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My old biophysicist friend told me that they used to joke that all effects are always 20%. For instance, they'd test a diet, and find that eating less salt increases life span by 20%. If they test eating less cucumbers it'd be the same 20% and so on. Yet if you eat less salt and cucumbers the life span wouldn't increase by 40%, it'd still be 20%.

Here, 20% is the arbitrary number, but the idea's the same. The way they calculate effect sizes in some fields would lead to this effect where the effect sizes are not additive, although it appears they should be. I think biology's prone to this thing, so I made up my example from the dietary "science".

Here's two example:

Now, if I eat 40% less food and exercise more, I'm going to live 24.5 years longer? Nope.

It's not a matter of my silly interpretation of the findings. I think it's research itself has this issue, where all effects are always reported with ridiculous effect sizes like above. If life expectancy was so easy to extend why aren't we living 142 years already? It took 52 years to bump France's life expectancy from 70 to 83 years. It's pretty fast, but not as fast at the above and similar research would make it look like.

Aksakal
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  • To what "fallacy" do you refer? – whuber Oct 12 '15 at 21:09
  • Maybe "fallacy" is not a good term here. It's the problem where researchers come up with effect sizes that are not additive, but are presented as if they were. Like in the example with diets or healthy habits. If you implement all of them you should live forever. – Aksakal Oct 12 '15 at 21:17
  • in addition to non-additivity of effects, a lot of these results are also subject to the irreproducibility problems of multiple comparisons, p-hacking/-fishing, [high false discovery rate due to low power](http://stats.stackexchange.com/questions/176384/do-underpowered-studies-have-increased-likelihood-of-false-positives), etc etc ... – Ben Bolker Oct 12 '15 at 23:54

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