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I have a database of companies for which I know their sizes (how many people work there) and how many people have an accident. An example is:

Enterprise size     |     People with accidents    |   Percentage
10                                 3                       .33
100                                15                      .15
1000                               12                      .12

I want to estimate if there is a correlation between the size of the enterprise and the People with accidents. If I run the test with corr(size, people) I get 0.3. If I run the test with corr(size, perc) I get -0.69.

Anyone can shed light on this difference? Is the second method wrong? Thanks

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  • $\begingroup$ Your "percentage" is a proportion. @Sympa's answer fixes that quietly. $\endgroup$
    – Nick Cox
    Commented May 2, 2020 at 17:25

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The first correlation is positive, but it does not tell you anything. It is inevitable that a larger enterprise with a larger workforce will have a larger number of people with accidents.

The second correlation is actually a lot more informative. It suggests that larger enterprises are safer with a smaller accident rate.

If you look at your data this is what you see. An enterprise with just 10 employees has 3 accidents for an accident rate of 3/10 = 33%. That enterprise is a lot less safer than the second one which has 100 employees and only 100/15 = 15% accident rate.

In my mind, your first correlation is somewhat "wrong" because it does not scale the number of accidents by the number of employees. The second correlation is scaled and therefore much more informative.

One thing to watch out for is that none of your correlations are statistically significant because your sample size, just three data points, is way too small to overcome the small sample error syndrome.

To infer some more reliable conclusion, I suspect you would need at least 10 if not 20 companies of each size to derive any reliable assessment of the relative risk of working for companies of different size.

Watch out for qualitative factors, so that your companies are very similar. If you compare small companies of industrial scuba divers vs. large retailers, the small companies will look artificially riskier. You would have to compare small retailers vs. large retailers to get a better assessment.

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  • $\begingroup$ Thanks for the answer. I indeed have millions of samples, the one posted was only to explain the problem. Thanks again $\endgroup$
    – SavioD
    Commented May 2, 2020 at 17:31

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