I am working on problems from the book "Quantifying the user experience" by Sauro. But couldn't figure out the right way to do it.
Assume you’ve been using a single 100-point item as a post-task measure of ease-of-use in past usability tests. One of the tasks you routinely conduct is installation. For the most recent usability study of the current version of the software package, the variability of this measurement (s2) was 25 (s = 5). You’re planning your first usability study with a new version of the software, and all you want to do is to get an estimate of this measure with 90% confidence and to be within ±2.5 points of the true value. How many participants do you need to run in the study?
Continuing with the review question given earlier, what if your research goal is to compare your result with a benchmark of having a result greater than 75? Also, assume that for this comparison you want a test with 80% power and want to be able to detect differences that are at least 2.5 points above the benchmark. The estimated variability of measurement is still 25 (s = 5) and desired confidence is still 90%. How many participants do you need to run in the study?
pwr.t.test(d=(77.5-75)/5,power=0.8,sig.level=0.1,type="one.sample",alternative="greater")
The answer for 1st is 13 participants and 2nd is 20 participants. For the first I am not sure how to do it, for the second I'm getting the wrong answer i.e 19. These problems require iteration to get to the final sample size estimate. Does the library iterates internally or I need to code it?