Role of effect size variance in PrecisionThe third element determining precision is the dispersion of the effect size index. For ttests, dispersion is indexed by the standard deviation of the group means. If we will be reporting precision using the metric of the original scores, then precision will vary as a function of the SD. (If we will be reporting precision using a standard index, then the SD is assumed to be 1.0 and so the SD of the original metric is irrelevant.) For tests of proportions the variance of the index is a function of the proportions. Variance is highest for proportions near .50 and lower for proportions near 0.0 or 1.0. As a practical matter, variance is fairly stable until proportions fall below .10 or above .90). For tests of correlations the variance of the index is a function of the correlation. Variance is highest when the correlation is zero. Role of effect size in PrecisionEffect size, which is a primary factor in computation of power, has little (if any) impact in determining precision. In the running example we would report a 20 point effect with a 95% confidence interval of plus/minus some 13 points. A 30 point effect would similarly be reported with a 95% confidence interval of plus/minus some 13 points. While effect size plays no direct role in precision, it may be related to precision indirectly. Specifically, for procedures that work with mean differences, the effect size is a function of the mean difference and also the SD within groups. The former has no impact on precision; the latter affects both effect size and precision (a smaller SD yields higher power and better precision in the raw metric). For procedures that work with proportions or correlations the absolute value of the proportion or correlation affects the index's variance, which in turn may have an impact on precision.

Home · What's
Power Analysis? · Precision
Analysis · In
Context · Effect Size 
