You can use a quasi-binomial model or a beta-regression model. As a poor-man's solution you could run a standard regression on the logit-transformed percentages.

What is the distribution like? A logit regression with the non-quasi binomial assumption might fit. A bit more information about your data would be useful (the n, the variables, etc.).

Hello Ann,

In addition to the suggestions of Daniel Wright and Jochen Wilhelm , note that solutions using school-level data are likely to differ from those derived using student-level data (or multi-level models), and sometimes dramatically so.

While the level of data which you are able to obtain may be a factor beyond your control, do acknowledge the distinction when you write up your results.

Good luck with your work.

Thanks! The unit of analysis is the school. I am trying to examine the relationship between intermediate measures of school quality like teacher student ratios, average teacher salary, and counselor student ratios and the percent of students scoring proficient on state tests. I realize there is a distinction between student level phenomenon and school level phenomenon but this analysis is focused on school quality rather than students. Does that work?

It is important then to make sure your conclusion are discussed about schools, not students. See RObinson's ecological fallacy paper in 1950 from Amer Soc Review.

Yes. I AM aware of the ecological fallacy. My concern is that there are a couple of schools who do extremely poorly and the rest are clustered in what looks like a normal distribution between 70 and 100 percent. My inclination is to do the analysis twice - with and without those low performing schools, but I am just not sure.

Your plan, re the potential outliers, is I think is a good one.

Do you have the denominator of the response percentage , that is how many pupils?