1. 2014.3.26 1 Medical Statistics Medical Statistics Tao Yuchun Tao Yuchun Practice 3 http://cc.jlu.edu.cn/ms.html

2. 2014.3.26 2 Review 1. 1. Comparing to a given population mean One-sample t test (One-sample t test) I. t test The formula of the test statistic for one-sample t test is:The formula of the test statistic for one-sample t test is: here μ is a given population mean.

3. 2014.3.26 3 2. 2. Comparison for Paired Data Paired-Samples t test (Paired-Samples t test) The formula of the test statistic for -samplesThe formula of the test statistic for paired-samples t test is: t test is: here and S d refer to the mean and SD of the variable “difference”.

4. 2014.3.26 4 3. 3. Comparison between two sample Independent-Samples t test means (Independent-Samples t test) The formula of the test statistic for independent-sampleThe formula of the test statistic for independent-sample t test is: t test is: here S c 2 is pooled estimation of sample variance.

5. 2014.3.26 5 II. Z test 1. 1. Comparing to a given population mean big One-sample Z test for a big sample (One-sample Z test) The formula of the test statistic for one-sample Z test is:The formula of the test statistic for one-sample Z test is: big means sample size n ≥ 50 or 100. big means sample size n ≥ 50 or 100.

6. 2014.3.26 6 2.big 2. Comparison between two big sample Two-Samples Z test means (Two-Samples Z test) The formula of the test statistic for two-samples Z testThe formula of the test statistic for two-samples Z test is: is: big means two sample size all n ≥ 50 or 100. big means two sample size all n ≥ 50 or 100.

7. 2014.3.26 7 III. Statistical description for enumeration data data 1. 1. Relative measures Absolute measure Absolute measure Relative measures : Relative measures : (1) (1) Frequency(proportion) (2) (2) Intensity (Rate) (3) (3) Ratio

8. 2014.3.26 8 2. 2. Standardization for crude frequency or crude intensity direct standardization approach direct standardization approach indirect standardization approach indirect standardization approach IV. Statistical Inference for enumeration data data 1. 1. Sampling error of frequency

9. 2014.3.26 9 2. 2. Confidence Interval of Probability  95% Confidence interval:  99% Confidence interval: required the sample size n is big enough. required the sample size n is big enough.

10. 2014.3.26 10 3. 3. The hypothesis testing of proportion (Z test) (1) Comparison of sample proportion and population proportion ( One-sample Z test) If |Z| ≥ Z α, then reject H 0 ; Otherwise, no reason to reject H 0 (accept H 0 ). π 0 is a constant.

11. 2014.3.26 11 (2) Comparison of two sample proportions ( Two-samples Z test) ( Two-samples Z test)

12. 2014.3.26 12 np > 5 and n(1-p) >5 The normal approximation condition 4. 4. The hypothesis testing of proportion (Chi-square test)  (1) Basic idea of χ 2 test the actual frequency ---- A the actual frequency ---- A the theoretical frequency ---- T the theoretical frequency ---- T

13. 2014.3.26 13 (2) Chi-square test for 2×2 table = (row-1)(column-1)  a.andevery a. If n≥40, and every T i ≥ 5,  2 test is applicable; b.or b. If n < 40 or T i < 1,  2 test is not applicable, you should use Fisher’s Exact Test Fisher’s Exact Test; c.andonly one c. If n≥40, and only one 1≤T i < 5,  2 test needs adjustment.

14. 2014.3.26 14 2  2 table The correction formula of  2 test for 2  2 table :  (3) Chi-square test for R×C table

15. 2014.3.26 15 Excel’s statistical method You can use Excel’s statistical function CHIINV(Probability,Deg_freedom) CHIINV(Probability,Deg_freedom) to get χ 2 α,ν, here Probability is α ， Deg_freedom is ν (degree of freedom). You can use Excel’s statistical function CHITEST(range1,range2) CHITEST(range1,range2) to get the P-value of χ 2 test, here range1 is the range of all actual frequencies, range2 is the range of all theoretical frequencies.

16. 2014.3.26 16 See the example updated ( stat1.xls updated ) You can use the macro for t-tests of statistical analysis tools to get Paired-Samples t Test and Two-Samples t Test directly.

17. 2014.3.26 17 Practice in class Exercise 1 Exercise 1: The weights (kg) of 12 volunteers were measured before and after a course of treatment with a “new drug” for losing weight. The data is given in Table 3-1. Please evaluate the effectiveness of this drug.

18. 2014.3.26 18 Exercise 2 Exercise 2: A physician made a survey of the roundworm infection of a rural region. There were 60 infected among the 300 randomly sampled males, and 30 infected among the 200 females. Did females have lower infection rate than males? Answer Answer See the Excel file ( practice3key.xls )

19. 2014.3.26 19 Homework 1. 1. Dr. L wants to evaluate one remedy, so she randomly chose 10 patients, and recorded the blood sedimentation rate (mm/h) of each patient before and after the treatment. The data is given in Table 3-2. Please evaluate the effectiveness of this remedy.

20. 2014.3.26 20 C 2. 2. A test is used for examination of two groups of children randomly selected from Urban and Rural areas of a city respectively. The results are listed in table3-3. Are the positive rates of two groups of children are significantly different ?