1. 2014.3.3 1 Medical Statistics Medical Statistics Tao Yuchun Tao Yuchun 3 http://cc.jlu.edu.cn/ms.html

2. 2014.3.3 2 Descriptive Statistics Descriptive Statistics 1. Statistical Description for Measurement Data (Continue)

3. 2014.3.3 3 1.3 Measures for variability See the numbers of 3 groups listing below. Group 1: 36.8 36.9 37.0 37.1 37.2 Group 2: 36.5 36.9 37.0 37.1 37.5 Group 3: 36.5 36.7 37.0 37.3 37.5 The mean of each group is same.

4. 2014.3.3 4 Look at the raw data like this below, what about the tendency of dispersion each group? Different each other !

5. 2014.3.3 5 (1) Range (1) Range R Difference of the smallest and the largest. Advantage: simpleAdvantage: simple Disadvantage: unstable,Disadvantage: unstable, crude crude R = Maximum - Minimum Simple method can’t solve complex problem!Simple method can’t solve complex problem!

6. 2014.3.3 6 Based on only two observations, it ignores the observations within the two extremes. The greater the number of observations, the greater the range is. Yao Ming & the Seven Dwarfs

7. 2014.3.3 7 (2) InterQuartile Range (2) InterQuartile Range IQR Q 1 : Lower Quartile: 25th percentile, Q 1 =P 25 Q 3 : Upper Quartile: 75th percentile, Q 3 =P 75 IQR is Difference of the Q 1 and Q 3.

8. 2014.3.3 8

9. 9 (3) Variance and Standard Deviation The average sum of squared deviations:

10. 2014.3.3 10 Standard deviation (SD) (1.6) Example 1-4 The weight of male infant 2.85,2.90, 2.96, 3.00, 3.05, 3.18 ★ A bigger value of S refers to a higher variation.

11. 2014.3.3 11 I. II.

12. 2014.3.3 12 (4) Coefficient of Variation (4) Coefficient of Variation CV 1. Comparison of the variation of two variables with different dimensions, 2. Comparison of the variation of two variables with bigger difference of means.

13. 2014.3.3 13 Example 1-5 Variation of height and variation of weight Example 1-6 Variation of height and variation of chest circumference

14. 2014.3.3 14 Summary 1.Range 1.Range: R Suitable to all kinds of data, but no useful. 2.InterQuartile Range 2.InterQuartile Range : IQR Suitable to all kinds of data, but usually skew distribution. Variance and Standard Deviation 3. Variance and Standard Deviation : S Suitable to symmetric distribution. S is very important statistic as mean.

15. 2014.3.3 15 C 4. Coefficient of Variation 4. Coefficient of Variation : CV Comparison of the variation of two variables with different dimensions or bigger difference of means. (http://en.wikipedia.org/wiki/Big_Wild_Goose_Pagoda)