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I asked users to complete a likert survey (1-5) at the start of an activity, and conclusion of the activity. What is the best manner to show the rate of change/difference between these two result sets? I was considering a Pearson correlation, but after thinking about things more I don't believe that it is the most appropriate correlation metric. My data looks similar to below:
Before After 1 2 1 2 2 2 3 3 3 4 4 2
Result: XXX?
Thanks all
If you are trying to see whether the survey had made any positive effect on the people, modeling a relationship between before and after with correlation is a fair approach while avoiding some edge cases. Correlation looks whether $X's$ and $Y's$ are linearly correlated or how one variable is influenced by other. But I guess what you might be looking for is just something simpler like average increase in rating after the activity. For example
import numpy as np
from scipy import stats
ratings_before = np.array([1,2,1,3,4,5])
ratings_after = np.array([5,5,5,5,5,5])
print "P.Corr: ",stats.pearsonr(ratings_before, ratings_after)[0]
print "Avg.Increase: ",np.mean(ratings_after-ratings_before)
which gives
Nan
2.333
And assume that your activity went so good that everyone rated you a 5-star. Then correlation turns as $NaN$ as denominator goes to zero as no $Y$ can be explained by $X$.
Hope this helps.
