# Type of statistical test for categorical variables?

What test am I supposed to use in this case:

• Categorical outcome [correct, partially incorrect, incorrect]
• Categorical predictors:
• Condition [2, 5 and 10 presentations of an image].
• Time in which they were tested after the presentation [1 hour, 1 week, 1 month].

Condition was between subjects and time within subjects. Each participant was tested for 6 images (so I have 6 correct/incorrect/partially correct responses every time I tested them).

What I want to know is if they will have less correct after a month compared to the first test (1 hour after the presentation), and if the number of presentations makes a difference.

I though I needed to do a chi-squared test because all my variables are categorical, but my outcome is not yes/no or correct/incorrect. It has three levels instead. And I don't know if I should average the 0s, 1s and 2s OR add them up and treat it as a continuous variable ranging from 0 to 12 per time of test, and use an ANOVA. Since I'm measuring the same people three times, could I also use linear mixed models?

I am using R, in case that's relevant.

Thank you very much!

Ordered categorical data is referred to as ordinal, this is in contrast with unordered categorical data (e.g. 'Alive' 'Dead'), which is coined nominal. You can try to fit an ordinal logistic or probit regression for your use case where the outcome is ordinal. This is explained on this link, using R.

Quoting from the link, the options you have are:

Ordered logistic regression: the focus of the link above.

OLS regression: This analysis is problematic because the assumptions of OLS are violated when it is used with a non-interval outcome variable.

ANOVA: If you use only one continuous predictor, you could “flip” the model around so that, say, gpa was the outcome variable and apply was the predictor variable. Then you could run a one-way ANOVA. This isn’t a bad thing to do if you only have one predictor variable (from the logistic model), and it is continuous.

Multinomial logistic regression: This is similar to doing ordered logistic regression, except that it is assumed that there is no order to the categories of the outcome variable (i.e., the categories are nominal). The downside of this approach is that the information contained in the ordering is lost.

Ordered probit regression: This is very, very similar to running an ordered logistic regression. The main difference is in the interpretation of the coefficients.