Comparison of total counts vs. comparison of mean counts per participant in exploratory data analysis I already came across this question: Difference in means vs difference in proportions, but could not answer my question based on the answers and comments there.
My question would be this: Suppose there are two groups, A and B, whose participants are asked to write texts. Let's say the participants of group A have produced a total of $90,000$ of characters and the participants of group B have produced $100,000$. I also know the number of characters per participant. Now I want to compare the results regarding the number of characters between the groups. Two things are not clear to me:
(1) What would, in this case, a binomial test check with an assumed probability of $0.5$ (and a present probability of $90,000 / 190,000 = 0.47$)?
(2) In comparison, what would a $t$-test check based on the individual character counts of the participants?
Possibly, Fisher's exact test or a $\chi^2$-squared test could take the place of the binomial test. Still, I wonder from what different "perspectives" the data are being viewed here, when either the total counts or the mean counts per participant are compared.

If I understand correctly, the "binomial test" is simply examining whether both groups have the same probability of producing a character. The way you stated the test, there is no accounting for differences among individuals within each group. You could have 1 individual in each group or 10,000 in each group and would get the same result.
The t-test takes the variance among individuals within a group into account. That should be more generally useful than just analyzing the overall number of characters per group.
