"can I do any analysis to show how meaningful this is"

yes

Unfortunately you will have to hope that somebody more familiar with probability than I will give more details. The fact that the personality assignment is uncertain is not too important, If it were perfectly random you would get 25% in each catagory anyway.

You want to find the probability that the actual % differs from 25% assuming random selection.

I cannot give you that calculation now

yes

Unfortunately you will have to hope that somebody more familiar with probability than I will give more details. The fact that the personality assignment is uncertain is not too important, If it were perfectly random you would get 25% in each catagory anyway.

You want to find the probability that the actual % differs from 25% assuming random selection.

I cannot give you that calculation now