# Figure out the number of samples needed to increase the precision of an estimate

Suppose I am calculating the average rating for several products that were rated by different people.

For example, assuming that if I choose 5 random people and calculate average ratings 100 times then the variance of each average is of course higher than if I chose 10 random people. I would like to figure out how many people I would need to obtain this average with as high precision as possible.

Therefore, I believe that I can do a bootstrapping experiment where I increase the number of people whose ratings I have averaged and demonstrate that the variance decreases as I include more and more people when calculating the average(s).

This would simply amount to choosing N ratings with replacement. Taking their average. Calculating the variance across bootstrap iteration. I'm then left of a plot of variance vs. number of samples.

Does it make sense to use this plot to gain insight on how many samples I should use in order to increase the precision of my estimate? Importantly, I may only have 3 people give a rating but I want to infer that I potentially need 5 people. How would I go about inferring that?

Is there any similar work and references associated with it that I can look at?

• With 100 x 5 observations, one can estimate mean and variance of the random variable and deduce the variance of the overall average. Nov 3, 2022 at 8:36
• This is a hypothetical. There aren't actually 100 x 5 observations. Nov 3, 2022 at 15:11