Reject the Null or Accept the Alternative? Semantics of Statistical Hypothesis Testing

If you are conducting a quantitative study for your dissertation, it is likely you have created a set of hypotheses to accompany your research questions. It is also likely that you have constructed your hypotheses in the “null/alternative” format. In this format, each research question has both a null hypothesis and an alternative hypothesis associated with it.

Let’s say, for example, that you were conducting a study with the following research question: “is there a difference in the IQs of arts majors and science majors?” The null hypothesis would state that there is no difference between the variables that you are testing (e.g., “there is no difference in the IQs of arts majors and science majors”). The alternative hypothesis would state that there is a difference (e.g., “there is a difference in the IQs of arts majors and science majors”). Typically, the researcher constructs these hypotheses with the expectation (based on the literature and theories in their field of study) that their findings will contradict the null hypothesis, and in turn support the alternative hypothesis. For instance, in our IQ example we may expect to see a difference between arts majors and science majors. Generally, it is difficult to justify conducting a study if you have no reason to believe that differences or relationships exist between your variables. Thus, studies are set up to provide evidence that the null hypothesis is “wrong,” and that the alternative hypothesis is “correct.”

Setting up the null and alternative hypotheses is usually a pretty simple task. However, students often run into trouble when they finish their analysis and must present their results using the “null/alternative” language. Confusion may arise over what words to use and how statements should be phrased. For your dissertation, some of this may come down to your reviewers’ preferences. However, below are some basic guidelines you may follow.

First, let’s assume you ran your analysis and your results were significant (e.g., arts majors and science majors had different IQ levels). In this case, it is generally appropriate to say “the null hypothesis was rejected” because you found evidence against the null hypothesis. This statement is often sufficient, but sometimes reviewers want you to go further and also make a statement about the alternative hypothesis. In this case, you could say “the alternative hypothesis was supported.” Personally, I would avoid saying “the alternative hypothesis was accepted” because this implies that you have proven the alternative hypothesis to be true. Generally, one study cannot “prove” anything, but it can provide evidence for (or against) a hypothesis. Additionally, the concept of challenging or “falsifying” a hypothesis is stronger than “proving” a hypothesis (for more in-depth discussion on this philosophy of science see Popper, 1959). Again, it is worth noting that your reviewers may have different preferences on the exact language to use here.

Now let’s consider the flip side and assume your results were not significant (e.g., there was no significant difference in IQ between arts majors and science majors). Here you could say “the null hypothesis was not rejected” or “failed to reject the null hypothesis” because you did not find evidence against the null hypothesis. You should NOT say “the null hypothesis was accepted.” Your study is not designed to “prove” the null hypothesis (or the alternative hypothesis, for that matter). Rather, your study is designed to challenge or “reject” the null hypothesis. People often compare this idea in statistical hypothesis testing to how verdicts are made in criminal court cases. If the prosecution does not have strong enough evidence that the defendant committed the crime, the defendant is judged as “not guilty” rather than as “innocent.” In other words, the court can provide evidence of guilt, but it cannot prove innocence. In the same way, a statistical test cannot prove the null hypothesis, but it can provide evidence against it. As for the alternative hypothesis, it may be appropriate to say “the alternative hypothesis was not supported” but you should avoid saying “the alternative hypothesis was rejected.” Once again, this is because your study is designed to reject the null hypothesis, not to reject the alternative hypothesis.

These are just some general tips to help guide the writing of your statistical findings. However, always defer to the requirements of your reviewers and your school when in doubt.

References

Popper, K. (1959). The logic of scientific discovery. London: Hutchinson.