Page "Null hypothesis" Paragraph 41

Most statisticians believe that it is valid to state direction as a part of null hypothesis, or as part of a null hypothesis / alternative hypothesis pair.

However, the results are not a full description of all the results of an experiment, merely a single result tailored to one particular purpose.

For example, consider an H < sub > 0 </ sub > that claims the population mean for a new treatmemnt is an improvement on a well-established treatment with population ( known from long experience ), with the one-tailed alternative being that the new treatment's.

If the sample evidence obtained through x-bar equals − 200 and the corresponding t-test statistic equals − 50, the conclusion from the test would be that there is no evidence that the new treatmnent is better than the existing one: it would not report that it is markedly worse, but that is not what this particular test is looking for.

To overcome any possible ambiguity in reporting the result of the test of a null hypothesis, it is best to indicate whether the test was two-sided and, if one-sided, to include the direction of the effect being tested.