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The setup: I am testing, if different instructions on playing a game result in different outcome. The game has fixed amount of N different possible outcomes. (I most likely set N to something around 2-5). The outcomes are measured on categorical scale (each possible outcome being one category).

Lets say I have two different instructions: A and B.

I want to plan an experimental design to test hypothesis: For each person, the outcome of the game is same for instructions A and B. Alternative hypothesis is: For each person, the outcome of the game depend on the instruction.

The amount of test subjects could be around 50-200. (I prefer less for economic reasons)

Do you have idea of what kind of experimental setup and statistical tests I can use?

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Unluckily no responses. But I discovered a test for this setup myself, so I'll report it here. If the amount of outcome categories, N, is 2, then McNemar's test does. If the amount of categories is more than 2, then generalized McNemar's tests, "tests for marginal homogeneity" by Stuart and Maxwell or Bhapkar will do. You can find papers about these in google scholar.

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