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If it were up to me, statistical hypothesis inference testing would be entirely replaced by confidence intervals. Both methods provide exactly the same information, however:
- Confidence intervals are graphical
- Confidence intervals are able to compare more than two hypotheses
- In any real-world situation the null hypothesis is always false. If your sample size is large enough you will always reject the null hypothesis. This often leads to positively silly behavior, such as many government regulations. Newspaper headlines are even sillier.
- The null hypothesis (literally, the hypothesis that there is no difference) is boring and uninteresting. Hypothesis testing promotes poor science by encouraging researchers to run one experiment and compare the results to this boring alternative. It would generally be better practice to develop and compare several hypotheses with each other.
- Confidence intervals are less confusing to students, lay persons, and quite frankly most statistics instructors
If you do some research you’ll find quite a body of literature complaining about the hypothesis testing approach. This is my small contribution to that cause.