Seven Ways To Increase Power Without Increasing N

Abstract

Many readers of this monograph may wonder why a chapter on statistical power was included. After all, by now the issue of statistical power is in many respects mundane. Everyone knows that statistical power is a central research consideration, and certainly most National Institute on Drug Abuse grantees or prospective grantees understand the importance of including a power analysis in research proposals.However, there is ample evidence that, in practice, prevention researchers are not paying sufficient attention to statistical power. If they were, the findings observed by Hansen (1992) in a recent review of the prevention literature would not have emerged. Hansen (1992) examined statistical power based on 46 cohorts followed longitudinally, using nonparametric assumptions given the subjects' age at posttest and the numbers of subjects. Results of this analysis indicated that, in order for a study to attain 80-percent power for detecting differences between treatment and control groups, the difference between groups at posttest would need to be at least 8 percent (in the best studies) and as much as 16 percent (in the weakest studies). In order for a study to attain 80-percent power for detecting group differences in pre-post change, 22 of the 46 cohorts would have needed relative pre-post reductions of greater than 100 percent. Thirty-three of the 46 cohorts had less than 50-percent power to detect a 50-percent relative reduction in substance use. These results are consistent with other review findings (e.g., Lipsey 1990) that have shown a similar lack of power in a broad range of research topics. Thus, it seems that, although researchers are aware of the importance of statistical power (particularly of the necessity for calculating it when proposing 184

Planning for Long-Term Follow-Up: Strategies Learned from Longitudinal Studies

“…Maintaining a high proportion of the original sample size is essential for maintaining statistical power to detect hypothesized relationships among variables of interest (Hansen & Collins, 1994). Furthermore, Hansen, Tobler, and Graham established that a target retention rate of 87% for studies of three or more years’ duration is required to minimize threats to internal and external validity (Hansen, Tobler, & Graham, 1990).…”

Maximizing the Yield of Small Samples in Prevention Research: A Review of General Strategies and Best Practices

“…Hansen and Collins (1994) proposed strategies for increasing the statistical power of a study without increasing the sample size. In reality, two of their proposed strategies refer specifically to strategies for maximizing sample size.…”

“…The remaining strategies suggested by Hansen and Collins (1994) concern increasing the size of the observed effect (i.e., difference between groups). Given the standard equation for computing effect size, which is a ratio of the effect of interest (e.g., difference between means, regression coefficient) and the population variance (expressed as standard deviation), there are two categories of approaches that, given a fixed sample size, would increase statistical power by increasing effect size: (1) increase the effect of interest, (2) decrease the population variance.…”

“…Such variance arises from two sources: sample heterogeneity and unreliability of measurement (Hansen & Collins, 1994). The consideration of sample heterogeneity is one of balance—maintaining the representativeness of the sample while minimizing within-group variance that contributes to inflated test statistics.…”

Statistical Power in Quantitative Diffusion MRI of Tumor Response

“…The general importance of statistical power is an old topic, yet studies continue to be performed across disciplines that do not adequately consider effect size, sample size, and degree of variability when designing experiments and performing analyses 16 . Prominent barriers to this end include an unknown variability of the data to be collected and uncertainty in the expected magnitude of an effect.…”