Test for consistency in user choices

#1
I have an experiment where each participant was presented with 20 questions, and for each had to choose their preferred answer from 2 given options. The options were generated from 2 different categories. I'm trying to investigate whether there was consistency in each user's choices between categories, i.e. whether users tend to pick from the same category more often than chance (no matter which of the two categories they tend towards). However, I have no idea how to test this. I can't just do a one-sample t-test, because that would just test whether users prefer one specific category over the other overall. It seems like I'm maybe looking to test whether there are two modes in the distribution, for picking one category over the other?
 

katxt

Active Member
#2
Have I got this right?
There is a collection of subjects (say 40). Each subject answers 20 questions which are scored (effectively) as A or B according to the category. If things were really random, you would expect 10 A and 10 B on average. You suspect that in fact subjects will tend to be something more like either 15 A 5 B or 5 A 15 B. How do we test that it is unreasonable assume random A and B given the data?
 

katxt

Active Member
#4
I can't think of a standard test off the top of my head, but you could devise a permutation test.
You need a measure of how spread out the data is. For instance if subjects tended to like one group over the other you might get data like 15 16 4 5 17 3..., whereas if there was no connection the data may be more like 7 11 9 8 12 ... So a suitable measure might be the variance of the subject scores - a high variance means your theory is correct, a low variance means probably random.
The main problem is how high is high?
Some reader may have a variance test to suggest but here is one way of doing a permutation test -
1 Collate the data, find the score (number of As perhaps) for each subject, find the variance of these scores. Write it down.
2 Now mix up all the data and allocate it to the subjects at random. Collate and find the variance. Record. Repeat 1000 times or so.
3 Find the percentile of the variance from 1 in the set of variances from 2. This is your p value.