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I’m looking for a statistical test, but having difficulty finding an analysis that fits all the conditions of the data.

My IV and the DV are categorical, each with 3 levels. For the IV, the experiment will have 3 conditions (e.g., easy, medium, difficult). For the DV, there are 3 possible responses. These responses are based on previous research which concluded that for this particular task, one of three responses is most likely.

It is a within-groups design, with each participant being tested in all 3 conditions.

My research question is whether the different conditions affect how individuals will respond (e.g., Are individuals in condition A most likely to respond with A, rather than B or C? Are individuals in condition C are most likely to respond with C, rather than A and B?, etc.). I could simply provide the percentage of participants who "chose" each response (A, B, or C) for each the 3 conditions, but want to test for significance. Cochran’s Q test seems to the closest I can find, but it only allows for a dichotomous DV.

To summarize, this is a repeated-measures experiment with 2 categorical variables, each with 3 levels. I plan to be working with SPSS. Any help would be appreciated.

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2 Answers 2

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This calls for a multinomial logistic regression, possibly with polynomial contrasts to account for the fact that the predictor is ordinal (it may or may not be better to simply treat the 3 levels as categorical).

To account for the non-independence (repeated measures), you would probably need to add a random effect (intercept and perhaps slope).

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    $\begingroup$ I wonder if it might be best to code the easy level as $(0,0)$, the medium level as $(0,1)$ and the hard level as $(1,1)$ to account for the ordinal nature. I think this is the standard way to approach ordinal features, right? $\endgroup$
    – Dave
    Commented Mar 7, 2023 at 19:41
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Is your DV nominal or ordinal? If I'm reading this table from UCLA correctly, perhaps the Friedman test if it's ordinal and repeated measures logistic regression if categorical. The table has links to instructions for using the procedures in SPSS.

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    $\begingroup$ Thanks for the feedback and suggestions. The DV is nominal, otherwise Friedman's ANOVA would be a good fit. I looked into logistic regression, but it allows only for a binary outcome. I've spent quite a bit of time looking into multinomial logistic regression, but I don't believe it can be used in a repeated measures study. Also, my understanding is that the IV would have to be continuous for such an analysis, which is not true in this case. Anyone know if those assumptions are false? Any other recommendations? $\endgroup$
    – Bob B.
    Commented Nov 12, 2015 at 21:22

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