It's probably not the most sophisticated approach, but, yes, Mann-Whitney --- as long as it's an implementation that can handle ties --- will work for this kind of data. ... I wonder, though, how you intend to handle the fact the same person is answering each category of questions. Are you analyzing the three categories separately ?

It depends, but first, why did some people not answer some? Were these not presented to them by some random mechanism, or were they the last few (and perhaps easier or harder than others), or did people see them but decide not to answer because they thought they would miss them or it would take to long to answer them, or etc. Second, I am not sure what the three categories means. Is it that they got say 5 items on math, 5 on reading, and 5 on science? or that there were three groups? The choice of statistic will depend on this. Third, what research questions do you have? And finally, Mann-Whitney is usually used for two categories of people (i.e., two groups).

In attachment an R script for your binary type of data and design. Note that the row means are calculated as your would want to do. It includes a nonparametric alternative.

Thanks for your all answers. Not-answered questions are at the end of the online test and test questions were randomly given so I assumed they just got bored with the test (given that the participants were children). Therefore I assume that it is not related to the questions but to the test length. That's why I choose to take the mean.

The categories are the way we presented emotions to the kids. For category one emotions are presented in congruent modalities, for category two in incongruent modality, with a body focus and for category three with a voice focus.

so i wrote the cod like this: pairwise_wilcox_test(

Mean_Score ~ Type_of_Question, paired = TRUE,

p.adjust.method = "bonferroni"

)

and also I applied group differences between different ages groups like this after including 2 age groups in 1 dataset, to see the overall impact of age on the test:

Mean_Score ~ age, paired = FALSE,

p.adjust.method = "bonferroni"

)

I assume you are also interested in the age by question type interaction (and what is the age range, why was it dichotomized?). Have you considered multilevel logistic regression of the form

library(lme4)

glmer(right ~ qtype*age + (1|subno) + (1|itemno), family=binomial)

? There are many other approaches also. And the default (Holm) is usually preferred for the p adjust method.