A multiple test for comparing two treatments with control: Interval hypotheses approach

In biological experiments, multiple comparison test procedures may lead to a statistically significant difference in means. However, sometimes the difference is not worthy of attention considering the inherent variation in the characteristic. This may be due to the fact that the magnitude of the change in the characteristic under study after receiving the treatment is small, less than the natural biological variation. It then becomes the job of the statistician to design a test that will remove this paradox, such that the statistical significance will coincide with the biological one. The present paper develops a multiple comparison test for comparing two treatments with control by incorporating within-person variation in forming interval hypotheses. Assuming common variance (unknown) for the three groups (control and two treatments) and the width of the interval as intra-individual variation (known), the distribution of the test statistic is obtained as bivariate non-central t . A level f test procedure is designed. A table of critical values for carrying out the test is constructed for f = 0.05. The exact powers are computed for various values of small sample sizes and parameters. The test is powerful for all values of the parameters. The test was used to detect differences in zinc absorption for two cereal diets compared with a control diet. After application of our test, we arrived at the conclusion of homogeneity of diets with the control diet. Dunnett's procedure, when applied to the same data, concluded otherwise. The new test can also be applied to other data situations in biology, medicine and agriculture.