## sample size for likert scale test

Hi,

I am conducting a 5-point Likert study to build a model. I have subjects vote on over 1000 items, but lets pretend I have them vote on 1 item.

My advisor wants to know, "how do you know when you have enough votes per item?"

For example, I think 5 votes per item is too small, because I have a 5 point Likert scale, and then I run into problems of how my results could be due to chance. What I know:

1. I feel like the variance of the votes per item is important. For example, if all 5 people voted "3" on a 1-5 scale, this tells me something (maybe), as opposed to if they all voted a different number, which is the same as random chance.

2. It was very difficult to get subjects for this study, so I have about 10 votes per item. My advisor says this is enough, but he wants me to prove it or explain it.

3. I have heard of t-test or chi-squared tests used with Likert scales, but I don't quite see if or how that will help me. I can see saying something like I am 95% confident that my sample mean is within 0.5 of the true theoretical mean - can I do this with a t-test? That number 95% should get smaller with the fewer samples I have, so in this way I can check to see if 10 votes is enough. It is important to note here I DO NOT KNOW the theoretical mean for any item, so I'm not sure if this is useful.

My biggest problems is that my sample size is small, and I don't know the theoretical mean. I only have sample means and variance. Can someone help me answer the question why about 10 votes per item, where the sample mean and variance is known (but the theoretical mean isn't) gives me a confidence of XYZ using the XYZ test?

Thanks!

Laura