医学统计学英文课件-Chi-squareTestforCat.pptVIP

* * * Chapter 6 ?2 Test for Categorical Variable Chi-Square Given a set of observed frequency distribution A1, A2, A3 … to test whether the data follow certain theory. If the theory is true, then we will have a set of theoretical frequency distribution: T1, T2, T3 … Comparing A1, A2, A3 … and T1, T2, T3 … 6.1 Basic logic of ?2 test Is this an even dice（ p. 117 ） Numbers： 1 2 3 4 5 6 Theoretical： Actual： 8 8 5 10 14 15 10 10 10 10 10 10 6.1.1 Chi-square distribution ~ ?2 distribution —— goodness of fit between fi ei ?2 distributions 1. Setting up hypotheses H0：the population follows a uniform distribution H1：the population doesn’t follow a uniform distribution α=0.05 Calculation to statistic： 6.1.2 ? 2 Test for Goodness of Fit 1 2 3 4 5 6 3. P-value： ν=k-1=6-1=5 4. Conclusion：With significance level α=0.05, H0is not rejected. The dice is an even one. 6.1.2 χ2 Test for Goodness of Fit 6.2 Comparison between two Independent Sample Proportions In chapter 4 the Z test can only be used for comparing ? with a given ?0 (one sample) or comparing ?1 with ?2 (two samples). If we need to compare two more samples, Chi-square test is widely used. Example 6.1 In a clinical survey, 215 patients with pulmonary heart disease in a hospital were collected , of which 164 patients have taken digitalis and 51 patients haven’t taken it. Each of them received an ECG examination. The results are listed in Table 6.2. ν＝1 ?2 test and Z test According to (4.25) Correction for continuity When n≥40, if there happens 1≤eij5, Fisher’s exact test When n≤40, if there happens eij1, ?2 test is not proper then. An exact P value, with SPSS, will be obtained for us to give conclusion. Example 6.9 Statistical description Statistica