Lecture 3 - 2012 生物统计课件.pptxVIP

E. Non-Parametric Tests: Comparison of Medians (p.37)SAS: proc univariate Add a normal curve to histogram- Goodness-of-fit tests for a variety of distributions including the normal Normality testGeneral Characteristics:No assumption is made about the distribution of the variable (e.g., data do not need to be normally distributed). – distribution-freeApplicable to variables that are continuous, discrete, or ordinalHypotheses about medians, rather than means, are testedE. Non-Parametric Tests: Comparison of Medians (p.37)Non-parametric analog of the paired t-testAlso known as Mann-Whitney U testNotation: X is the variable under investigation in some populationPaired difference d = X2 - X1Let Md be the true (population) median of the difference dForms of hypotheses: H0: Md = 0H1: Md 0 (one sided alternative)H1: Md 0 (one sided alternative)H1: Md ? 0 (two sided alternative)Paired Samples: Wilcoxon Signed Rank Test (p. 37)Wilcoxon Signed Rank Test (Mann-Whitney U test)Test statistic: Compute the differences d = X2-X1 (for each observation)If d = 0, eliminate that data point from calculations and reduce n accordinglyRank the differences, ignoring the signs of the differences. If there are equal differences, average the corresponding ranks.Affix the sign of each difference to its rankCompute T = sum of the positively signed ranks, or the absolute value of the sum of the negatively signed ranks, whichever is smaller.If n 12: One-sided P-values are given in Table A.4 Two-sided tests, multiply P-values given in Table A.4 by 2.If N 12: Assume that T is approximately normal with mean ?T and standard deviation ?T and calculate a z-test defined as: P-values are obtained from Table A.1Wilcoxon Signed Rank Test (continued)Example 1: Wilcoxon Signed Rank Test (p.39)Research Question:“Does a pericardial tamponade affect blood flow of the left ventricle in anesthetized dogs? ”Design: measure coronary blood flow pre and post a pericardial tamponadeH0: Md = 0 vs. H1: Md