The love of ratios

Why do ratios occur so often in junk science? The answer is simple they multiply the apparent effect by a factor that is always greater than one and is actually four where the results are least significant.

Taking a simple numerical example:

If the proportion of, say, boys to girls is even, then out of 100 children we have 50 boys and 50 girls and the ratio is 50/50 which is 1. If we have one extra boy per hundred, however, we have to have one less girl to make up the total, so the ratio now becomes 51/49 or 1.04. Thus the proportion has changed by 1%, while the ratio has changed by 4%.

 

Mathematical explanation

The proportion to ratio conversion is a special case of the bilinear transformation:

and the slope is given by

As the proportion varies from 0 to 1, the ratio varies from 0 to infinity, while the slope varies from 1 to infinity. Thus the change in the ratio is always bigger than the change in the proportion. At the neutral (or agnostic) point, the proportion is 0.5 and the ratio is 1, but the slope is 4.

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