Hypothesis Testing Part I

Mather, K.

“A hypothesis can never be proved or disproved by a test of significance. If the data do not show a significant deviation from expectation they agree with the hypothesis, but they may also agree with several other hypotheses giving closely similar expectations. The simplest or most relevant hypothesis is considered and is not discarded if the data agree with it, irrespective of how many more complicated hypotheses are also in agreement with observation....

If the data show a high deviation from the expected segregation they do not generally disprove the hypothesis; they only make it a more or less unlikely one. In the case considered above, when only one family was grown, a deviation which would be exceeded or equaled once in twenty trials was found. The hypothesis is then rendered unlikely as it could account for such a family only once out of twenty times. When twenty families are grown it can account for one such family in each trial and is not unlikely.”

Mather, K. 1963. The Measurement of Linkage in
       Heredity. 2^nd ed. John Wiley and Co., New York.

There is a degree of uncertainty associated with statistical tests. We might make the wrong decision because the observed sample was an unusual one. Failure to reject Ho does not prove Ho is true.