Alternative Hypotheses

Substantive or Conceptual Alternative

It is important to distinguish between the substantive (or conceptual, scientific) alternative and the statistical alternative. The conceptual alternative is that which is inferred by the scientist given a rejected null. It is an explanation or theory that attempts to account for why the null was rejected. The statistical alternative, on the other hand, is simply a logical complement to the null that provides no substantive or scientific explanation as to why the null was rejected. When the null hypothesis is rejected, the statistical alternative is inferred in line with the Neyman—Pearson approach to hypothesis testing. At this point, the substantive alternative put forth by the researcher usually serves as the “reason” that the null was rejected. However, a rejected null does not by itself imply that the researcher's substantive alternative hypothesis is correct. Theoretically, there could be an infinite number of explanations for why a null is rejected.

Example

An example can help elucidate the role of alternative hypotheses. Consider a researcher who is comparing the effects of two drugs for treating a disease. The researcher hypothesizes that one of the two drugs will be far superior in treating the disease. If the researcher rejects the null hypothesis, he or she is likely to infer that one treatment performs better than the other. In this example, the statistical alternative is a statement about the population parameters of interest (e.g., population means). When it is inferred, the conclusion is that the two means are not equal, or equivalently, that the samples were drawn from distinct populations. The researcher must then make a substantive “leap” to infer that one treatment is superior to the other. There may be many other possible explanations for the two means’ not being equal; however, it is likely that the researcher will infer an alternative that is in accordance with the original purpose of the scientific study (such as wanting to show that one drug outperforms the other). It is important to remember, however, that concluding that the means are not equal (i.e., inferring the statistical alternative hypothesis) does not provide any scientific evidence at all for the chosen conceptual alternative. Particularly when it is not possible to control for all possible extraneous variables, inference of the conceptual alternative hypothesis may involve a considerable amount of guesswork, or at minimum, be heavily biased toward the interests of the researcher.

A classic example in which an incorrect alternative can be inferred is the case of the disease malaria. For many years, it was believed that the disease was caused by breathing swamp air or living around swamplands. In this case, scientists comparing samples from two populations (those who live in swamplands and those who do not) could have easily rejected the null hypothesis, which would be that the rates of malaria in the two populations were equal. They then would have inferred the statistical alternative, that the rates of malaria in the swampland population were higher. Researchers could then infer a conceptual alternative—swamplands cause malaria. However, without experimental control built into their study, the conceptual alternative is at best nothing more than a convenient alternative advanced by the [Page 12]researchers. As further work showed, mosquitoes, which live in swampy areas, were the primary transmitters of the disease, making the swamplands alternative incorrect.

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