28.7 About writing conclusions

When reporting a conclusion, three things should be included:

1. The answer to the RQ;
2. The evidence used to reach that conclusion (such as the \(t\)-score and \(P\)-value, clarifying if the \(P\)-value is one-tailed or two-tailed); and
3. Some sample summary statistics (such as sample means and sample sizes), including a CI (which indicates the precision with which the statistic has been estimated).

Conclusions can never be made with certainty from one sample. Partly this is because a sample has been studied, while the RQ asks about the whole population: The entire population wasn’t studied.

For this reason, care must be taken when answering the RQ. A hypothesis test never proves. anything: It might conclude that evidence exists (perhaps weak evidence; perhaps strong evidence) to support the alternative hypothesis. Of course, there may be no evidence to support the alternative hypothesis either.

Since the value of the parameter in the null hypothesis is assumed true, the onus is on the data to provide evidence to refute this default position. For this reason, conclusions are worded in terms of the level of support for the alternative hypothesis.

Conclusions are always made in terms of how much evidence supports the alternative hypothesis. Hypothesis tests assume the null hypothesis is true, so the onus is on the data to provide evidence in support of the alternative hypothesis.

Think 28.1 (Conclusions) What is wrong with the following conclusion?

The evidence proves that the mean internal body temperature has changed.