Why the Null Hypothesis is Not Accepted (3 of 5)
One experiment might provide data sufficient to reject the null hypothesis, although no experiment can demonstrate that the null hypothesis is true. Where does this leave the researcher who wishes to argue that a variable does not have an effect? If the null hypothesis cannot be accepted, even in principle, then what type of statistical evidence can be used to support the hypothesis that a variable does not have an effect. The answer lies in relaxing the claim a little and arguing not that a variable has no effect whatsoever but that it has, at most, a negligible effect. This can be done by constructing a confidence interval around the parameter value.
Consider a researcher interested in the possible effectiveness of a new psychotherapeutic drug. The researcher conducted an experiment comparing a drug-treatment group to a control group and found no significant difference between them. Although the experimenter cannot claim the drug has no effect, he or she can estimate the size of the effect using a confidence interval. If µ1 were the population mean for the drug group and µ2 were the population mean for the control group, then the confidence interval would be on the parameter µ1 - µ2.