Power computations

Power computations can be performed in SPSS and R only using syntax. For SPSS users Chris Aberson has syntax for power calculations in his book. See reference below.

For a theoretical background and details of specialist software have a look at graduate seminar on power at the Graduate Statistics Programme October-December 2006. There is also a worked example using "Method 2" on a t-test. F. Y. Hsieh, Philip W. Lavori, Harvey J. Cohen and John R. Feussner (2003) An Overview of Variance Inflation Factors for Sample-Size Calculation Eval Health Prof 26 239-257 mentions various formulae for power calculations.

Note in some cases one needs to inflate the total sample size required if there is a natural clustering in the data such as patients being assessed by different exercise therapists. For example if there are b patients assessed by each exercise therapist with an intra-therapist correlation (ICC) then the design effect equals 1 + [(b-1)ICC]. The total sample needs to be multiplied by this design effect to give sample size adjusted for the clustering effect.

Sample sizes required for a given power

• One sample t-test

• Unpaired t-tests (equal group sizes)

• Unpaired t-tests (unequal group sizes)

• Paired t-tests

• Regression including One-Way ANOVA and ANCOVA

• Comparing a single proportion with a constant (sign test)

• Comparing two independent proportions

• Comparing three or more independent proportions

• Comparing two related proportions (McNemar test)

• Comparing two independent correlations from two different samples

• A term in any Anova (including repeated measures)

• A single predictor in a multiple binary logistic regression

• Survival analysis

Power required for given sample sizes

• One sample t-test

• Unpaired t-tests (equal group sizes)

• Unpaired t-tests (unequal group sizes)

• Paired t-tests

• Regression including One-Way ANOVA and ANCOVA

• Comparing a single proportion with a constant (sign test)

• Comparing two independent proportions

• Comparing three or more independent proportions

• Comparing two related proportions (McNemar test)

• Comparing two independent correlations from two different samples

• A term in any Anova (including repeated measures)

• A single predictor in a multiple binary logistic regression

• Survival analysis

Additional power freeware (including the popular G*POWER (currently version 3)) is available for download from here. Some examples using G*POWER 3 are in Howell (2013). There are also some power calculators mentioned in the Power Grad talks and here.

References

Aberson CL (2010) Applied power analysis for the behavioral sciences. Routledge:London. This book contains examples of computing effect sizes and power using SPSS.

Howell DC (2013) Statistical methods for psychology. 8th Edition. International Edition. Wadsworth:Belmont,CA.