Correlation Test
We do a correlation test to see if the data parameters are changing. I have noticed that in some of the questions, we try to see correlations of claim counts and elsewhere we see the frequency ([claim count]/[exposures]). The results of these two approaches can be quite different.
Please help me out to understand if claim frequency should be used or claim counts.
Comments
Frequency and exposure are related. The important piece is accounting for changes in the exposure base. For example, if we double our exposure we would expect our claim count to double so if we look solely at the expected number of claims we would think there is a shift.
If we purely look at claim frequency then we're implicitly giving all observations the same weight. We don't want this to happen if we have different levels of exposure in different years. A small difference between the actual and expected isn't going to amount to much if the exposure is low; however, if there is a large volume of exposures then it's much more likely to indicate something has changed.
To answer your question: Either can be used but the expected quantity must take into account the size of the exposure. So really, you're using weighted claim frequency where the weights are the exposures. This means you're using claim counts where the expected number of claims varies based on the exposure.