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>They could simply be understood to be saying that the two groups must be similar enough to not have ruled out the null hypothesis in their study The groups ne

>They could simply be understood to be saying that the two groups must be similar enough to not have ruled out the null hypothesis in their study The groups need not be similar to fail to rule out the null. It can also be that the measurements are too noisy and too few. Also on the flip side, if you do reject the null, it doesn't mean the the groups are different. It could also be that you have so many measurements that you are picking up tiny biases in your experiment or instruments. Null hypothesis testing is almost always too weak of a test to be useful.

BenoitEssiambre 8y ago
To add to this, the main problem with null hypothesis testing IMO is that mathematically you are comparing a infinitesimally small hypothesis: effect exactly equals 0.000000000000... to an infinitely large one: effect is somewhere between 0.00000...00001 and infinity. A tiny effect is very easy to reject (p<0.0000...000001). I can tell you before running the experiment that any two objects close enough for long enough to be in each other's light cone have at least a tiny effect on each other. The null hypothesis is hereby rejected for most anything relevant to humans. No need to calculate p-values. Just reference this comment.