# a problem with “Lower bound of Wilson score confidence interval”

Hi,

I am trying to calculate the 'Most helpful' review. I found a solution few days ago on Calculating the "Most Helpful" review

I have a new problem now..

Let's say I have two items. The first item has "480 people found this review helpful among 961 people". The second item has "3 people found this review helpful among 5 people".

first item: 480 people liked it, but 481 people didn't. second item: 3 people liked it, but 2 people didn't.

I personally think that the second item should have higher rank than the first item because more than 50% of people didn't like the first item.

When I use "Lower bound of Wilson score confidence interval for a Bernoulli parameter", I get the following value for the two items.

first: 0.467932469089
second: 0.230724282841


the first item has higher point than the second item.

Is this correct??

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I think the "solution" is wrong, just less (flagrantly) wrong than some other approaches. You are going to find some examples where you find this method to be unsatisfactory, and perhaps this is one of them. – Douglas Zare Mar 29 '11 at 9:26

This is an old question now but as I've been looking into this stuff tonight ...

You are calculating the confidence interval for a binomial distribution and using the lower bound as your "score" of helpfulness. A confidence interval defines a plausible range of values for the true mean given your observed values and sample size.

When the sample size is small (like just 5 people) this range will generally be larger as there is less confidence that the true mean has been observed. As such your lower bound could well be lower than the lower bound for another sample with a lower observed mean (like the first item in your example).

So yes, I think it probably is correct (although I haven't checked the answer myself!)

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