Sample Size: A vendor processes 900,000 claims per month....

[skyguy]

Ok, several have been helpful on here getting me through my recent stats class . . . now it's time to apply a real world application.

In the class I'm in, we learned how to compute sample size, etc - but the problem was, several key factors for solving the equation were given. Now, out in the real world, I struggle with how to apply some of this (and get the numbers to plug in to the formulas).

Here's the gig.

I manage a vendor who pays claims. We are looking to pull a statiscally valid sample (would like one at a 95% confidence level, and one at a 99% confidence level) to see if the claim paid correctly. This will be binomial, as either the claim paid correctly, or it didn't - no credit for a good try.

The vendor currently processes about 900,000 claims per month. I don't have a varience, standard deviation, etc at this point.

Can somebody help me get started here?

 

[JohnM]

Since you want to estimate the percentage of correctly-paid claims, the required sample size formula is slightly different - you don't need a variance or standard deviation, just an initial estimate of how accurate you think the vendor is.

n >= ((p*q)/d^2) * Z^2

where p is the percentage of correct claims, q=1-p, d is the margin of error you want (how close to the actual percentage do you need or want to be), and Z is the z score for the desired level of confidence (=1.96 for 95% and 2.576 for 99% confidence).

If you have absolutely no idea how accurate the vendor is, a good rule of thumb is to set p = 0.5, which will end up giving you the maximum sample size for a given d and Z.

 

[JakeD]

Re: Sample Size: A vendor processes 900,000 claims per month

Ok, several have been helpful on here getting me through my recent stats class . . . now it's time to apply a real world application.

In the class I'm in, we learned how to compute sample size, etc - but the problem was, several key factors for solving the equation were given. Now, out in the real world, I struggle with how to apply some of this (and get the numbers to plug in to the formulas).

Here's the gig.

I manage a vendor who pays claims. We are looking to pull a statiscally valid sample (would like one at a 95% confidence level, and one at a 99% confidence level) to see if the claim paid correctly. This will be binomial, as either the claim paid correctly, or it didn't - no credit for a good try.

The vendor currently processes about 900,000 claims per month. I don't have a varience, standard deviation, etc at this point.

Can somebody help me get started here?

To start, you are looking for a confidence interval on your sample estimate of the proportion \(\displaystyle p\) of claims correctly paid. A confidence interval requires two things: margin of error and a level of confidence. For example, you want to be 95% confident the estimated proportion is within 3 percentage points of the true value. 3 percentage points is the margin of error.

To calculate the confidence interval for a sample of size \(\displaystyle n\), you should use the normal approximation to the binomial distribution. The standard deviation to use will be \(\displaystyle \sqrt{p(1-p)/n .\) For a 95% confidence level using the normal distribution, the confidence interval is \(\displaystyle p \pm 1.96\sqrt{p(1-p)/n}.\) For a margin of error of 3%, you want to set \(\displaystyle n\) so that \(\displaystyle 1.96*sqrt{p(1-p)/n} = .03.\) Since you don't have an estimate of \(\displaystyle p\) at this point, the most conservative thing to do is put \(\displaystyle p = .5,\) which produces the largest sample you will need.

So for 95% confidence level and 3% margin of error, the required sample size is \(\displaystyle n = .5(1-.5)1.96^2/.03^2 = 1067.\)

I haven't explained every step here, but to solve this problem, you should have been introduced to these concepts in your stat class. Good luck!