I am trying to figure out the best statistical test for a data set I've collected. I presented a group of adults (n=9) with a 21 different auditory cues. For each cue I asked them to choose the corresponding word from list of four words, one which was "correct" and three "incorrect." I then had them take the test again (I would have run more trials, but I didn't have enough time).
Mainly I want to test if their answers show that they recognized the cue and assigned meaning to it, or if they chose it by chance. But I'm getting caught up in the details and it has been a while since I took a stats course.
I want to compare the number of correct choices to the theoretical amount of correct choices (1/4). Should I use a binomial test or Chi-squared? Or do you recommend something totally different? Also should I look at each patient's individual data or the aggregate?
I also wanted to analyze the amount "recognized" for each patient - the amount of times the patient chose the same word for both the test and retest (despite if it was right or wrong). This is where I am really lost - could I simply compare the total "recognized" to the expected 1/4? (I got 1/4 by looking at the probability of selecting the correct twice [1/4*1/4=1/16] and selecting the same wrong twice [3/4*1/4= 3/16])?
I'm sure there is a simple solution, but I may be overthinking this. Any help is much appreciated!