“ Sample Size and Power, When is More, Less?"
All things being equal, increasing the sample size for an analysis will increase the power. However, when things are not equal, specifically if the effect size for the additional observations is low, power may not increase, and in some circumstances it may even shrink. An equation is derived which will yield the breakeven point when the two characteristics of a new group of potential additional observations are considered. As long as the effect size for the additional group is at least 50% of the effect size for the starting group, adding observations will not decrease power. For a sample size ratio of 1:1, the breakeven effect size is 41.4% of that for the starting group. For a drug trial of three equally spaced doses, if there is a linear dose response relationship, when comparing an average of doses to an untreated control group, averaging the two highest doses, but omitting the lowest, will give the best power.
George Divine, Ph.D. is a Senior Research Biostatistician in the Department of Public Health Sciences (formerly Biostatistics and Research Epidemiology) at the Henry Ford Health System (HFHS). He is past head for the PHS Division of Biostatistics. He has been involved in a range of research projects from Stroke to Cancer and including Health Services Research. He is the current head of the WSU/HFHS CTSA(“MACTS”) Workgroup for Biostatistics. His research interests include multiple comparisons and sample size calculation methods.