First, this section discusses whether rejection of the null hypothesis should be an all-or-none proposition. Then, it discusses how to interpret non-significant results; for example, it explains why the null hypothesis should not be accepted or should be accepted with caution. It also describes how a non-significant result can increase confidence that the null hypothesis is false.
Interpreting Significant Results
Some textbooks have incorrectly stated that rejecting the null hypothesis that two population means are equal does not justify a conclusion about which population mean is larger. Instead, they say that all one can conclude is that the population means differ. The validity of concluding the direction of the effect is clear if you note that a two-tailed test at the 0.05 level is equivalent to two separate one-tailed tests each at the 0.025 level. The two null hypotheses are then
If the former of these is rejected, then the conclusion is that the population mean for obese patients is lower than that for average-weight patients. If the latter is rejected, then the conclusion is that the population mean for obese patients is higher than that for average-weight patients.