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Traditionally, statisticians have used a "cut-off" probability level of 5%.
If the probability of obtaining a certain set of results is less than 5% (given the null hypothesis), then scientists and statisticians have agreed that it is reasonable to reject the null hypothesis.
Schachtman: Statisticians and careful scientists are well aware of the fallacy of embracing the so-called null hypothesis of no association from a study that has not found a statistically significant disparity.
That's the trap that judges, lawyers, and even statisticians fall into.
But there has been a lot of writing on this issue, going back at least to the great statistician, Sir Ronald A.
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