Not Rejecting Ho Doesn't Mean It's True
In Chapter 7, we explained why a null hypothesis that is not rejected should not be considered to be true. Researchers sometimes forget this important point, especially when they compare groups in terms of pretest means or otherwise compare two groups so as to evaluate a research hypothesis that the groups do not differ. Excerpt 11.11 (presented earlier in this chapter) is a case in point.
In Excerpt 11.11 [not shown here], the null hypothesis associated with the F-test comparison of the male and female samples was: Ho: m1 = m2, with each ,m representing the mean "age" of each of the two populations. If that null hypothesis had been set up to say that the female population was, on the average, two years older than the male population, a fail-to-reject decision also would have been reached. That is also what would have happened if Ho had specified a one-year difference or a three-year difference. Since the data support multiple null hypotheses that could have been set up (and that are in conflict with each other), there is no scientific justification for believing that any one of them is right while the others are wrong.
(From Chapter 11, pp. 314-315)
Copyright © 2012
Schuyler W. Huck