Null Hypothesis

Defining the Null Hypothesis

The alternative hypothesis is a statement of the relationship between variables or differences between groups. In contrast, the null hypothesis is a statement that there is no relationship between variables or no differences between groups. A null hypothesis is at once a point hypothesis and a nil hypothesis. A point hypothesis predicts that a parameter will take on a specific numerical value. A nil hypothesis states that the specific predicted numerical value will be zero.

Very rarely do researchers wish to show that two variables are not correlated or that two groups are exactly the same; indeed, usually researchers are attempting to show that relationships do exist between variables. The question that arises is why would researchers direct their focus toward the hypothesis that no relationship exists between variables. The answer lies within two interconnected philosophies.

The first is a concern that statistical tests must address an exact, precise hypotheses. Alternative hypotheses rarely contain this level of precision. For example, an alternative hypothesis may be that groups will vary on dependent variable. However, the magnitude of this discrepancy may be unknown. This instability in the alternative hypothesis makes it difficult to directly test. On the other hand, the null hypothesis offers an extremely precise formulation—the relationship between two variances is either zero or it is not. Thus, statisticians such as R. A. Fisher argued that to introduce precision into statistical testing, the focus of tests should be on the null hypothesis.

Beyond the concern regarding precision, the widespread adoption of null hypothesis may also have come about due to a philosophical focus on falsification. Both Fisher and Karl Popper argued that hypotheses are only falsifiable, never confirmable. The convergence in the late 1940s of Popperian social scientific philosophy and Fisherian statistical philosophy regarding the goal of science and statistical analyses as falsifying precise statements led to the widespread adoption of null hypothesis significance testing.

Popper’s philosophy, while widely adopted by social scientists, presents a quandary for those putting forth hypotheses regarding positive relationships between social variables. Researchers are generally not interested in falsifying these research hypotheses but rather in searching for evidence that supports the hypothesis. Fisher’s null hypothesis, although developed prior to Popper’s theoretical treatise provided an elegant solution. Researchers could propose a precise null hypothesis that the relationship between two variables is zero. They could then falsify that hypothesis by showing conflicting evidence (i.e., the two variables do show some level of correlation, at least within a given sample). Repeated falsification of the null hypothesis in multiple samples could provide further support for the possibility that the alternative hypothesis does exist. Nevertheless, the alternative hypothesis is never fully proven but rather evidence compiles suggesting the null hypothesis should be rejected.

...