Power Analysis Example PDF

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Power Analysis: SPSS and G*Power Procedures and Results This file will cover how to determine statistical power using SPSS and G*Power (a power analysis software program available free online; there is a link to it in Vista under the “Web Links” tab). We will again be using the “hourlywagedata.sav” which includes data from nurses. In this file, there are four variables; we will be focusing on two: “agerange” and “hourwage”. Unfortunately, only post-hoc power can be calculate using SPSS, but it is fairly easy to do so. Basically, you need to follow the procedures for running a one-way Analysis of Variance (as was done in Unit 2), and select “Observed power” in the “Options” window:

To see what the statistical power is, look at the table labeled, “Tests of Between Subjects Effects” (a few columns were eliminated for space concerns): Tests of Between-Subjects Effects Dependent Variable:Hourly Salary Source Corrected Model Intercept agerange Error Total Corrected Total

Type III Sum of Squares 256.880a 290272.921 256.880 14260.924 408679.974 14517.804

df 2 1 2 967 970 969

Mean Square F 128.440 8.709 290272.921 19682.729 128.440 8.709 14.748

Sig. .000 .000 .000

Observed Powerb .970 1.000 .970

a. R Squared = .018 (Adjusted R Squared = .016) b. Computed using alpha =

As you can see, the observed power was .970, which is well above the standard value of .80. However, this example is merely illustrative; because the F test was statistically significant, power would not be a concern here. Using G*Power, you can conduct both a priori and post-hoc analyses (this is likely true of other statistical power software programs as well). To do so, you must first select the type of analysis you wish to conduct. We will conduct an analysis to determine what our sample size should be in order to obtain a power level of .80 (In this data set, we already have a large enough sample to obtain a power of .970, so we are just going to see how much smaller our sample could be in order to obtain adequate statistical power).

So, after opening G*Power, select “F tests”:

Then, select “ANOVA: Fixed effects, omnibus, one-way”:

Finally, select “A priori: Compute required sample size – given , power, and effect size”:

After selecting the appropriate analysis, you can now enter data. We’ll use an  of . 05, statistical power of .80, and 3 groups. You can calculate the f effect size value by selecting “Determine”. When you do so, the following window will open:

From here, we can determine effect size by entering the means and sample sizes, which can be found in the SPSS output: Descriptive Statistics Dependent Variable:Hourly Salary Age Range Mean Std. Deviation 18-30 19.0438 3.76446 31-45 20.1828 3.74823 46-65 20.6869 4.05268 Total 20.1582 3.87069

N 144 548 278 970

First, you want to set the number of groups to 3. Then, for the standard deviation within each group, we use a value of 3.84 (this is the square root of the Mean Square Error from the SPSS ANOVA table, which is equal to 14.748). After the means are entered, you can select “Calculate and transfer to the main window”. You’ll see that our f effect size is approximately 0.135. So, after we input the appropriate values and select “Calculate”, we find out that our total sample size should be 537.

So, in order to obtain a statistical power level of .80, we would need a total of 537 participants, or 179 per group. This is quite a bit smaller than the original sample size of 970. So, we could obtain adequate sample size with a much smaller sample....