Measuring "divisiveness" in film scores? I have a a set of films, and for each films, a set of reviews - varying between 1 review and several hundred reviews for each film. Each review has a star rating from 1 to 5. 
I am using Wilson's confidence interval for a Bernoulli parameter to estimate whether the film is likely to be good or not, taking into account the number of ratings (I just count any 3+-star reviews as positive, anything else as negative). 
However, I'd also like to figure out how likely to be divisive a film is, given the number of ratings. 
So a film with 200 reviews - 100 1-star reviews and 100 5-star reviews - is more likely to be divisive than a film with 2 reviews = 1 1-star review and 1 5-star review. However, both films clearly have the same standard deviation of ratings.
I don't think I can use the same Wilson's confidence interval calculation that I'm using for 'goodness', since the ratings aren't Bernoulli in nature (EDIT: I'm assuming they are normal). 
Does anyone have any ideas on how to measure 'divisiveness' in this way?
 A: What you calls divisiveness seems analogous to what in ecology (and other fields) is called  diversity, as in biodiversity.  There are many possible measures, much used ones is entropy and the Simpson index.  There are many posts on this site, some is

*

*Statistical test to perform on species diversity / Simpson's diversity index


*How to measure the "well-roundedness" of SE contributors?
Now, the usual diversity indices takes the categories (in ecology, species) as categorical and treats them all the same. Applied to your application of "diviseveness" or "disagreement" it would treat probability vectors $(1/2,1/2,0,0,0)$ the same way as $(1/2,0,0,0,1/2)$, which is not appropriate. So we need to take into account distances among the rating scores, 4 and 5 being more similar that 1 and 5! That means to treat the rating scores as a metric space, and we can use the metric
$$ d(i,j)= \vert i-j \vert $$
and use the ideas outlined at How to include the observed values, not just their probabilities, in information entropy?
That can lead to (a version of) the Rao's quadratic entropy, with
$$ d(i,j)= 1- e^{\vert i-j \vert}
$$ as a measure of disagreement. A paper with theoretical studies of Rao's quadratic entropy.
Some numerical examples, in R:
 quadent( rep(0.2, 5))
          [,1]
[1,] 0.6403669
> quadent(c(1, 0, 0, 0, 0))
     [,1]
[1,]    0
> quadent( c(0.5, 0.5, 0, 0, 0))
          [,1]
[1,] 0.3160603
> quadent( c(0.5, 0, 0, 0, 0.5))
          [,1]
[1,] 0.4908422

