I have the responses from a survey where people had to provide a rating on a scale from one to five, where five was most positive side of things. I would like to assume it is interval scale where the differences between each point on the scale are the same, as I would like to compute quantitative summary statistics such as mean and standard deviation of the ratings. The idea is to see what the variation is in the ratings. I don't know how much data I need before I can trust the rating, but I thought about using a test to see if the standard deviation of the ratings was equal to 0 (null is that sigma equals 0, alternative sigma greater than 0). Sometimes I only have a few responses, however if they were all the same I feel as though I could trust them because the standard deviation is 0 in that case. One problem (or two or more problems) is the ratings are often skewed (tend to be high), and this is a sample of convenience (look out assumptions) as not everyone who had the option to do the survey did one. So people who did one were probably going to provide a high rating. Can I perform a test like I want to here on data like this? What are your thoughts?
Thank you in advance.
Thank you in advance.