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Sample Size Estimation: A Glimpse beyond Simple Formulas¹

¹ From the Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University, Central Radiology Viewing Area, Room 117, 600 N Wolfe St, Baltimore, MD 21287. Received February 21, 2003; revision requested April 10; revision received July 18; accepted July 21. Address correspondence to the author (e-mail: jeng@jhmi.edu).

View larger version (41K): [in a new window]   Figure 1. Study design characteristics that affect sample size and statistical power.

View larger version (19K): [in a new window]   Figure 2. Graph shows the relationship between sample size and the ratio of meaningful difference to SD for studies in which means are compared. The graph was created by using Equation (1) and illustrates the fact that sample size increases exponentially as the ratio decreases.

View larger version (61K): [in a new window]   Figure 3a. (a) Graph shows relationship between sample size and proportions being compared in a study involving comparison of proportions. Sample size increases dramatically as the meaningful difference decreases. Sample size also increases if the proportions being compared (ie, the mean of the two proportions) are near 0.50. (b) Extension of the circled corner of the graph in a, with x and y axes magnified; this corner corresponds to a region that is of particular interest to the design of clinical investigations.

View larger version (74K): [in a new window]   Figure 3b. (a) Graph shows relationship between sample size and proportions being compared in a study involving comparison of proportions. Sample size increases dramatically as the meaningful difference decreases. Sample size also increases if the proportions being compared (ie, the mean of the two proportions) are near 0.50. (b) Extension of the circled corner of the graph in a, with x and y axes magnified; this corner corresponds to a region that is of particular interest to the design of clinical investigations.

View larger version (53K): [in a new window]   Figure 4. Graph shows the relationship between sample size, smallest meaningful difference, and number of readers in an ROC study in which Az is used as the index of accuracy. Sample sizes were calculated by using the method described in the Appendix. The values used for all variables except J and are the same as those in the example in Table A1.