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Hypothesis Testing I: Proportions¹

¹ From the Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, Mass (K.H.Z., J.R.F., S.G.S., C.M.C.T.); and Department of Health Care Policy, Harvard Medical School, 180 Longwood Ave, Boston, MA 02115 (K.H.Z.). Received September 10, 2001; revision requested November 8; revision received December 12; accepted December 19. Supported in part by Public Health Service Grant NIH-U01 CA9398-03 awarded by the National Cancer Institute, Department of Health and Human Services. Address correspondence to K.H.Z. (e-mail: zou@bwh.harvard.edu).

View larger version (18K): [in a new window]   Graph illustrates the normal distribution of the test statistic Z in a two-sided hypothesis test. Under H0, Z has a standard normal distribution, with a mean of 0 and a variance of 1. The critical values are fixed at ±1.96, which corresponds to a 5% significance level (ie, type I error) under H0. The rejection regions are the areas marked with oblique lines under the two tails of the curve, and they correspond to any test statistic lying either below -1.96 or above +1.96. Two hypothetical test statistic values, -0.5 and 2.5, result in not rejecting or rejecting H0, respectively.