = 0.05) of women in those communities may be depressed. Using power of 0.8 and α of 0.05, we found from the program in the Sample Size for Comparison of Two Proportions Program Page that we need 435 cases of each sex for the study.

  Unfortunately, in retirement communities, women outnumbers men by 2 to 1, and we wanted the same sex ratio in our study. Using the program in Unequal Sample Size Adjustments Program Page and adjust the original sample size of 435 each group to a ratio of 2, we estimate that the sample sizes required to achieve the same statistical power are 653 women and 327 men.

• Adjustment by the sample size in one group This converts sample size per group of two equal size groups to two samples sizes with a nominated number in one group, retaining the original statistical power. The data required are the original sample size per group, and the nominated sample size for one of the groups. Please note : that the nominated sample size cannot be <= half of the original samle size, or an error in calculation will result.

  An example We wish to study the cost of delivering babies with breech presentation, comparing vaginal delivery and Caesarean section. From experience, we estimate the standard deviation of costs for delivery to be $1000, and we would conclude that costs are different if they differ more than $500 (effect size = diff / sd = 0.5). Using power of 0.8 and α of 0.05, we found the program in the Sample Size for Unpaired Differences Program Page that we need 64 cases for each of the two methods of delivery.

  Unfortunately, most of the babies with breech were delivered by Caesarean section, and we can only find 40 records of vaginal delivery. We therefore need to know how many records of Caesarean Section we will need to be able to compare with the same statistical power as the original model hat assumed equal size groups. Using the program in Unequal Sample Size Adjustments Program Page and adjust the original sample size of 64 each group to 40 for vaginal delivery, we estimated that we will require 160 records of Caesarean Section to enable a comparison with the same power as 64 per group.

Altman, DG. Practical Statistics for Medical Research London, UK; Chapman & Hall; 1991.

Altman, DG. How large a sample? In: Gore SM, Altman DG. , editor. Statistics in Practice. London, UK: British Medical Association; 1982.

Whitley E and Ball J (2002) Statistics review 4: Sample size calculations Crit Care. 6(4): 335-341.

Gerald van Belle (2002). Statistical Rules of Thumb. John Wiley and Sons, New York. ISBN 0-471-40227-3. p. 45-46