Reject the Null or Accept the Alternative? Semantics of Statistical Hypothesis Testing
In a quantitative dissertation, you likely create 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 states that a difference exists (e.g., ‘arts majors and science majors have different IQs’).
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. Justifying a study is difficult without a reason to believe that differences or relationships exist between your variables. Researchers set up studies to provide evidence that the null hypothesis is ‘wrong’ and 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. People may become confused about what words to use and how to phrase statements. 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, you generally reject the null hypothesis because you found evidence against it. This statement is often sufficient, but some reviewers may also want a statement about the alternative hypothesis. In this case, you could support the alternative hypothesis. I personally avoid saying ‘I accepted the alternative hypothesis’ because this implies I have proven it 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 ‘you did not reject the null hypothesis’ or ‘you failed to reject the null hypothesis’ because you did not find evidence against it. You should not accept the null hypothesis because your study does not aim to prove either the null or alternative hypothesis. 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 lacks strong enough evidence to prove the defendant committed the crime, the court judges the defendant as ‘not guilty’ rather than ‘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, you design your study 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.