The website I linked to does this kind of calculation.Linear regression is used to predict the value of an outcome variable Y based on one or more input predictor variables X. Then there may be many more candidate terms. One could include multivariate polynomial terms such as x1*x3^2, x3*x5^-1, etc. On the other hand, we don’t want to miss relationships that may exist in the data. On one hand, we don’t want to be guilty of “p-hacking” by creating so many candidate terms. Yet the final model might have only a few terms. In this case, there are 1024 possible candidate “independent variables,” including the synthetic ones. This could be critical if you are including interaction terms.įor example, if there are ten independent variables, the interaction terms could include x1*x2, x1*x3, … x1*x2*x3, … all the way to Productsum(x(i)) i = 1…10. Is the power calculation influenced by the use of stepwise regression, where there may be many more potential independent variables than are used in the final model? I have some more general questions which I include here: When we press the OK button the results shown in the lower part of Figure 4 appear.įigure 4 – Multiple Regression Power dialog box ![]() Next, we select the Multiple Regression on the dialog box that appears as Figure 3.įigure 3 – Statistical Power and Sample Size dialog boxįinally, we fill in the dialog box that appears as shown in the upper part of Figure 4. Real Statistics Data Analysis Tool: Statistical power and sample size can also be calculated using the Power and Sample Size data analysis tool.įor Example 1, we press Ctrl-m and double click on the Power and Sample Size data analysis tool. We see from Figure 2 that the sample size required is 85 and the actual power achieved is 90.26%.įigure 2 – Sample size required Data Analysis Tool Sample Size ExampleĮxample 2: What is the size of the sample required to achieve 90% power for a multiple regression on 8 independent variables where R 2 =. Similarly, we can calculate the power for Example 1 of Multiple Regression using Excel to be 99.9977% and the power for Example 2 of Multiple Regression using Excel to be 98.9361%. ![]() We can, therefore, calculate the power for Example 1 using the formula The calculation of the infinite sum for the noncentral F distribution stops when the level of precision exceeds prec (default 0.000000001) or the number of terms in the infinite sum exceeds iter (default 1,000). 80) for multiple regression where type = 1 (default) and effect = Cohen’s effect size f 2. If type = 2 then effect = R 2 instead. REG_SIZE( effect, k, 1−β, type, α, iter, prec) = the minimum sample size required to obtain power of at least 1− β (default. REG_POWER( effect, n, k, type, α, iter, prec) = the power for multiple regression where type = 1 (default), effect = Cohen’s effect size f 2 and n = the sample size. If type = 2 then effect = the R 2 effect size instead and if type = 0 then effect = the noncentrality parameter λ. Real Statistics Functions: The following functions are provided in the Real Statistics Pack: 05?įigure 1 – Statistical Power Worksheet Functions To calculate the power of a multiple regression, we use the noncentral F distribution F( df Reg, df Res, λ) where df Reg = k, df Res = n − k − 1 and the noncentral parameter λ (see Noncentral F Distribution) isĮxample 1: What is the power of a multiple regression on a sample of size 100 with 10 independent variables when α =. ![]() To compute statistical power for multiple regression we use Cohen’s effect size f 2 which is defined byį 2 =.
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