The Null Hypothesis
Recall that a hypothesis is is a testable conjecture. It is a claim or prediction that can, in principle be compared to existing or future observations. An example of a hypothesis might be:
Most listeners prefer familiar music over unfamiliar music.
It is common in empirical research to refer to the research hypothesis using the upper-case letter H. Since empirical studies often test more than one hypothesis, it is common to number the hypotheses. Even if there is only a single hypothesis, authors commonly still refer to it as H1.
H1. The use of rhyming words in musical lyrics increases the likelihood that listeners will understand the sung word.
Recall that refutation is easier than confirmation. It is easier to show that the statement “All swans are white” is wrong (by observing a single non-white swan) than to show that the statement is right (by observing all possible swans). This asymmetry is captured in our slogan: Aim not to be right, but to be not not right.
There are an infinite number of incorrect hypotheses, and most of these hypotheses are not interesting. Usually, a researcher is hoping that their hypothesis is correct. However, it is impossible to show that a hypothesis is true. It is easier to show that a hypothesis is incorrect. As a result, empirical researchers restate their hypothesis in a reverse formulation. Here is an example:
H0. The use of rhyming words in musical lyrics does not increase the likelihood that listeners will understand the sung word.
This “reverse formulation” of a hypothesis is referred to as the null hypothesis. The null hypothesis is abbreviated using the upper-case letter H followed by the subscript zero: H0. For convenience, it is often simplified to H0 without the subscript.
In empirical research, we rarely directly test the research hypothesis. Instead, we test the null hypothesis. Rather than testing the research hypothesis (and vainly hoping that it is “confirmed”), we test the null hypothesis (and hope that it is rejected). (Once again, we aim to be not not right, rather than aiming to be right.)
In analyzing our observations, we will use statistical methods to measure, not the probability that our research hypothesis is consistent with our data, but the probability that the null hypothesis is consistent with our data. If the probability is low, then we will conclude that the null hypothesis is inconsistent with our data. We will conclude that our data provides no reason to accept the null hypothesis. Having dismissed the null hypothesis, our research hypothesis will have survived the test. (“The best research invites failure.”)
In many books on statistics, the rejection of null hypothesis is considered grounds for “accepting the research hypothesis.” This is a old traditional formulation that should be avoided. A better formulation is the one given in the previous paragraph: having concluded that the data are not consistent with the null hypothesis, we will infer that the data are consistent with the research hypothesis. Said another way, we can claim that the research hypothesis has survived an empirical test.
Once again, in empirical research, we do not engage in “confirmation.” We never show things are “true.” Our data don’t “support” or “prove” or “demonstrate” anything. At best, we can claim that the data are consistent with the hypothesis.
So let’s review. Because refutation is easier than confirmation, we test hypotheses by attempting to refute them. The researcher reformulates the research hypothesis as the null hypothesis. Statistical methods are then used to calculate the probability that the data are consistent with the null hypothesis. If the probability is low, we conclude that the data are not consistent with the null hypothesis, and instead infer that the data are consistent with the reverse of the null hypothesis—namely, the research hypothesis. Traditionally, statisticians refer to this procedure as disproving the null hypothesis. However, good researchers avoid this language. Instead, we conclude simply that the data are not consistent with the null hypothesis—and conversely, that the data are consistent with the research hypothesis.