Null and Alternative Hypotheses

Stating null and alternative hypotheses has become one of the basic cornerstones of conducting epidemiological research. A hypothesis is typically defined as a tentative proposal or statement that explains certain observations or facts and is testable by further investigation. Testing [Page 749]hypotheses allows researchers to assess scientifically whether the explanation in question can be falsified. Critical to this process is the idea that, in research, it can never be directly proven that a proposition is true. To do so would imply that the results of a single study would hold across all time, all persons, and all cultures. Therefore, falsification of the null hypothesis has become the basis of scientific investigation as currently practiced.

Researchers approach the idea of ‘truth’ indirectly by developing and testing null and alternative hypotheses. Typically, null and alternative hypotheses are stated so that they are mutually exclusive and exhaustive. The null hypothesis, written as H0, is the statement that the researcher hopes to reject. Specifically, it is a claim about a population parameter that is assumed to be true until it is declared false. Many times, but not always, the null hypothesis represents a null effect (i.e., there is no relationship between the independent and dependent variable). For example, in a cohort study examining tobacco use and lung cancer, the H0 might be that smoking status is not significantly associated with the development of lung cancer. The alternative hypothesis, denoted as HA or H1, is the basic statement that is tested in the research; in the tobacco study example, the HA might be that smoking status is significantly associated with the development of lung cancer. After stating the null and alternative hypotheses, researchers aim to find evidence to reject the null hypothesis; otherwise, they would state that they ‘failed to reject’ the null. If researchers do find enough evidence to reject the null hypothesis, they still might not be able to theoretically ‘accept’ the alternative hypothesis. This is because, in theory, the methods of hypothesis testing are probabilistic, and by definition, probability includes some level of uncertainty. This idea is similar to the guilty/not guilty decision in our judicial system. In finding a defendant not guilty, the jury determines that there is insufficient evidence to find the person guilty; this is not the same as claiming that he or she is innocent. However, in practice, when researchers reject the null hypothesis in their study, they generally do ‘accept’ the alternative at least under the conditions of their specific experiment.

Because hypotheses are developed to be testable, they must be stated in a clear, unambiguous manner. The alternative hypothesis might describe a relationship with a specific direction (e.g., μ ≥ 100 or ‘smoking status is positively associated with the development of lung cancer’) or could relate to the statistical test being employed (e.g., the odds ratio ≠ 1or β ≠ 0).

Conversely, the null hypothesis could indicate no effect (e.g., smoking status is not associated with the development of lung cancer or β = 0) or could describe the opposite direction of what researchers are investigating (e.g., μ < 100). It is important to note that when writing null or alternative hypotheses, the population parameters (e.g., μ or p) are used instead of the sample statistics (e.g., x or p∘) since researchers aim to make inferences to the population level.

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