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I have collected ratings on a scale from 0 to 100 for two different conditions: A and B. I want to show now, that the ratings collected under both conditions are very similar and that their range overlap.

How can I do that best? I thought about drawing a box plot for both conditions, but I would prefer a number / numbers to show.

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  • $\begingroup$ how about plotting them on a histogram, you could also add descriptive statistics as desired, e.g, mean, mode, median, st dev $\endgroup$
    – Robert Jones
    Commented Feb 3, 2018 at 13:19

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The Bhattacharyya distance is a coefficient in the [0;1] range showing the overlap between two probability distributions. Intuitively, it seems to give the answer you desire.

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  • $\begingroup$ Although I think this could answer this (dated) question, the Bhattacharyya distance is a measure of dissimilarity (distance between two probability distributions). As I'd have to assume the OP specifically asked for showing similarity when looking at the question, IMO it does not completely answer the question. If you (@abaumann) could expand this answer with how you'd use Bhattacharyya distance to show similarity, I feel the effort would be complete. $\endgroup$
    – IWS
    Commented Jan 2, 2018 at 10:53
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Why not just use the numbers from the box plot, that is a table with the minimum, 25 percentile, 50 percentile (median), 75 percentile, and maximum? Alternatively, you could simply say what percentage of X values lie in the range of observed Y values.

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