Best way to compare several cases to a null model

Question

At the moment I am doing analysis in some data that is (currently) divided by number of individuals in a group. More or less like:

Groups w/ two individuals: Value_1, Value_2, ..., Value_N

Groups w/ three individuals: Value_1, Value_2, ..., Value_M

In this case there were N groups of 2 individuals and M groups of 3 individuals. And so on until groups of about 300 individuals. Basically, I have different amount of data for each group size. For example: N (and M) is the number of groups with 2 (or 3 in the case of M) individuals which the value was measured. If we had 50 individuals in the groups of size 2, N=25. And so on for all groups sizes.

I am trying to compare these experimental results with simulations I've ran as a null model. Currently, I run my simulation for each different group size then do a t-test for the means.

However, I am left wondering: Is there any better/more interesting way to test how the experimental data differs from my null model/simulation instead of doing individual t-tests for each group size? Is there a way to aggregate all these tests into just one thing?

The whole thing is a bit of a complex biological system. My simulation is what would happen if the system itself behaved in a certain (super simple, totally trivial manner) way. I'm trying to show that the experimental data is different enough from this trivial behaviour (that is, the individuals actually follow some specific behaviour and do not just do randomly uniform actions).

Answer 1

It sounds as if you'd want to compare multiple means at the same time. Perhaps a straight forward ANOVA would do the trick with an F-test to see if all means (including the null group one) are the same. If you indeed reject the Null hypothesis of equal means across all groups you can then do post-hoc t-tests with an appropriate correction for multiple comparisons.