Tests of Quantitative Laws

In Chapter 1 1, the N-of-1 designs and tests wer e presented as means of detecting causal relationships between certain treatment manipulations and certain types of r esponses. However, N-of-1 experimentation for assessing theories should go beyond simply testing the null hypothesis of no dif ferential treatment effect and the same is tr ue of multiple-subject experiments. An investigator can be certain of the existence of a causal r elationship between a treatment and a r esponse but may question a law (or model) of that causal r elationship. Such laws may be quantitative and this chapter concerns randomization tests of those laws. (Although some r elationships that formerly were called laws ar e now called models, that distinction will be ignored and all tests of quantitative relationships between treatments and effects will be called tests of quantitative laws.)

Quantitative laws in the physical sciences, such as the law of gravity or Boyle’s law, have an acceptance that is not characteristic of quantitative laws for biological organisms. This chapter concerns the testing of quantitative laws regarding the relationship between treatment magnitudes and quantitative responses of subjects. The randomization tests to be discussed test the null hypothesis that the r elationship between treatment and response measurements is that specified by a particular law , and r ejection of the null hypothesis implies acceptance of the complementary hypothesis that the law did not hold in the experiment that was conducted. Because the null hypothesis concerns the lawful relationship applying to all experimental units, the complementary hypothesis is that the law does not hold for one or mor e experimental units.