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On this page we publish questions and answers about how to perform power analyses with G*Power.
List of Questions |
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QuestionPlease can you give me some inforamtion on how I estimate "w" in the Chi-squared a-priori unit of your program. I am unable to find information my my texts as to how to estimate the "effect" in chi-squared analyses. Your help would be appreciated as I have a need to calculate the required number of samples in a chi-squared reasonably often. AnswerAgood source of information is Jacob Cohen's book "Statistical Power Analysis for the Behavioral Sciences". In a nutshell, w is the square root of w^2, and w^2 is the Pearson chi-square statistic applied to the H0 and H1 cell probabilities. Thus, if you have a discrete variable comprising m categories or a multivariate contingency table comprising m cells then where p0(i) and p1(i) denote the cell probabilities for the i-th cell according to H0 and H1, respectively. You can use the Calc "effect size" option of G*Power to calculate w from the H0 and H1 cell probabilities directly (first select "Chi-square test, then click the Calc "w" button).
QuestionI see in ANOVA that it expects equal group sizes, but doesn't exactly ask for the sizes directly. I happened on this because I had a four group example, and the sum of the n's was not divisable by 4. So G*Power told me that it would proceed using an average groups size. I said OK and then tried to find in the user guide exactly what went on inside. What sort of average did it use? The usual in this situation is a harmonic mean, but the documentation did not address the question. AnswerIn fact, G*Power uses the total N directly to compute the noncentrality parameter lambda for the noncentral F-distribution as Lambda = f2 * N This means that G*Power will always, that is, for any N, be able to compute a noncentrality parameter, but the underlying assumption is that the N is the sum of equally large n's. You can use the Calc "effect size" option of G*Power to calculate f easily for situations with unequal n's (first select "F-Test (ANOVA), then click the Calc "f" button). G*Power computes f as where pi = ni / N, ni = the number of subjects in group i, i = 1 ... k, N = the total number of subjects, mui = mean in group i, i = 1 ... k, mu = Grand Mean, and sigma2 = error variance within cells (constant across groups).
QuestionWhere do the suggested effect sizes come from? I know about .2, .5, and .8 from Cohen, but where are the others from? AnswerThe suggested effect sizes other than the effect size index d for t-tests on means also come from Cohen. In his 1977 book, for instance, you find the conventions for r on p. 79f
QuestionThere seems to be no way to do a matched pairs t test (or Z for that matter). If "Other t-tests" is the way to do one sample tests, then I could use that for matched pairs, but that still does not solve the problem of not having the a priori option. Or am I way off base here? AnswerIndeed, you need to use the "Other t-Tests" option. The guide to G*Power shows how to do matched-pairs t-tests as well as z-Tests and one-sample t-tests.
QuestionWhen trying to calculate the effect size one piece of information required is "Sigma". What does "Sigma" refer to? AnswerAssume that you want to compute the effect size index d for a t-test on means according to (see Cohen, 1977). Sigma in this formula refers to the standard deviation in the population (as opposed to the standard deviation in a sample). Likewise, "mu" refers to the population mean. In general, G*Power assumes that all parameters which you enter refer to the underlying population, not to a particular sample (however, parameters may be estimated from sample data).
QuestionI have a question about effect size calculation which might be related to statistics: The program only asks for one sigma (standard deviation assumed to be equal), but this is not always the case. I am not very good with statistics but I might suggest to have the option of unequal variance. AnswerIn general, G*Power requires sigma to be equal in all groups. For simple t-test on means, Cohen (1977, p. 44) suggests an adjustment procedure (see t-Test on Means, Unequal Sigma section). However, the power values computed by G*Power will only be approximations in this case. Computer simulation results on the appropriateness of this approximation are not yet available. As a general warning, you should keep in mind that G*Power results are valid if the statistical assumptions underlying the tests are met (e.g., normal distributions and homogeneous variances within cells). Some work has been done on the robustness of these tests, that is, the deviation of actual and nominal alpha error probablities when the distribution assumptions are not met. However, little is known on a test's power given a misspecified distribution model. Thus, G*Power results may or may not be useful approximations to the true power values in such cases.
QuestionIs there a simple way to print the whole manual without going from page to page? AnswerUnfortunately, there is no way to print the whole manual without going from one page to another. In order to facilitate the printing, however, here is a complete list of the manual’s pages. Simply click on the links and print the pages one by one:
QuestionIt would be great to see a 16 or 32-bit version for the Window/Intel world, especially to enhance the graphics. AnswerWe are currently planning G*Power 3.0. There will be two versions, one for the MacOS and one for the Windows/Intel world. However, we all are involved in several other projects, so it may take some time until version 3 will see the light of day.
QuestionI find the use of the term "Sigma (within each group)" a bit confusing in the "Calculate Effect Size" section. Is this the overall standard deviation? AnswerNo, the overall standard deviation of the data across groups depends on (a) the error variance within groups, (b) the variance of the group means (i.e., effect variance), and (c) possible sample size differences between groups. The overall standard deviation is irrelevant for power analyses. "Sigma (within each group)" is just the square root of the error variance within groups.
QuestionWhat if the variance is different between groups? AnswerNote that in t-tests and ANOVAs the error variances are assumed to be equal in all groups. Precise statements about alpha levels and statistical power are impossible if the error variances vary between groups simply because the H0- and H1-sampling distributions of F and t are unknown in such cases. However, the ANOVA is known to be relatively robust against violations of the underlying assumptions if the sample sizes do not differ between groups. Thus, you might get quite good approximations to the true power values if you refer to the pooled error variance in case of variance differences between groups. For more information, see the Two Group t-Test, Equal Group Sizes, Unequal Sigma section.
QuestionTo me, power is more an a priori concept, estimated even before collecting the data. We need the concept of power and sample size in the designing the study stage. So I wonder about the necessity of "post hoc" analysis. Or may be I misunderstood the purpose of the post hoc analysis in your program? AnswerWe agree entirely with this statement. A priori power analyses are definitely the best way to control beta error probabilities! However, sometimes it may be impossible to control the sample size, for example, when re-analyzing data sets that have been collected by other researchers before. In such cases post hoc power analyses may make sense (see, e.g. Cohen, 1988, among others). QuestionI would like to know if there is a formula whereby one can convert the effect size index for F-tests that you use (Cohen's f) to r or r^2. I am doing a meta-analysis and need to use a single measure to calculate the overall effect size. AnswerThe conversion formulae are |
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