I'm analysing data collected from a call centre activity in which agents are calling prospective leads. For each call made, if the lead coverts the call is a success and if the lead does not convert the call is a fail.
The data are for 5 agents. Each agent made a different number of calls in a unspecified period of time, and each has a different success rate. Boiled down, I have 5 percentages for the success rates.
I need to find a way to determine if the variability of the success rates is statistically significant, but can't think of an appropriate test. The main problem being that I have no benchmark value to test against. Of course, the data should have been collected in a better-designed experiment. However this is a typical 'here's some data' in an Excel spreadsheet scenario.
None of the tests I'm more familiar such as t-tests, Binomial tests, ANOVA, CHI Sq GOF, regressions, hypothesis testing against a null value, etc, seem to make sense. Is there a method I'm not thinking of for testing statistical significance in the variability in performance with this type of data?