Re: How to identify flat (even) distributions?

On Dec 10, 8:27 am, Steve555 <foursh...@xxxxxxxxxxxxxx> wrote:
Hi

If I have 1000 people and their opinion ratings for, say, 100 songs
each (on a scale 1-10) How do I test for those users that have rated
10 1s, 10 2s, 10 3s etc i.e. a flat distribution?
I know I can use standard deviation to spot those that tend to give
the same rating, or polar extremes, but there's nothing uniquely
identifiable about the SD for these 'flat' users.

I'm writing a program in C to find these; I know I could brute-force
count the frequencies to find them, but hoped there might be a
statistical measure of this.

Thanks

Steve

Try Simpson's Reciprocal Index: k' = (sum f_i)^2 / (sum f_i^2),
where f_i is the number of ratings in category i.

1 <= k' <= k, where k is the number of available categories.

k' may be thought of as the "effective" number of categories
over which the ratings are uniformly distributed.

But note that the categories are treated as unordered.
.

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