A commonly heard rule of thumb for choosing sample size is “10 participants per cell of the design.” The purpose of this exercise is to determine the magnitude of statistical power that results from following this rule of thumb for various designs. We assume throughout that we are interested in the power associated with a large effect size, as defined by Cohen (1977). It can be shown that the value of 0 for a large effect size in a one-way design is given by where n is the number of participants per group. For factorial designs, this formula generalizes to or, equivalently Where are the numerator and denominator degrees of freedom, respectively, for the F test. Use the Pearson-Hartley power charts to calculate the power of detecting a large effect for each of the following designs, assuming 10 participants per cell. a. Omnibus effect in a one-way design with two groups b. Omnibus effect in a one-way design with five groups c. Main effect in a 2 x 2 design d. Interaction effect in a 2 x 2 design e. Main effect in a 3 x 3 design f. Interaction effect in a 3 x 3 design g. It is often recommended that the power of a test to be performed be at least 8. For which of the above effects is the power this high for detecting a large effect with 10 participants per cell? h. In light of your answers to Parts a through g, what is your reaction to the general utility of the “10 participants per cell” rule?
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