# Power & Effect Size for Multiple Regression - HELP

2 IV's: Pregnant/Non Pregnant & Physically Active/Not Physically Active

1 DV: Cognitive Functioning (Inhibition - SSRT scores)

AIM: Investigate whether there is a difference in physical activity levels are present between Preg/Non Preg & if this has an effect on cognitive functioning.

Hypothesis:

1. Preg will not meet physical activity levels and will have lower cognitive functioning scores compared to non-preg

2. Preg will show no difference in cognitive functioning tasks/reaction time compared to non preg when Physical Activity is controlled for.

Okay, so STATs-wise. I am in need of some guidance around how to go about calculating power and effect size for my final research topic.

I believe that this particular research requires multiple regression. But am unsure what statistics to analyse the difference.

Do I need to look at moderation/mediation for Physical activity being an influencing variable?

How do I go about computing power and effect size? I am trying to figure out the sample size using power calculation through the use of G*power.

Would the statistical test be: linear multiple regression: fixed model, R2 increase

Would effect size f2 be 0.15 a err prop 0.05 and power 0.95, would my number of predictors be 4?

Am I on the right track :( Need some guidance

Your hypothesis seem to be getting at effect moderation. Though I can't specifically speak to any of those analyses, I can tell you how to go about computing the sample size for a linear regression. Here are the steps...

a) Write down the regression model. This will inform which effects can be assessed. So, for instance, the simplest linear model would be

$$y = \beta_0 + \beta_1\mbox{Is Active} + \beta_2\mbox{Is Pregant}$$

The model will depend on what hypotheses you are evaluating.

b) Pick a smallest meaningful effect size. There is always a difference between groups, but sometimes those differences are so small that they don't practically matter to us. Decide on the smallest effect you are interested in finding.

c) Compute the sample size using

$$n \approx \dfrac{8\sigma^2_y}{(\beta \sigma_x)^2(1-\rho^2)}$$

Where

• $$\sigma^2_y$$ is the variance of the outcome conditioned on the covariates

• $$\beta$$ is the smallest meaningful effect size in part b)

• $$\sigma_x$$ is the standard deviation for the effect of the co variate you are interested in testing.

• and $$\rho^2$$ is the multiple correlation between your covariate of interest and the other covariates you are controlling for. All that is needed in practice for all of these is a good enough guess. You don't need to be bang on here. Sample size is an educated guess.