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We will discuss this in the context of (a) studies involving a comparison of two or more treatments such as in a clinical trial and (b) observational studies∗ . CLINICAL TRIALS Usually one wishes to compare two or more treatment groups where one (or more) of the treatment groups may serve as a control group(s). This is generally done in other medical specialties by either (a) randomly assigning treatments to different groups of individuals or (b) assigning both treatments to the same individual at different points in time using a crossover design and making intra-individual comparisons.

If dL,α/2 > 0, then H0 is contradicted with respect to δ > 0; if dU,α/2 < 0, then H0 is contradicted with respect to δ < 0; and if dL,α/2 0 dU,α/2 , then H0 is not contradicted and δ is interpreted as being near 0 in the sense of the confidence limits (dL,α/2 , dU,α/2 ). When support for δ > 0 is the objective of an investigation, the cost for the two-sided confidence interval’s or test’s additional capability for distinguishing between δ < 0 or δ near 0 is either reduced power for the same sample size or increased sample size for the same power.

58, 527–536. 23. Robinson, D. R. 492–495. (1983). Biometrika, 70, 24. Rodman, L. (1978). Ann. , 6, 491–498. 25. Rothschild, M. (1974). J. Econ. Theory, 9, 185–202. 26. Smith, C. V. and Pyke, R. (1965). Ann. Math. , 36, 1375–1386. 27. Sobel, M. and Weiss, G. H. (1970). Biometrika, 57, 357–365. ONE-SIDED VERSUS TWO-SIDED TESTS correspondingly smaller sample size becomes preferable. Thus, both one-sided tests and two-sided tests are useful methods, and the choice between them requires careful judgment.

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