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From a reply by John

What is true is that trivially small effects can be found with very large sample sizes. That does not suggest that you shouldn't have such large sample sizes. What it means is that the way you interpret your finding is dependent upon the effect size and sensitivity of the test. If you have a very small effect size and highly sensitive test you have to recognize that the statistically significant finding may not be meaningful or useful.

Why "If you have a very small effect size and highly sensitive test you have to recognize that the statistically significant finding may not be meaningful or useful"?

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  • $\begingroup$ The other answers in the thread you reference appear to answer this question. $\endgroup$ – whuber Aug 18 '13 at 14:36
  • $\begingroup$ The question confuses two quite different matters: whether a particular finding is useful (John's comment) and whether the test that produces that particular finding is useful (your question). For example, a search for buried treasure is useful if some is found and useless otherwise. There is no need to confuse method with result. Any way, that detecting very small effects may not be meaningful or useful seems to be John's main point here, and it's neither obscure nor contentious. $\endgroup$ – Nick Cox Aug 18 '13 at 14:37
  • $\begingroup$ @whuber: Could you point out which are the other answers in the thread? $\endgroup$ – Tim Aug 18 '13 at 14:39