Timeline for Does the ratio fallacy apply when calculating a Pearson's correlation between one ratio variable and one absolute variable (no common term)?
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| Sep 19, 2014 at 11:23 | vote | accept | Dark | ||
| Sep 18, 2014 at 17:00 | history | edited | Rob Hall | CC BY-SA 3.0 |
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| Sep 18, 2014 at 14:05 | history | edited | Rob Hall | CC BY-SA 3.0 |
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| Sep 18, 2014 at 14:04 | comment | added | Rob Hall | I have amended the answer above to give a simulation example for the situation you are describing. The formula on Wikipedia contains the pairwise Pearson correlations r12, r14, r23, and r24. These would all be 0 for x1, x3 pairwise independent of x2, x4. Hence, the estimate for the correlation between x1/x3 and x2/x4 would also be 0. | |
| Sep 18, 2014 at 14:00 | history | edited | Rob Hall | CC BY-SA 3.0 |
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| Sep 18, 2014 at 13:28 | comment | added | Hong Ooi | Maybe you should have a closer look at that formula involving x1, x2, x3 and x4. Hint: consider what happens if $r_{ij} = 0$. | |
| Sep 18, 2014 at 13:06 | comment | added | Dark | @Hong Ooi: I'm not sure that's true. On the wikipedia page it reads "Pearson derived an approximation of the correlation that would be observed between two indices (x_1/x_3 and x_2/x_4), i.e., ratios of the absolute measurements x_1, x_2, x_3, x_4:" followed by some math and implication that this would commit the ratio fallacy as well. As I don't understand how that could be, I became worried that the same would apply in my case. I assume they also refer to independent variables x1 through x4. Why would the fallacy be relevant when it involves 2 ratios and not relevant with 1? | |
| Sep 18, 2014 at 12:54 | comment | added | Hong Ooi | The fallacy occurs because the ratios x/z and y/z are not independent of each other, due to the common denominator z. This is not the case with your data. | |
| Sep 18, 2014 at 12:42 | comment | added | Dark | Thank you for that explanation! I'm afraid x and y are not independent of each other though. They are each independent of z. Am I still in the clear in that case? | |
| Sep 18, 2014 at 12:32 | history | edited | Rob Hall | CC BY-SA 3.0 |
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| Sep 18, 2014 at 12:26 | history | answered | Rob Hall | CC BY-SA 3.0 |