Lets say I was conducting a very basic educational research study (not to be published but for interest) and I was wondering if different pupil personality types preferred different types of practical work. Each pupil has been assigned to one of four personality types (this assignment is crude and is in itself unreliable). I then ask each pupil which of 4 types of practical work they prefer. what type of statistical analysis can I perform, if any, to see if there is any significance in my answers?
I am presuming if there was no significance then pupils from category A, for example, would pick practical types 1-4 at random giving roughly 25% in each practical type. If 75% or 90% of pupils in category A picked practical type 1, can I do any analysis to show how meaningful this is, if at all?
I only remember working with numerical data and not categorical data like this. Having a brief look around for 'assocations between categorical variables' (e.g. personality type and practical type) I have seen residual analysis suggested. I have also seen odds and odds ration suggested.
I have also seen on wikipedia that I might need a 4*4 contingency table.
If you suggest a method, please can you say whether it can be done in Excel or something else free!!