1. 2014.3.10 1 Medical Statistics Medical Statistics Tao Yuchun Tao Yuchun 4 http://cc.jlu.edu.cn/ms.html

2. 2014.3.10 2 Normal Distribution and Reference Range Normal Distribution and Reference Range 1. Normal Distribution

3. 2014.3.10 3 1.1 Normal Distribution See the histogram of Example1-1.

4. 2014.3.10 4 n inc. n  n is increasing; the number of sub-intervals is increasing; A characteristic shape likened to that of an Normal Distribution Curve upside down bell - Normal Distribution Curve When What will happen ?

5. 2014.3.10 5 1.2 The Property of Normal Distribution Normal Distribution (Gaussian Distribution)Gaussian Distribution The probability density function of a normal distribution: μ is population mean ， σ is population standard deviation (SD) ， π=3.14159…, e=2.71828….

6. 2014.3.10 6 I. centrosymmetric

7. 2014.3.10 7 II. μ — position parameter determine location of the peak (center) for a normal distribution

8. 2014.3.10 8 III. σ — shape parameter determine shape of a normal curve

9. 2014.3.10 9 N (0,1 2 ) N (0,1.5 2 ) N (1,2 2 ) A normal distribution with μ and σ denoted with

10. 2014.3.10 10 IV. The area under the curve probability The area under normal curve is probability The area under certain distribution curve is also probability

11. 2014.3.10 11 μ±1.96σ 95% μ±2.58σ 99% The area of certain range under normal curve

12. 2014.3.10 12 1.3 Standard Normal Distribution For convenience of application If standard normal distribution Z follows standard normal distribution. A normal distribution with μ =0 and σ =1 denoted with

13. 2014.3.10 13 2. Reference range 2.1 What is reference range? Examples: WBC 4-10 (10 9 /L) Lead in urine <0.08mg/L a. a. Medical measurement X (such as physiological, Biochemical, … measurements) b. b. “Normal persons” c. c. The interval which covers the values of most normal persons. (http://en.wikipedia.org/wiki/Reference_range)

14. 2014.3.10 14 2.2 How to work out a reference range? a.Well define “normal person” b.Needs grouping or not? (male-female? Age groups?…) c.Determine sample size d.Random sampling e.Measurement (instrument, method, quality control…) f.Two sides? One side? g.“Most person”? (99%? 95%? 90%?…) h.Statistical method?

15. 2014.3.10 15 2.3 Statistical method If the frequency distribution is close to a normal distribution: Two side (1-α)range: One side (1-α)range: or Two side: One side:

16. 2014.3.10 16 Example 4-1 Height data of 130 girls (14 years old ), we knew: Calculate its reference range. 143.084±1.96×6.58=130.18~155.98(cm) If the frequency distribution is skew: By percentiles Two side (1-0.05)range: One side (1-0.05)range: or

17. 2014.3.10 17 Example 4-2 Urine lead (mmol/L) data of 308 children (<6 years old ), see table4-1. Calculate its reference range. For urine lead, high value has significance, but low no.

18. 2014.3.10 18 Which method, normal distribution or percentile ? The key is below! It’s a skew distribution, so using percentile.It’s a skew distribution, so using percentile.

19. 2014.3.10 19 C The reference range: (http://en.wikipedia.org/wiki/Great_Wall_of_China)

20. 2014.3.10 20