# What's the difference between power calculations for an OLS vs LPM model?

[I reworded this post]

There's a lot of information on calculating sample sizes on proportion changes using a power analysis. That makes sense to me. But is it any different if I am calculating sample size for a bivariate LPM model? Like, if I wanted to run a model of Death(0, 1) = beta * Treatment + epsilon, what would I do to calculate power? Would I use the proportions technique? It would help if you illustrated an example either using G*Power or -power- Stata.

(Before it gets mentioned, I come from economics, where linear probability models are more conventional than logistic models)

## 1 Answer

Depends on what model you want to use to estimate the difference. Plenty of power calculations exist for power to detect a difference in means for a binary variable which are based on a difference in proportions z test.

If you want to use logistic regression, the power can be computed using the following equation

$$\gamma=1-\Phi\left[z_{1-\alpha / 2}-\left|\beta\right| \sigma_{x} \sqrt{n p(1-p)}\right]$$

Here

• $$\mathbf{\Phi}$$ is the standard normal CDF
• $$\beta$$ would be the estimated coefficient in your model
• $$\sigma_x$$ is the variance of the predictor
• $$p$$ is the prevalence of the outcome

And of course, you could use LPM. The differences in these approaches may be appreciable when sample sizes are small but they should converge with enough data.

• Could you explain it in an applied setting? I'd be interesting in knowing how to do it for both the LPM and Logistic setting. I'm familiar with G*Power, Optimal Design, PowerUp, R, and -power- in Stata if you can phrase it in that context. I'd be super appreciative! May 23, 2020 at 0:16