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I have a binary predictor variable (situation1, situation2) and another one that's ordinally scaled (levels in an n-back task, they're called no-back,0-back,1-back & 2-back with 2-back being the highest level). I have a continuous outcome variable (illusion rate).

I wanted to run an ANOVA, but my data is not normally distributed, so I'd like to use a nonparametric test. I thought about using a logistic regression, but I think my outcome variable would have to be binary to be able to do so.

Does anyone have an idea of which test I could use for that?

Thanks so much in advance!

P.S.: I'm an undergrad trying to do my best statistics-wise, so please be nice! ;-)

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    $\begingroup$ What is your goal? ANOVA and the “predictive models” tag you’ve included are almost polar opposites (at least in some sense). $\endgroup$
    – Dave
    Commented May 9, 2020 at 21:25
  • $\begingroup$ I ran an the same experiment with the same participants in the lab & online (= binary predictor variable). In the experiment the subjects get a task in which they can perceive an optical illusion, and in each block (there are 4, that's the ordinal predictor variable) the illusion rate should go up a little bit. I wanted to compare the datasets from online & the lab & if I don't find a sign. difference with a two-sided wilcox test & alpha = 20%, I wanted to run Friedman tests + post-hoc tests to check whether there's a sign. difference between the illusion rates in the different blocks. $\endgroup$
    – Merle
    Commented May 10, 2020 at 9:27
  • $\begingroup$ The problem is that in some cases the datasets are not sign. different (there are different kinds of illusion rates), in other cases they are. My advisor told me to see if I can use a logistic ordinal regression but we're both not quite sure whether that's the right approach. Actually, I need a nonparametrical 2x2 Anova. $\endgroup$
    – Merle
    Commented May 10, 2020 at 9:29

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You mentioned an ANOVA as well as prediction of an outcome. So you can run a linear regression with the predictors being an indicator for the binary variable and dummy variable for three of the four categories of the ordinal variable. You'd only need 3 dummy variables since you need to drop one as the base case. (In case you don't know, a dummy variable is just a variable that's a 1 if the ordinal variable equals a particular category and a 0 if it doesn't). That way you can get some interpretation of each of the variables impact as well as a prediction.

If you have a larger amount of data, you could also throw in some interaction terms to the regression (like being no-back and situation two) to get a complete picture. If you're limited on data, you can run a regression of just the binary predictor and ordinal variable and hope the ordinal variable's impact increases linearly.

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  • $\begingroup$ Thanks for your super-quick & nice answer @norvia!!! I don't know if I understood you correctly, do you mean I can run a linear regression with the binary variable as the outcome and a dummy variable & the continuous variable as predictors? Could you maybe explain the second sentence again? How would the model look like? (Sorry, I'm really a beginner!) $\endgroup$
    – Merle
    Commented May 10, 2020 at 9:01

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