Power Analysis for MANCOVA: Examples for
Dissertation Students & Researchers
This is the report you want to include in your discussion section. I would mention that you wanted to detect a large effect, as the power is largest for your analysis with a large effect. However, the large effect size (f²=.35) is not observed very often in research. As such, I've also enclosed the power analysis for a medium effect size (f²=.15) for both MANCOVA models you tested. The study was definitely underpowered and only achieved 9% power for a medium effect size and 17% power for a large effect size.
Model One
Medium Effect Size
The study was underpowered. More specifically, MANCOVA, covarying for age, with one between-subjects factor (fitness level) was used to analyze the resting pulmonary function variables which included FVC, FEV1, FEV1/FVC, and MVV. A medium effect size (f²=.15), and a total sample of 45 (15 in each fitness level group) provided 9% power (power =.0947) to detect difference at the 0.05 significance level (F (10, 80) =1.9512).
Large Effect Size
The study was underpowered. More specifically, MANCOVA, covarying for age, with one between-subjects factor (fitness level) was used to analyze the resting pulmonary function variables which included FVC, FEV1, FEV1/FVC, and MVV. A large effect size (f²=.35), and a total sample of 45 (15 in each fitness level group) provided 17% power (power = .1721) to detect difference at the 0.05 significance level (F (10, 80) =1.9512).
Model Two
Medium Effect Size
A MANCOVA, covarying for age, with one between-subjects factor (fitness level) was used to analyze the dynamic pulmonary function variables from the GXT which included peak VO2, VEmax, VD/VT, DI, VEmax/VCO2, and RR/VEmax. A medium effect size (f²=.15), and a total sample of 45 (15 in each fitness level group) provided 9% power (power=.0945) to detect difference at the 0.05 significance level (F (10, 78)=1.9544).
Large Effect Size
A MANCOVA, covarying for age, with one between-subjects factor (fitness level) was used to analyze the dynamic pulmonary function variables from the GXT which included peak VO2, VEmax, VD/VT, DI, Emax/VCO2, and RR/VEmax. A medium effect size (f²=.35), and a total sample of 45 (15 in each fitness level group) provided .17% power (power=.1717) to detect difference at the 0.05 significance level (F (10, 78)=1.9544).
Reference:
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates.
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