# How to statistically validate that one clustering technique is more effective than other on Binary data

Problem statement - Idea is to cluster students based on their assessment pattern and score.

Data = I have a data set that contains Binary data of students answers(Correct/incorrect) which i have recoded as 1 & 0. Its a 10*100 matrix of 10 students answering 100 questions. Looks like this I have tried distance calculation formula of following 2 techniques

Let be the contingency table of binary data such as n11 = a, n10 = b, n01 = c and n00 = d. All these distances are of type d = sqrt(1 - s) with s a similarity coefficient.

1. Sokal & Michener formula= (a+d) / (a+b+c+d)
2. Jaccard Index formula = a / (a+b+c)

I have found that "Sokal & Michener" works best for me just by looking at the clusters it found and i already knew the pattern in the data very well(i created dummy data) and hence i came to this conclusion of choosing "Sokal & Michener"

But is there a way to statistically verify that 1 algorithm works better then another?

Also can you suggest any other clustering technique for this problem statement?

Thanks

• How do you define "works better"? – Michael Chernick Apr 20 '17 at 7:11
• Intuitively i would like students clustered together who have similar pattern of answering and similar scores. Hence i went with Sokal & Michener as it works using intersection and union – James Rodriquez Apr 20 '17 at 16:34
• Jaccard is a widely accepted measure of "similarity", and it also works using intersection and union, doesn't it? So how do you define "better similarity"? – Anony-Mousse Apr 22 '17 at 18:30
• Yes it does but jaccard only uses 11 and doesn't consider 00. In my case even 00 is a pattern that should be considered. – James Rodriquez Apr 24 '17 at 4:55