# determining if ordering is random

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?

• Could you explain what you mean by "random"? You use this word as if it meant that the answers are equiprobable. That's both a stronger condition (not all random variables have equal probabilities) and a weaker condition (random means far more than yielding expected frequencies) and so is not equivalent. Moreover, you don't appear to mean "ordering" in any standard sense, either, because different orderings of the answers would not change their frequencies. Please clarify. – whuber Nov 13 at 22:43