Sample Size and Power Calculations

One-Way ANOVA

When you are planning to analyze data from more than two groups with a one-way ANOVA, you need to calculate your sample size and power accordingly. These computations are available, prospectively, for use in the planning stages of the study, using the Sample Size task. Retrospective calculations are available, for use in the analysis stage, from the One-Way ANOVA task. This section discusses the prospective computations available in the Analyst Application, which assume equally sized groups.

You must supply two quantities in order to produce these computations: the corrected sum of squares of means (CSS) and the standard deviation. CSS is calculated as

$CSS = \sum_{g=1}^G (\mu_g - \mu_.)^2$

where

$\mu_g$ = mean of the gth group

$\mu_.$ = overall mean

You must enter one or more values for the standard deviation, which in this case is the square root of the Mean Squared Error (MSE).

Requesting Power Computations for ANOVA

The following is an example of calculating the power for a one-way ANOVA with specified values of sample size. Suppose that you are comparing three groups, the overall mean is 5.5, and the group means are 4.5, 5.5, and 6.5. Therefore, the corrected sum of squares of means (CSS) is

(4.5 - 5.5)² + (5.5 - 5.5)² + (6.5 - 5.5)² = 2

The standard deviation is the square root of the MSE, which is 1.4142. You are interested in studying sample sizes that range from 6 to 20.

To perform these computations, select

Statistics

Sample Size

One-Way ANOVA ...

Figure 12.13 displays the resulting dialog. For this analysis, you need to enter the number of treatments, or factor levels, the CSS of means, the standard deviation, and the alpha level.

Figure 12.13: Sample Size Dialog for One-Way ANOVA

To produce power computations for the preceding problem, follow these steps:

Select Power.
Enter 3 for # of treatments:
Enter 2 for CSS of means:
Enter 1.4142 for Standard deviation:
Enter 0.05 for Alpha:
Enter 6, 20, and 1 for the fields N per group:, for From:, To:, and By:, respectively.
Click OK to perform the analysis.

Figure 12.14 displays the completed dialog.

Figure 12.14: Sample Size Dialog for One-Way ANOVA

Requested are power computations for sample sizes ranging from 6 to 20.

Figure 12.15: Results for Power Computations for One-Way ANOVA

The results are displayed in Figure 12.15. Note that, to achieve a minimum of 80% power, 11 units per group would be needed.

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