Seven ways to increase power without increasing N.
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 research), they somehow are failing to end up with adequate power in their completed studies. This chapter argues that the failure of many prevention studies to maintain adequate statistical power is due to an overemphasis on sample size (N) as the only, or even the best, way to increase statistical power. It is easy to see how this overemphasis has come about. Sample size is easy to manipulate, has the advantage of being related to power in a straight-forward way, and usually is under the direct control of the researcher, except for limitations imposed by finances or subject availability. Another option for increasing power is to increase the alpha used for hypothesis-testing but, as very few researchers seriously consider significance levels much larger than the traditional .05, this strategy seldom is used. Of course, sample size is important, and the authors of this chapter are not recommending that researchers cease choosing sample sizes carefully. Rather, they argue that researchers should not confine themselves to increasing N to enhance power. It is important to take additional measures to maintain and improve power over and above making sure the initial sample size is sufficient. The authors recommend two general strategies. One strategy involves attempting to maintain the effective initial sample size so that power is not lost needlessly. The other strategy is to take measures to maximize the third factor that determines statistical power: effect size.