Power Analysis using GPower 3.1

Transcription

1 Power Analysis using GPower 3.1 a one-day hands-on practice workshop (session 1) Dr. John Xie Statistics Support Officer, Quantitative Consulting Unit, Research Office, Charles Sturt University, NSW, Australia gxie@csu.edu.au

2 Topics to cover in this session Basic concepts of Statistical Power Analysis and GPower3.1 The simplest possible case for determining sample size A first touch with Gpower3.1 t-test: means difference from constant (one group or matched pairs) t-test: means difference between two independent means (two groups) t-test: linear regression (size of slope, one group) F test: fixed effects ANOVA one way F test: multiple regression omnibus (deviation of R² from zero), fixed model 14/12/2017 2

3 Primary reference: G*Power 3.1 manual (March 1, 2017) Basic concepts of Statistical Power Analysis and GPower3.1 (manual pages 2-7) t-test: means difference from constant (one group or matched pairs) (manual pages 47-48; pages 45-46) t-test: means difference between two independent means (two groups) (manual page 49) t-test: linear regression (size of slope, one group) (manual pages 31-32) F test: fixed effects ANOVA one way (manual pages 24-25) F test: multiple regression omnibus (deviation of R² from zero), fixed model (manual pages 33-35) 14/12/2017 3

4 Basic concepts of power analysis Type I and Type II errors Disease Status Screen Status Disease No Disease Test + Type I error Test - Type II error 14/12/2017 4

5 Basic concepts of power analysis Type I Error (α): probability of rejecting the null hypothesis when it is true Type II Error (β): probability of not rejecting the null hypothesis when it is false statistical power = 1-β (or simply power ). Therefore, power is defined by the probability of rejecting the null hypothesis when it is false. The major objective of power analysis is to help researchers to determine how big a sample size should be selected for a designed experiment. Alternatively, to determine what is the statistical power for a statistical model with a given data set (i.e., post-hoc analysis). 14/12/2017 5

6 Basic concepts of power analysis Sample size calculation involves a few components. They are: Type I error α and Type II error β; Variance / standard deviation under the null and alternative hypotheses (σ² or σ in one sample case; σ0 and σ1 under H0 and H1, respectively, in two sample case); Sample size N (N = N1 + N2, if it is the two sample case); The effect size Effect size: a standardized measure which represents the minimal difference between H0 and H1 which we would like to be able to detect given the specified α and β levels. 14/12/2017 6

7 G*Power was created by faculty at the Institute for Experimental Psychology in Dusseldorf, Germany. It offers a wide variety of calculations along with graphics and protocol statement outputs on statistical power analysis. The primary website for downloading G*Power software and access to resources related to G*Power is Best of all, it is free! 14/12/2017 7

8 An example implemented in GPower3.1 to show the basic concepts of power analysis: A prior analysis (The procedure: Tests -> Means -> One group: Difference from constant) 14/12/2017 8

9 An example implemented in GPower3.1 to show the basic concepts of power analysis: Post-hoc analysis (The procedure: Tests -> Means -> One group: Difference from constant) 14/12/2017 9

10 An example implemented in GPower3.1 to show the basic concepts of power analysis: Post-hoc analysis x-y plot for a range of values (The procedure: Tests -> Means -> One group: Difference from constant) 14/12/

11 References: G*Power 3.1 manual (March 1, 2017) can be downloaded free from Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf (accessed 6 October 2017) F. Faul, E. Erdfelder, A.Lang, and A. Buchner. G*Power 3: A flexible statistical power analysis program for the social, behavioural, and bioedical sciences, Behavior Research Methods, 2007, 39(2), Chapter 2 of Statistical Rules of Thumb (1 st Edition, 2002 or 2 nd Edition 2008) by Gerald van Belle. For statistical models/statistical analysis in general, you may refer to The R Book (2 nd Edition, 2013) by Michael J. Crawley. 14/12/

12 End of Session 1 Thank You John Xie contact details: gxie@csu.edu.au Phone: /12/