A2.3 Calculs de puissance pour une différence de proportions

Power calculations for two proportions

Here is an example:

Estimate the sample size needed to compare the proportion of people who smoke in two populations. From previous work, you think that 10% of the people in population A smoke, and that an absolute increase of 5% in population B (compared to population A) would be clinically significant. You want 90% power, and a 5% significance level.

In this scenario we use the ‘pwr.2p.test’ command in the power package.

### alpha = sig.level option and is equal to 0.05
### power = 0.80
### p1 = 0.10
### p2 = 0.15

power4<-pwr.2p.test(h=ES.h(p1=0.1, p2=0.15), sig.level=0.05, power=0.9)

With this command, you can specify ‘h=’ for an effect size, or you can ask R to compute an effect size for two propotions with the ‘ES.h(p1, p2)’ option, as we did here.

> power4<-pwr.2p.test(h=ES.h(p1=0.1, p2=0.15), sig.level=0.05, power=0.9)
> power4

Difference of proportion power calculation for binomial distribution (arcsine transformation)

h = 0.1518977
n = 910.8011
sig.level = 0.05
power = 0.9
alternative = two.sided

NOTE: same sample sizes

You estimate that you need 911 participants from each population, with a total sample of around 1,821. If you wanted different sample sizes in each group, you would use the command ‘pwr.2p2n.test’ instead.

If we type ‘plot(power4)’ we can see how the power level changes with varying sample sizes:

> plot(power4)

Question A2_3: Unfortunately, the funding body has informed you, you only have enough resources to recruit a fixed number of people. Can you estimate the power of a study if you only had 500 people in total (with even numbers in each group)? (hint: type ?pwr.2p.test if you need help setting up the command)