Here's the question I was asked: look at the ordering of multiple choice answers a, b, c, d in a test of 100 questions and determine if their ordering is random - or uniform - pardon the terminology. I understood this as all outcomes are equiprobable - abcd vs bacd vs cdab etc. I think this means that I can look at each position and expect all letters to appear 25 times, but I am not sure if this is the correct interpretation?
Assume I observed - in position 1 - 22 a's, 27 b's, 30 c's and 20 d's. How do I go about that?
I am thinking: H0: ordering is random (no dependency between letter and position) H1: it is not
Under H0, I would expect to see 25 of each option. Compare these to actual observed counts, take the squared difference and then do a chi-sq test? Would this be the same as doing individual Z tests for ratio of a's, b's, etc?