# How do I determine goodness of fit for a test of n binary decisions?

by Jonathan   Last Updated August 14, 2019 18:19 PM

Let's say I have $$n$$ pairs of items. For each pair I select one item over another due to some perceived trait. This could be anything, for example, identifying which image is brighter than the other or something.

I want to then do this exact same test with a bunch of participants and determine if their perception agrees with mine.

My initial thought was to collect the data, and then do a set of binomial tests for each pair, the null hypothesis being that they make the same choice as me, thus treating my choice as an expected value (p=1 or p=0 of picking item 1 over item 0 for example). Does this make sense? Or is there some way I can use the chi-squared test or something? I'm a novice when it comes to these sorts of statistical tests.

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