G*Power: One-Way Independent Samples ANOVA



G*Power: 3-Way Factorial Independent Samples ANOVAThe analysis is done pretty much the same as it is with a two-way ANOVA. Suppose we are planning research for which an A x B x C, 2 x 2 x 3 ANOVA would be appropriate. We want to have enough data to have 80% power for a medium sized effect. The omnibus analysis will include seven F tests – three with one df each (A, B, and A x B) and four with two df each (C, A x C, B x C, and A x B x C). We plan on having sample size constant across cells.For the tests of A, B, and A x B:F tests - ANOVA: Fixed effects, special, main effects and interactionsAnalysis:A priori: Compute required sample size Input:Effect size f=0.25α err prob=0.05Power (1-β err prob)=.80Numerator df=1Number of groups=12Output:Noncentrality parameter λ=8.0000000Critical F=3.9228794Denominator df=116Total sample size=128Actual power=0.8009381Remember that Cohen suggested .25 as the value of f for a medium-sized effect. 1. The number of groups here is the number of cells in the factorial design, 2 x 2 x 3 = 12. When you click “Calculate” you see that you need a total N of 128. That works out to 10.67 cases per cell, so bump the N up to 11(12) = 132.For the effects with 2 df:F tests - ANOVA: Fixed effects, special, main effects and interactionsAnalysis:A priori: Compute required sample size Input:Effect size f=0.25α err prob=0.05Power (1-β err prob)=.80Numerator df=2Number of groups=12Output:Noncentrality parameter λ=9.8750000Critical F=3.0580504Denominator df=146Total sample size=158Actual power=0.8016972That works out to 13.2 cases per cell, so bump the N up to 14(12) = 168.Suppose that you anticipate obtaining a significant triple interaction and following that with analysis of the A x B simple interactions at each level of C. Playing it conservative by using individual error terms, you will then need at each level of CF tests - ANOVA: Fixed effects, special, main effects and interactionsAnalysis:A priori: Compute required sample size Input:Effect size f=0.25α err prob=0.05Power (1-β err prob)=.80Numerator df=1Number of groups=4Output:Noncentrality parameter λ=8.0000000Critical F=3.9175498Denominator df=124Total sample size=128Actual power=0.8013621That is 128/4 = 32 cases for each A x B cell. Since there are three levels of C, the total sample size needed is now 3 x 128 = 384.Suppose the A x B interaction were to be significant at one or more of the levels of C. You likely would then test the simple, simple, main effects of A at each level of B (or vice versa). For each such comparison (which would involved only two cells):F tests - ANOVA: Fixed effects, special, main effects and interactionsAnalysis:A priori: Compute required sample size Input:Effect size f=0.25α err prob=0.05Power (1-β err prob)=.80Numerator df=1Number of groups=2Output:Noncentrality parameter λ=8.0000000Critical F=3.9163246Denominator df=126Total sample size=128Actual power=0.8014596You need 128 scores, 64 per cell. Since we have a total of 12 cells, that works out to 768 cases. You might end up deciding that you can get by with having less power for detecting simple effects than for detecting effects in the omnibus analysis.Suppose you ended up with 20 scores per cell, total N = 20(12) = 240. How much power would you have for detecting medium-sized effects in the omnibus analysis?For the one df effects:F tests - ANOVA: Fixed effects, special, main effects and interactionsAnalysis:Post hoc: Compute achieved power Input:Effect size f=0.25α err prob=0.05Total sample size=240Numerator df=1Number of groups=12Output:Noncentrality parameter λ=15.0000000Critical F=3.8825676Denominator df=228Power (1-β err prob)=0.9710633For the two df effects:F tests - ANOVA: Fixed effects, special, main effects and interactionsAnalysis:Post hoc: Compute achieved power Input:Effect size f=0.25α err prob=0.05Total sample size=240Numerator df=2Number of groups=12Output:Noncentrality parameter λ=15.0000000Critical F=3.0354408Denominator df=228Power (1-β err prob)=0.9411531How much power would you have if you got down to the level of comparing one cell with one other cell:F tests - ANOVA: Fixed effects, special, main effects and interactionsAnalysis:Post hoc: Compute achieved power Input:Effect size f=0.25α err prob=0.05Total sample size=40Numerator df=1Number of groups=2Output:Noncentrality parameter λ=2.5000000Critical F=4.0981717Denominator df=38Power (1-β err prob)=0.3379390LinksKarl Wuensch’s Statistics LessonsInternet Resources for Power AnalysisKarl L. WuenschDept. of PsychologyEast Carolina UniversityGreenville, NC USA ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download