G*Power 3.1 manual

1 G * manualJanuary 21, 2021 This manual is not yet complete. We will be adding help on more tests in the future. If you cannot find help for your testin this version of the manual , then please check the G*Power website to see if a more up-to-date version of the manualhas been made Introduction22 The G * power calculator73 Exact: Correlation - Difference from constant (onesample case)94 Exact: Proportion - difference from constant (onesample case)115 Exact: Proportion - inequality, two dependentgroups (McNemar)146 Exact: Proportions - inequality of two independentgroups (Fisher s exact-test)177 Exact test: Multiple Regression - random model188 Exact: Proportion - sign test229 Exact: Generic binomial test2310 F test: Fixed effects ANOVA - one way2411 F test: Fixed effects ANOVA - special, main effectsand interactions2612 t test.

2 Linear Regression (size of slope, one group) 3113 F test: Multiple Regression - omnibus (deviation ofR2from zero), fixed model3314 F test: Multiple Regression - special (increase ofR2), fixed model3615 F test: Inequality of two Variances3916 t test: Correlation - point biserial model4017 t test: Linear Regression (two groups)4218 t test: Linear Regression (two groups)4519 t test: Means - difference between two dependentmeans (matched pairs)4820 t test: Means - difference from constant (one sam-ple case)5021 t test: Means - difference between two independentmeans (two groups)5222 Wilcoxon signed-rank test: Means - difference fromconstant (one sample case)5323 Wilcoxon signed-rank test: (matched pairs)5524 Wilcoxon-Mann-Whitney test of a difference be-tween two independent means5925 t test: Generic case6326 2test: Variance - difference from constant (onesample case)6427 z test: Correlation - inequality of two independentPearson r s6528 z test: Correlation - inequality of two dependentPearson r s6629 Z test: Multiple Logistic Regression7030 Z test: Poisson Regression7531 Z test: Tetrachoric Correlation80 References8411 IntroductionG * power (Fig.)

3 1 shows the main window of the program)covers statistical power analyses for many different statisti-cal tests of the Ftest, ttest, 2-test and ztest families and some exact * Powerprovides effect size calculators and graphicsoptions. G * Powersupports both a distribution-based anda design-based input mode. It contains also a calculator thatsupports many central and noncentral probability * Poweris free software and available for Mac OS Xand Windows XP/Vista/7 Types of analysisG * Poweroffers five different types of statistical poweranalysis:1. A priori (sample size N is computed as a function ofpower level 1 , significance level , and the to-be-detected population effect size)2. Compromise (both and 1 are computed as func-tions of effect size, N, and an error probability ratioq= / )3.

4 Criterion ( and the associated decision criterion arecomputed as a function of 1 , the effect size, and N)4. Post-hoc (1 is computed as a function of , the pop-ulation effect size, and N)5. Sensitivity (population effect size is computed as afunction of , 1 , and N) Program handlingPerform a power AnalysisUsing G * Powertypically in-volves the following three steps:1. Select the statistical test appropriate for your Choose one of the five types of power analysis available3. Provide the input parameters required for the analysisand click "Calculate".Plot parametersIn order to help you explore the param-eter space relevant to your power analysis, one parameter( , power (1 ), effect size, or sample size) can be plottedas a function of another Select the statistical test appropriate for your prob-lemIn Step 1, the statistical test is chosen using the distribution-based or the design-based approach to test selectionFirst selectthe family of the test statistic ( , exact,F ,t , 2, orz-test) using theTestfamily menu in the main window.

5 TheStatistical testmenu adapts accordingly, showing a list of alltests available for the test :For the two groupst-test, first select the test familybased on selectMeans: Difference between two independent means(two groups)option in theStatictical approach to the test selectionAlterna-tively, one might use the design-based approach. With theTestspull-down menu in the top row it is possible to select the parameter class the statistical test refers to ( ,correlations and regression coefficients, means, propor-tions, or variances), and the design of the study ( , number of groups, inde-pendent vs. dependent samples, etc.).The design-based approach has the advantage that test op-tions referring to the same parameter class ( , means) arelocated in close proximity, whereas they may be scatteredacross different distribution families in the distribution-based :In theTestsmenu, select Means, then select Two inde-pendent groups" to specify the two-groups t 1:The main window of G * Choose one of the five types of power analysisavailableIn Step 2, theType of power analysismenu in the center ofthe main window is used to choose the appropriate analysistype and the input and output parameters in the windowchange.

6 If you choose the first item from theType of poweranalysismenu the main window will display input and outputparameters appropriate for an a priori power analysis (for t testsfor independent groups if you followed the example providedin Step 1).In ana priori power analysis, sample sizeNis computedas a function of the required power level(1 ), the pre-specified significance level , and the population effect size to be detected with probabil-ity(1 ).In acriterion power analysis, (and the associated deci-sion criterion) is computed as a function of 1- , the effect size, and a given sample acompromise power analysisboth and 1 arecomputed as functions of the effect size, N, and an error probability ratioq= / .In apost-hoc power analysisthe power (1 )is com-puted as a function of3 , the population effect size parameter, and the sample size(s) used in a asensitivity power analysisthe critical population ef-fect size is computed as a function of , 1 , and Provide the input parameters required for the anal-ysisIn Step 3, you specify the power analysis input parametersin the lower left of the main.

7 An a priori power analysis for a two groupsttestwould require a decision between a one-tailed and a two-tailedtest, a specification of Cohen s (1988) effect size measuredun-derH1, the significance level , the required power (1 )ofthe test, and the preferred group size allocation ration2 us specify input parameters for a one-tailedttest, a medium effect size ofd=.5, =.05, (1 ) =.95, and an allocation ratio ofn2/n1=1 This would result in a total sample size of N = 176 ( , 88observation units in each group). The noncentrality parameter defining thetdistribution underH1, the decision criterionto be used ( , the critical value of thetstatistic), the degreesof freedom of thettest and the actual power value are that the actual power will often be slightly largerthan the pre-specified power in a priori power analyses.

8 Thereason is that non-integer sample sizes are always roundedup by G * Powerto obtain integer values consistent with apower level not less than the pre-specified Cohen s book on power analysis Cohen (1988)appears to be well known in the social and behavioral sci-ences, we made use of his effect size measures wheneverpossible. In addition, wherever available G * Powerpro-vides his definitions of " small" , " medium" , and " large" effects as " Tool tips" . The tool tips may be optained bymoving the cursor over the " effect size" input parameterfield (see below). However, note that these conventions mayhave different meanings for different :The tooltip showing Cohen s measures for the effectsizedused in the two groupsttestIf you are not familiar with Cohen s measures, if youthink they are inadequate for your test problem, or if youhave more detailed information about the size of the to-be-expected effect ( , the results of similar prior studies),then you may want to compute Cohen s measures frommore basic parameters.

9 In this case, click on the Determinebutton to the left the effect size input field. A drawer willopen next to the main window and provide access to aneffect size calculator tailored to the selected :For the two-groupt-test users can, for instance, spec-ify the means 1, 2and the common standard deviation ( = 1= 2) in the populations underlying the groups to cal-culate Cohen sd=| 1 2|/ . Clicking theCalculate andtransfer to main windowbutton copies the computed effectsize to the appropriate field in the main windowIn addition to the numerical output, G * Powerdisplaysthe central (H0) and the noncentral (H1) test statistic distri-butions along with the decision criterion and the associatederror probabilities in the upper part of the main supports understanding the effects of the input pa-rameters and is likely to be a useful visualization tool in4the teaching of, or the learning about, inferential distributions plot may be copied, saved, or printed byclicking the right mouse button inside the plot.

10 The menu appearing in the distribution plot for thet-test after right clicking into the input and output of each power calculation in aG* power session are automatically written to a protocolthat can be displayed by selecting the "Protocol of poweranalyses" tab in the main window. You can clear the proto-col, or to save, print, and copy the protocol in the same wayas the distributions plot.(Part of) the protocol Plotting of parametersG * Powerprovides to possibility to generate plots of oneof the parameters , effectsize, power and sample size, de-pending on a range of values of the remaining Plotwindow (see Fig. 2) is opened by click-ing theX-Y plot for a range of valuesbutton locatedin the lower right corner of the main window.