# Sample size for multiple regression using G*Power

I am running a study on school children to compare psychometrics in physically active and sedentary children. My IV is physical activity with 2 levels - physically active / sedentary and DV psychometrics with 3 levels - coping styles / coping efficacy / physical self description.

I have chosen to use a Multiple regression analyses. I am trying to figure out the sample size using power calculation through the use of G*power. However, I am not so great with statistics and I can not figure out how to do this.

Would the statistical test be: linear multiple regression: fixed model, R2 deviation from zero OR linear multiple regression: fixed model, R2 increase?

Would effect size f2 be 0.15 a err prop 0.05 and power 0.95, and what would my number of predictors be?

• You wouldn't use multiple regression for this problem because your DV is a nominal measure. I suggest that you use the ch-square test for independence. – Dr. N May 18 '18 at 11:51

It sounds like your model is about inference: you have some key variables, and a design to assess their effect on outcome(s). When we fit models for inference, we look at the effects--the coefficient terms--to see if the 1-$\alpha$% CIs include 0 or not, and that is the same as measuring if the p-value is less than $\alpha$.
This type of test is essentially a one sample t-test: Is the 95% CI for $\beta$, the regression coefficient, different from 0? For grants, I have used G*Power, and other software, to calculate power for multiple linear regression using the t-test power calculator. You need only specify the mean and the standard deviation of the sample to calculate that power. Those values are identified from previous literature: you need only calculate the half-width of the CI and divide it by the critical value to find the standard error of the mean (for symmetric CIs). If no literature exists, you must make a guess and rationalize it; but again drawing on the literature strengthens your guess.