What's the right test to use to find significance in a table of incidence rates? I have some data about conversion rates on different browsers, as follows.
            Opera   |    Firefox   |    Chrome   |    ...
Site A |     55%           75%            76%         ...
Site B |     45%           70%            71%         ...
Site C |     55%           10%            57%

Except that I have more sites and more browsers than this in reality!
What's the best test to use to compare these? 
I'd like a test that can identify when a particular site has an unusually low conversion rate on a particular browser - for example, site C on Firefox, in the above table. 
I'm not sure if a chi-squared test is the right test to use here. 
I do also have the underlying raw data, if that helps. 
 A: What might be 'unusual' will depend on your model. It's a good thing you still have the raw data, because you'll need it.
You suggest using a chi-squared test, and (assuming I understand the situation in your question correctly) that can work but you have to be very careful. You'd need to have a three-dimensional table with two "layers" (one for the successes and one for the failures, and with each as counts, rather than proportions). The unusually low cells would be ones with a large negative signed square-root contribution to chi-square ($\frac{O-E}{\sqrt{E}}$), or perhaps ones with a large Pearson residual (a standardized $O-E$ treating the value as multinomial).
Consider this as a two-factor model for the counts (each of your values is a ratio of two counts; you need both numbers in the ratio); in effect, a two-way ANOVA for counts. This is quite similar to what I just described for the chi-square, so if you're happy with that, it might well suffice.
Typical approaches would be either a binomial glm (typically with a logit link, so the model would be linear in the log-odds) or, possibly a log-linear model for the table.
In either case, in a main effects model, an unusually low rate would show up as a large (negative) residual, and in an interaction model an unusually low rate should show up as a large negative interaction effect on the relevant combination. However, you may need to take some care over how the contrasts are coded for that to work well;
in particular, there may be a difficulty in spotting it if the factor is coded with a reference level ("dummy coding"), and the unusually low cell is at the intersection of two reference levels. Something like what this link calls "simple coding" may suffice, though it is a little trickier with unbalanced designs.
