版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
1、Medical Statistics (full English class)Ji-Qian FangSchool of Public Health Sun Yat-Sen UniversityIntroduction to Medical StatisticsMedical Statistics: Application of mathematical statistics inthe field of medicineWhy we need to study statistics? Three reasons:(1)Basic requirement of medical research
2、.(2)Update your medical knowledge.(3) Management and treatment for your own data.Basic conceptsHomogeneity: All individuals have similar characteristics and belong to same category. Variation: the differences in some features such as height, weight1. Homogeneity and VariationRandom By chance!Random
3、event: the event may occur or may not occur in one experiment. Before an experiment, nobody is sure whether the event occurs or not. However, there must be some regulation in a large number of experiments.3. ProbabilityMeasure the possibility of occurrence of a random event. A : random event P(A) :
4、Probability of the random event A P(A)=1 , if an event always occurs. P(A)=0, if an event never occurs.Estimation of Probability-Frequency n : number of observations (large enough) m : number of occurrences of random event A : relative frequency or frequency of event A P(A) frequency The Basic Steps
5、 of Statistical Work1. Design of study2. Collection of data3. Data Sorting4. Data Analysis5. Interpret the resultsAbout This course- Teaching and LearningAim: Training essential concepts and statisticalthinking Learning some skills in design and analysisLectures - Concepts and thinkingPractice sessi
6、on - experiments and discussion Chapter1 Descriptive StatisticsChapter1 Descriptive Statistics Statistics: Statistical description Statistical inference Statistical description: Describes the feature of the sample. Main forms: tables, plots and numerical indexes1.1 Variables and Data1.1.1 Structure
7、and feature of data 1.1.2 Types of variables1. Quantitative Variable (定量变量)Continuous variable (连续变量) Values obtained through measurement : height, weight, blood pressure, pulse and Taking values in a continuous interval.Discrete variable (离散变量) Taking values in a set of integers. 2. Qualitative Var
8、iable (定性变量)Categorical variable (分类变量) : Taking “values” within several possiblecategories, such as Gender (male, female),occupation. Binary variable is a simplest special case of it. Example 1.1 The variable for gender can be defined with a binary variable X.Ordinal variable (有序变量) : There exists
9、order among all possiblecategories, such as education (primary school,high school, university, postgraduate)Table 1.3 The frequency table for occupation of 108 patientsTable 1.4 The frequency table for the results of certain semi-quantitative test among 150 patients2. Continuous type frequency table
10、 Example 1.3 120 normal male adults were randomlyselected from the residents of a county. Their red cell counts (1012 /L) were observed and listed as the follows:5.12 5.13 4.58 4.31 4.09 4.41 4.33 4.58 4.24 5.45 4.32 4.844.91 5.14 5.25 4.89 4.79 4.90 5.09 4.04 5.14 5.46 4.66 4.204.21 3.73 5.17 5.79
11、5.46 4.49 4.85 5.28 4.78 4.32 4.94 5.214.68 5.09 4.68 4.91 5.13 5.26 3.84 4.17 4.56 3.52 6.00 4.054.92 4.87 4.28 4.46 5.03 5.69 5.25 4.56 5.53 4.58 4.86 4.974.70 4.28 4.37 5.33 4.78 4.75 5.39 5.27 4.89 6.18 4.13 5.224.44 4.13 4.43 4.02 5.86 5.12 5.36 3.86 4.68 5.48 5.31 4.534.83 4.11 3.29 4.18 4.13
12、4.06 3.42 4.68 4.52 5.19 3.70 5.514.64 4.92 4.93 4.90 3.92 5.04 4.70 4.54 3.95 4.40 4.31 3.774.16 4.58 5.35 3.71 5.27 4.52 5.21 4.37 4.80 4.75 3.86 5.69 Please try to establish a frequency table for this set of data.(1) Range R maximum= 6.18, minimum=3.29 R=6.183.29=2.89(2) Length of sub-intervals i
13、 Divide the whole range into 8-15 sub-intervals R/10=2.89/10= 0.289 0.30 then let i =0.301.2.2 Frequency plot and histogram 1. Frequency plot for discrete variable bar chart2. Frequency plot for continuous variable histogram 1.3 Measurement for average level Numerical characteristics (数字特征): Average
14、 level (平均水平) Variation (变异)1.3.1 Arithmetic mean (算术均数) Useful when the histogram looks symmetric. Denote the observed values of the individuals with , the arithmetic mean (1.1)1.3.2 Geometric mean (几何均数) It is useful when the histogram of the logarithms is close to symmetric.Example The concentrat
15、ions of certain antibody are measured for a set of sample and the corresponding titers are 4, 8, 16, 16, 64, 128. Arithmetic mean = 39.3 Geometric mean = 20.16 1.3.3 Median (中位数) When the histogram shows skew, the median can be applied to measure the average level. Median = the value in the middleEx
16、ample 1 Data set 1,1,2,2,3,4,6,9,10 n = 9 Median = 3Example 2 Data set 1,1,2,2,3,4,6,9,10,13 n = 10 Median = (3+4)/2=3.5When n is odd, Median = the observed value with rank (n+1)/2 When n is even, Median=values with rank n/2+ values with rank n/2 + 12 Think about Px = x-percentile = x% of the values
17、 less than it and (1- x%) of the values greater than it Median = the value in the middle = 50% of the values less than it and 50% of the values greater than it = 50 percentile = P50 How to calculate x-percentile (百分位数)? P25 ? P75 ? 1.4 Measurement for Variation1.4.1 Range (极差) R = maximal value - mi
18、nimal valueR is worse in robustness. Disadvantage: Based on only two observations, itignores the observations within the two extremes. The more the observations, the greater therange is.1.4.2 Inter- quartile range (四分位数差距) Lower Quartile (下四分位数): 25 percentile, P25 or Upper Quartile (上四分位数): 75 perc
19、entile, P75 or Difference between two Quartiles = P75 - P25 = - = 13.120 8.083 = 5.0371.4.3 Variance and standard deviationDeviation (偏差) from the mean: Squared deviation: Population variance (总体方差): average squared deviation throughout the population, Population standard deviation (总体标准差): When the
20、 population mean (总体均数) is unknown, it is replaced by Squared deviation: Sample variance (样本方差) : average squared deviation throughout the sample Sample standard deviation (样本标准差) : Degrees of freedom (自由度) : (n-1) Example The weight of male infant 2.85,2.90, 2.96, 3.00, 3.05, 3.18Conventionally, me
21、an and standard deviation are often expressed together asFor instance, for height, mean and standard deviation are 1706 (cm)1.4.4 Coefficient of variationExample 9-10 For normal young males, comparing their height and weight, which one has more variation?Coefficient of variation (变异系数) is defined as
22、1.5 Relative Measures and Standardization Approaches1.5.1 Ratio, frequency and intensity Relative measures are widely used in vital Statistics(生命统计) and epidemiology(流行病学). Caution: There are three types of relative measures although they are often named with “ rate”. Ratio (比): It is simply a ratio
23、 of any quantity to anotherFor example, mass index (身体指数)2. Relative frequency (频率) A special type of ratio:Both of the numerator(分子) and denominator(分母) are counted numbers; The numerator is a part of the denominator;Within the interval of 0,1For example,3. Intensity (强度) Another special type of ra
24、tio:The denominator: total observed person-years (人- 年) during certain period;The numerator: number of certain event happening during the period.Not necessary within the interval of 0,1For example, Unit: “person/person-year”The mortality rate can be regarded as adjusted relative frequency per year. In general, intensity could be understood as “relative frequency per unit of time”, reflecting the chance of certain event happening in a unit of time.1.5.2 Crude death rate and standardizationTable 1.9 Age specific mortality rates (年龄别死亡率) for two cities Which city has a high
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 小学六年级下册数学期末测试卷带答案(综合题)
- 人教版六年级下册数学期末测试卷【新题速递】
- 人教版六年级下册数学期末测试卷带答案(完整版)
- 人教版六年级下册数学期末测试卷附答案【能力提升】
- 人教版六年级下册数学期末测试卷(黄金题型)
- 小学六年级下册数学期末测试卷及参考答案【研优卷】
- 小学六年级下册数学期末测试卷带答案(考试直接用)
- 小学六年级下册数学期末测试卷附完整答案(历年真题)
- 小学数学六年级下册 期末测试卷【含答案】
- 小学数学六年级下册 期末测试卷含答案【综合卷】
- 核心素养下教师课程实施能力结构及提升策略研究
- 2022年副高(中医内科学)考试真题卷
- 【中小企业内部控制存在的问题及优化建议分析(数据图表论文)11000字】
- 《脊髓和椎管内病变》课件
- 《分娩镇痛》课件
- 韩国《寄生虫》电影鉴赏解读
- 张家口煤矿机械制造高级技工学校招聘真题
- 新企业的起源与演进
- 《健康教育学》PPT13-个人卫生与保健
- 长春一汽汽车专业个人实习报告总结
- 安全生产标准化自评管理制度全
评论
0/150
提交评论