calculating sample size

[#1]

need your advice please

I need to calculate a minimum number of subjects for an experiment aimed at evaluating the ability to control a new device.

The average success rate in the population is unknown and the assumption is that it is completely random 50%.

We claim that the ability to control the device is at least 80%. In the experiment.

each subject receives 15  attempts in which there is a possibility of success or failure, then the average number of successes is calculated for each subject.

What statistical test should be performed and what is the minimum number trials and subjects required if alpha = 0.05 and power 0.8. Basically, there are two questions here that affect each other:

1. How many attempts is enough for each subject to perform in order to calculate his average
2. Given 1, how many subjects are required for the experiment where The null hypothesis is H0=0.5 Alternative hypothesis H1=0.8

To calculate how many trials are needed for each subject, I am considering a binomial comparison test with a constant of 0.5 and an alternative hypothesis of 0.8 After calculating averages, I consider whether Z test > Proportions: Difference from constant (one sample case)

[#2]

Hi @yaron: Welcome to the community!  There is a lot to unpack here. For clarity, I have a few questions/comment/etc. In no particular order.

1. What exactly are you trying to show/prove? You say "The average success rate in the population is unknown and the assumption is that it is completely random 50%. We claim that the ability to control the device is at least 80%."

On one hand you say it is assumed to be 50%, and on the other you claim it is 80%. When you say you claim the ability to control the device is 80% in the population, what are you basing that 80% on? If you are trying to show that the success rate in the population is >50%, then the hypothesis are:

H0: p=50%

Ha: p>50%

Power is then Prob(rejecting H0, assuming Ha is true). Then you power the experiment for some p>50%.

If you want to prove that the ability to control the device is at least 80% in the population, then the hypotheses are:

H0: p=80%

Ha: p>80%.

In other words, Ha is what you are trying to prove.

2. Why are you taking an average for each subject? The n=15 (in your example)  trials for a given subject are not independent, and presumably there is learning going on as well; if each subject gets better at controlling the device as they try more times, at some point they will get it right all the time so as n gets larger, so does the average for that subject. Not good. If you are interested in success rate in the population, there is no need to take an average; n=1 per subject will do, and won't force you down the road of normal approximations either. That said, is recruiting for such a trial difficult?