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1、1,Chapter 2 The Description of Quantitative Data定量资料的统计描述,刘 沛 流行病与卫生统计学系,2,Outline,频数与频数分布 Frequency Drawback: Wasteful of information. Preferable when data are not symmetric,34,Examples for Median,values of Hg (hydrargyrum) of hair 1.1, 1.8 3.5 4.2 4.8 5.6 5.9 7.1 10.5 M=4.8,1.1, 1.8 3.5 4.2 4.8 5.
2、6 5.9 7.1 16 M=4.8,1.1, 1.8 3.5 4.2 4.8 5.6 5.9 7.1 10.5 16 M=(4.8+5.6)/2=5.2,35,Percentile,100 centile, percentile X% PX (100-X)% Quartiles: First quartile: 25% (QL) Second quartile:median Third quartile:75% (QU),36,Mode,The mode is defined as the most frequently occurring value in the data set. Ea
3、mple: 4 5 5 6 1 4 8 9 5 2 The mode is 5,37,Which measure should we use?,Mean: symmetric, unimodal; G: if log transformation creates symmetric, unimodal; Mode: unimodal; M: distribution free. uncertain data The subjects should be homogeneity when we calculate average!,38,Mean, mode and median,Mean=me
4、dian=mode,39,Mean, mode and median,Modemedianmean,40,Mean, mode for variables with more different means.,51,Example: Comparing the dispersion of two variables,mean sd Height: 166.06(cm)4.95(cm) Weight:53.72(kg)4.96(kg),52,Which measure should we use?,sd, variance for unimodal, symmetric, CV for diff
5、erent units; for more different means. Range for any distribution, Wasteful of information. Interquartile for any distribution, robust, Wasteful of information. The subjects should be homogeneity!,53,What do the variance and sd tell us?,Large variance (sd) means: more variable, wider range, lower de
6、gree of representativeness of mean. small variance (sd) means: less variable, narrower range, higher degree of representativeness of mean.,54,Average and dispersion,Meansd(min,max) Medianinterquartile range(min,max) Using both average and dispersion.,55,Summarize:,Each variable has its own distribut
7、ion; Descriptive Using graphs Using statistics average：Mean, G, M , Mode Dispersion: sd, variance, Q, CV, R Choosing appropriate measurement； Using average with dispersion.,56,Part III,Description of the relationship between two quantitative variable,57,example what is the relationship between a mot
8、hers weight and her babys weight? What is the relationship between the height and age of young boys?,58,Description of association between 2 quantitative variable,Correlation: When two variables varies together, we would say they are correlated.,59,Measure of correlation,Pearsons Linear Correlation
9、Coefficient coefficient of product-moment correlation Always be abbreviated as Correlation Coefficient -1, 1 It measures the strength and direction of the correlation. Populations Correlation Coefficient: Samples Correlation Coefficient: r,60,The larger the absolute value of correlation coefficient
10、, the stronger the correlation. If the sign is positive, the two variables varies at the same direction. Else, they varies at the opposite direction.,61,Values of correlation coefficient,Values near 1 indicate a strong positive association. Values near -1 indicate a strong negative association. Valu
11、es around 0 indicate a weak association.,62,Different Patterns of Correlation,63,Computation of correlation coefficient,64,y,big,small,Small,65,The association of heights of 2 years-old and 20 years old。,66,67,68,Awful computation?,Practical Class In your schedule Enjoy the power of STATA!,69,Statis
12、tical discription of categorical data,70,outline,Table and graph Relative number,71,FREQUENCY TABLE OF BLOOD TYPE,72,binary data,73,Multiple Data,74,Ranked data,75,Two-way Frequency Table,Table for analysis,76,numerical methods-Relative number,Rate Proportion Ratio,77,Rate-Force Index,A single figur
13、e that measures the forces of specific events, for example death, disease. mortality & morbidity) a=the frequency with which an event has occurred during some specified period of time. a+b= the number of person exposed to the risk of the event during the same period of time K=some number such as %,
14、and so on. The denominator should not be two small(=50%)?,78,Vital Statistics-Rates as measure of health status.,Incidence rate prevalence rate Case fatality ratio,79,Proportion,Composing index, The relative frequency of every composition taking account of special factor, such as race, sex, age grou
15、p in a whole group. For example, sex proportion, race proportion, age proportion.,80,Homogenous in some factors,Comparison of morbidity between two region, effective rate between 2 treatment group. Sex, age distribution and so on should be equal significantly. For the sex, age may be the factor that
16、 effect the mortality.,81,Ratio-comparison index,C & d are the frequency or relative frequency of occurrence of some events or terms, such as the person-doctor ratio,the person-hospital bed ratio. K used in ratio are mostly 1 and 100.,82,Sex ratio at birth in China in 2000,(65355units/64228 units)X100=106.74 1 unit=10,000 ( 万 ),83,Summary of relative number,BMI (body mass index)CHD (coronary heart disease),84,Thank You,