# Proportions Test for Dollars

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• #54277

Johnson
Participant

Would it ever be acceptable/correct to use a 2 proportions test for dollars. For example if I wanted to test the percent of ‘leakage dollars’ out of ‘total dollars’ both pre and post improvement. A mean or median test does not provide the percentage perspective that the company is interested in? Athough dollars are continuous data in this case, I am categorizing them as leakage or non leakage.

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#194557

Johnson
Guest

Thank you!

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#194598

Jeff Marth
Participant

Will it work, yes. However, a better way to run it is by making each day a data point (percent) and running it as a standard hypothesis test (ANOVA, 2-sample T, etc.) for the before/after time periods.

Based on what you explained, you could run the before and after (columns) with the number of days there is/isn’t leakage (rows) or acceptable/unacceptable levels of leakage.

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#194629

Johnson
Participant

When I run the comparisons as percentages both set of data are non normal, so I I am left using the Mann Whitney test for medians. Because a high percentage of the claims in the sample do not have any leakage, the medians become zero.

Regression shows that the leakage varies by size of the claim, but it is not a strong predictor (p-value of .001 and R-Sq (adj) of 29.3.)

The challenge is that there is a large improvement in dollars between the two years, but a median test is not picking it up…..that is why I was asking about the 2 proportions test.

I am open to a better way…..Thanks!

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#194631

Robert Butler
Participant

You might want to go back and take a look at that regression again.

Some thoughts:

What does the relationship between leakage and size of claim look like with just the accounts that have leakage?

What does the residual pattern look like for the regression when run against all of the data? – patterns, clusters, banding, etc.

Same question for just the leakers

Is the percentage of non-leakers the same before and after?
Is the kind of leaker account the same before and after?
If the claims have some kind of classification are there any differences in proportions of claims within classification before and after?
If the claims have some kind of classification are there any differences in amounts leaking before and after?
If the claims have some kind of classification what happens to your regression when you include a dummy variable for claim type when running the analysis of leakage vs. claim size?

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#194643

Johnson
Participant

1) Without the files that have no leakage, the p-value is .002 with an R-Sq (adj) of 51.7%, so there is a relationship, but still not a strong predictive capability. The residual pattern is acceptable…no ‘unusual’ patterns…. and the residuals are ‘close’ to a normal dist.
2) The percentage of files with leakage is lower after the improvement, but not a statistically significant number. (p-value of .25) That is what is so challenging…… there was a 10%+ improvement in the dollar impact of the improvement, which is big money. Just doing a hypothesis test on the criteria ‘is there is leakage or not on a claim’, does not capture, the company’s ‘true interest’ of the dollars leakage. The company would not be as concerned if 75% of the claims had leakage if the dollar amount were very minor. On the other hand if 40% of the claims have higher dollar values of leakage, then that leakage significantly impacts loss ratios. This was the rationale for the original question, of using the 2 proportion test for leakage vs. non leakage claim dollars……To focus on the dollars vs. the claimsand as indicated above a median test does not capture a significant improvement due to the number of claims with no leakage.
3) The scope of the project has already been narrowed to one category of claim so there would not be a quick or easy ability to further separate by a type of classification.
I realize that the most highly recommended answer is to continue to collect larger sample sizes over time, but this audit process incurs external cost for each claim reviewed so there is a cost to larger sample sizes.
Thanks so much for the great input and discussions.

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#194644

Robert Butler
Participant

So what was the result of the test of the two proportions?

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#194647

Johnson
Participant

Using ‘dollars’ in a 2 proportions test (accurately assigned claim dollars vs. leakage dollars), the p-value is .000 showing a 10.5% improvement (pre vs. post improvement) (valued at \$600,000+)

Using the 2 proportions test for ‘claims having leakage or not having leakage’ the p-value is .25 and does not show statistically significant improvement. But as described about, the issue is not so much if the claim has leakage or not but what magnitude is the leakage \$.

This brings us back to the original Q&A, I think….. Is a 2 proportions test ever acceptable/correct for continuous data like dollars. (pre and post)(leakage dollars vs. non leakage dollars) I know the 2 proportions test is not optimal, but I am not able to identify another test that truly measures the improvement in leakage dollars. Thanks again!

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#194648

Johnson
Participant

Running a 2 x 2 chi square test, I also get a p-value of .000.

Thanks!

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