[R] how to prove that the factor makes no difference

[Dieter Menne]

Xiang Gao-2 wrote:
> 
> How can we prove that the treatment did not make any difference in the
> amount of protein A. In another word, Pre- and post- are the same.
> 

There is no way to "prove" that there is no difference. While you could use
some alternative hypothesis, people rarely understand the combination of an
assumption in mm and a p-value. 

The preferred way in medical context is to quote the 90% confidence interval
of the difference. When you say "The confidence interval of the difference
between implant type A and B is -0.2 to 0.3 mm of new tooth bone growth",
you give a hint about the reliability of your measurement, and leave it to
the reader to judge if this is medically relevant. The story is that the new
treatment with only 5% probability leads to 0.2 mm less growth (pardon,
strictly not correct, but you must tell the story ...).

It might be relevant for dental implants, and not relevant for the thigh.

Dieter


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