I want to enhance a photo and I have 3 software to do that, out of which 2 are my own. I show users 2 photos and ask them to choose a better one. Now, I compare software 1 vs. 2, 1 vs. 3. Software 2 and 3 are mine. Now, I can clearly see from the votes, that people choose 2 and 3, over 1, in both sessions.
Task 1: Show that 2 is better than 1, then 3 is better than 1.
A published paper (not on statistics) handled the same task and used a paired t-test. I can do the same, and show that 2 is the better method. I intend to that in MATLAB as follows:
[h,p]=ttest(votes_for_software1,votes_for_software2) %similarly for 1 vs. 3
I do the above and I get,
h = 1 and p = 7.2372e-04
This confirms (at least I think so) that a mean value of the observed size or greater magnitude will occur with a probability
p (interpretation taken from here).
So different people are looking at same set of photos and voting them, am I right in using a paired t-test? Also, am I doing the overall process right? (including the implementation).
Task 2: Is there any way I can compare software 2 and 3 (both of my software)?
The data compared in the comparison of software 1 vs. 2 and 1 vs. 3 remains same. So, I calculate the mean rank obtained for all the three software (lower the better), and I can see that,
rank_3 < rank_2 < rank_1 -> Software 2 of mine is the best.
How could show this statistically?