计量资料的统计描述全科医师.ppt

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1、第二章 数值变量资料的统计分析 Descriptive Statistics2 统计描述统计分析 统计推断2023/2/233【例例7-17-1】某某地地用用随随机机抽抽样样的的方方法法对对130130名名健健康康成成年年男男性性红红细细胞胞数数进进行行了了检检测测，资资料料如如表表1 1，请请描描述男性红细胞的情况。述男性红细胞的情况。2023/2/23表表1 1 某地某地130130名正常成年男子红细胞数（名正常成年男子红细胞数（10 101212/L/L）3.79*3.79*4.574.575.195.194.864.864.284.284.674.675.375.374.984.984

2、.454.455.88*5.88*4.534.535.165.164.844.844.154.154.664.665.315.314.974.974.434.434.774.774.784.785.15.14.834.834.114.114.634.635.285.284.944.944.44.44.744.745.675.675.055.054.814.813.983.984.614.615.235.234.94.94.354.354.74.75.465.465.035.034.494.493.893.894.574.575.215.214.874.874.294.294.674.675.3

3、85.384.984.984.464.464.784.784.544.545.165.164.854.854.174.174.664.665.325.324.974.974.434.434.774.775.075.075.135.134.834.834.134.134.644.645.295.294.954.954.424.424.744.745.695.694.534.534.814.814.014.014.624.625.265.264.914.914.364.364.734.735.495.495.045.044.784.783.943.944.574.575.235.234.94.94

4、.314.314.684.685.395.394.994.994.484.485.085.084.544.545.175.174.864.864.274.274.664.665.365.364.984.984.434.434.774.774.534.535.155.154.844.844.134.134.644.645.295.294.964.964.424.424.754.755.695.694.84.84.824.824.14.14.624.625.265.264.934.934.394.394.744.745.615.615.045.045.15.13.983.984.584.585.2

5、35.234.94.94.334.334.684.685.45.45 54.494.494.84.82023/2/234问题？n n表表1 1的的130130个数据，无论多认真审视，也说不清这些人红细个数据，无论多认真审视，也说不清这些人红细胞的情况怎样、特征如何。胞的情况怎样、特征如何。n n你应该如何着手整理，整理的目的是什么？你应该如何着手整理，整理的目的是什么？n n结合学过的知识，你认为用什么方式描述这份资料能让人结合学过的知识，你认为用什么方式描述这份资料能让人对资料内容一目了然？对资料内容一目了然？n n统计描述统计描述就是解决此问题的方法，即用统计表、统计图和就是解决此问题的方

6、法，即用统计表、统计图和统计指标来描述样本数据的特征统计指标来描述样本数据的特征2023/2/235第一节 计量资料的统计描述频数表与频数分布平均指标（算术均数、几何均数、中位数、众数）变异指标（极差、百分位数与四分位间距、方差、标准差、变异系数）2023/2/236一、频数表与频数分布一、频数表与频数分布 (frequency table and frequency distribution)(frequency table and frequency distribution)频数（频数（frequencyfrequency）：）：变量值出现的次数，即例数变量值出现的次数，即例数 频数表（

7、频数表（frequency distribution tablefrequency distribution table）：）：反映变量值与频数之间关系的统计表反映变量值与频数之间关系的统计表2023/2/237表表1 1 某地某地130130名正常成年男子红细胞数（名正常成年男子红细胞数（10 101212/L/L）3.79*3.79*4.574.575.195.194.864.864.284.284.674.675.375.374.984.984.454.455.88*5.88*4.534.535.165.164.844.844.154.154.664.665.315.314.974.97

8、4.434.434.774.774.784.785.15.14.834.834.114.114.634.635.285.284.944.944.44.44.744.745.675.675.055.054.814.813.983.984.614.615.235.234.94.94.354.354.74.75.465.465.035.034.494.493.893.894.574.575.215.214.874.874.294.294.674.675.385.384.984.984.464.464.784.784.544.545.165.164.854.854.174.174.664.665.32

9、5.324.974.974.434.434.774.775.075.075.135.134.834.834.134.134.644.645.295.294.954.954.424.424.744.745.695.694.534.534.814.814.014.014.624.625.265.264.914.914.364.364.734.735.495.495.045.044.784.783.943.944.574.575.235.234.94.94.314.314.684.685.395.394.994.994.484.485.085.084.544.545.175.174.864.864.

10、274.274.664.665.365.364.984.984.434.434.774.774.534.535.155.154.844.844.134.134.644.645.295.294.964.964.424.424.754.755.695.694.84.84.824.824.14.14.624.625.265.264.934.934.394.394.744.745.615.615.045.045.15.13.983.984.584.585.235.234.94.94.334.334.684.685.45.45 54.494.494.84.82023/2/2381.频数表的编制步骤（1）

11、求极差（range）：即最大值与最小值之差，又称为全距。本例极差：R=5.88-3.79=2.09（1012/L）。（2）决定组数、组段和组距：根据研究目的和样本含量n确定。组距=极差/组数，通常分10-15个组，为方便计，组距参考极差的十分之一,再略加调整。本例i=R/10=2.09/10=0.2090.2。（3）列出组段：第一组段的下限略小于最小值，最后一个组段上限必须包含最大值，其它组段上限值忽略。（4）划记计数：用划记法将所有数据归纳到各组段，得到各组段的频数。2023/2/239622.8622.8130130合计合计5.85.85.85.81 1 5.75.75.95.922.42

12、2.45.65.64 45.55.548.648.65.45.49 9正正5.35.388.488.45.25.21717正正正正正正5.15.11051055.05.02121正正正正正正正正 4.94.91201204.84.82525正正正正正正正正正正4.74.7101.2101.24.64.62222正正正正正正正正4.54.570.470.44.44.41616正正正正正正 4.34.337.837.84.24.29 9正正4.14.116.016.04.04.04 43.93.97.27.23.83.82 2 3.73.7 fX fX(5)=(3)(4)(5)=(3)(4)组中值

13、，组中值，X X（4 4）频数，频数，f f（3 3）划划 记记（2 2）组段组段 （1 1）表表2 2 某地某地130130名正常成年男子红细胞数名正常成年男子红细胞数频数分布频数分布2023/2/23102023/2/23112.频数表的分布特征集中趋势(central tendency):变量值集中位置。本例在组段“4.74.9”。平均水平指标离散趋势(tendency of dispersion):变量值围绕集中位置的分布情况。本例4.35.1，共有101人，占77.7；离“中心”位置越远，频数越小；且围绕“中心”左右对称。变异水平指标2023/2/2312二、平均指标总称为总称为平均

14、数平均数（averageaverage）反映了资料的集中趋势（）反映了资料的集中趋势（central tendencycentral tendency ）。常用的有：）。常用的有：1.1.算术均数算术均数(arithmetic mean)(arithmetic mean)，简称，简称均数均数 (mean)(mean)2.2.几何均数几何均数(geometric mean)(geometric mean)3.3.中位数中位数 (median)(median)2023/2/23131.均数（mean）为求和符号，读成sigma适用条件：资料呈正态或近似正态。(1)直接法(2)加权法（频数表法）基本

15、思想：以组中值代表组内的变量值（近似法），简化计算2023/2/2314红细红细胞数胞数(1)(1)组组中中值值X X(2)(2)频频数数f f(3)(3)fXfXi i(4)=(2)(3)(4)=(2)(3)fXfXi i2 2(5)=(2)(4)(5)=(2)(4)3.703.703.803.802 27.607.6028.8828.883.903.904.004.004 416.0016.0064.0064.004.104.104.204.209 937.8037.80158.76158.764.304.304.404.40161670.4070.40309.76309.764.504.

16、504.604.602222101.20101.20465.22465.224.704.704.804.802525120.00120.00576.00576.004.904.905.005.002121105.00105.00525.00525.005.105.105.205.20171788.4088.40459.68459.685.305.305.405.409 948.6048.60262.44262.445.505.505.605.604 422.4022.40125.44125.445.705.905.705.905.805.801 15.805.8033.6433.64合合计计-

17、130130623.0623.03009.123009.12表2 某地区130 名正常成年男子红细胞数（1012/L）的均数和标准差的加权计算2023/2/2315均数623.0/1304.7942.几何均数（geometric mean）几何均数：变量对数值的算术均数的反对数。2023/2/2316几何均数的适用条件与实例适用条件：呈倍数关系的等比资料或对数正态分布（正偏态）资料；如抗体滴度资料 血清的抗体效价滴度的倒数分别为：10、100、1000、10000、100000，求几何均数。此例的算术均数为22222，显然不能代表滴度的平均水平。同一资料，几何均数中位数 负偏态分布时：均数中位

18、数 2023/2/2328三、变异（variation）指标 反映数据的离散度（反映数据的离散度（DispersionDispersion ）。即个体观察值的变）。即个体观察值的变异程度。常用的指标有：异程度。常用的指标有：1.1.极差极差(RangeRange）(全距全距)2.2.百分位数与四分位数间距百分位数与四分位数间距(Percentile and Quartile rangePercentile and Quartile range)3.3.方差方差 (Variance)(Variance)4.4.标准差标准差(Standard DeviationStandard Deviation

19、)5.5.变异系数变异系数(Coefficient of VariationCoefficient of Variation)2023/2/2329盘编号盘编号 甲甲乙乙丙丙1 1 1 14404404804804904902 2 2 24604604904904954953 3 3 35005005005005005004 4 4 45405405105105055055 5 5 5560560520520510510合计合计250025002500250025002500250025002500250025002500均数均数50050050050050050050050050050050

20、0500 例：设甲、乙、丙三人，采每人的耳垂血，然后红细胞计数，每人数5个计数盘，得结果如下（万/mm3）甲乙丙2023/2/23301.极差(Range）(全距)优点：简便缺点：1.只利用了两个极端值2.n大，R也会大3.不稳定12040202023/2/23312.百分位数与四分位数间距 Percentile and quartile range百分位数：数据从小到大 排列;在百分尺度下，所占百分比对应的值。记为Px。四分位间距：QRP75 P25四分位半间距quartile deviation：QDQR/2P100(max)P75P50(中位数中位数)P25P0(min)Px2023/2

21、/233233（2）中位数和百分位数的频数表法：L为百分位数对应组段的下限值，i为该组段的组距，fx为该组段频数，fL为前一组累计频数2023/2/23红细红细胞数胞数(1)(1)频频数数f f(3)(3)累累计频计频数数(4)(4)累累计计百分率百分率(5)(5)3.703.702 22 21.5(0.01.5(0.01.5)1.5)3.903.904 46 64.6(1.5-4.6)4.6(1.5-4.6)4.104.109 9151511.5(4.6-11.5)11.5(4.6-11.5)4.304.301616313123.8(11.5-23.8)23.8(11.5-23.8)4.50

22、4.502222535340.8(23.8-40.8)40.8(23.8-40.8)4.704.702525787860.0(40.8-60.0)60.0(40.8-60.0)4.904.902121999976.2(60.0-76.2)76.2(60.0-76.2)5.105.10171711611689.2(76.2-89.2)89.2(76.2-89.2)5.305.309 912512596.2(89.2-96.2)96.2(89.2-96.2)5.505.504 412912999.2(96.2-99.2)99.2(96.2-99.2)5.705.905.705.901 113013

23、0100(99.2-100.0)100(99.2-100.0)合合计计130130-表2 某地区130 名正常成年男子红细胞数（1012/L）中位数的加权计算P254.5+0.2x(130 x25%-31)/224.51P754.9+0.2x(130 x75%-78)/215.09QR0.582023/2/2334潜伏期潜伏期(天天)人数人数累计频数累计频数累计频率累计频率0 01 11 17 72 232323 311114 411115 54 46 62 27 71 1881 1合计合计70702023/2/2335百分位数的应用确定医学参考值范围(reference range)如95参

24、考值范围P97.5P2.5；表示有95正常个体的测量值在此范围。中位数Md与四分位半间距QD一起使用，描述偏态分布资料的特征2023/2/23363.方 差 方差（variance）也称均方差（mean square deviation），样本观察值的离均差平方和的均值。表示一组数据的平均离散情况。2023/2/23374.标准差 标准差（standard deviation）即方差的正平方根；其单位与原变量X的单位相同。2023/2/2338标准差的计算盘编号盘编号甲甲乙乙丙丙甲甲2 2乙乙2 2丙丙2 21 14404404804804904901936001936002304002304

25、002401002401002 24604604904904954952116002116002401002401002450252450253 35005005005005005002500002500002500002500002500002500004 45405405105105055052916002916002601002601002550252550255 5560560520520510510313600313600270400270400260100260100合计合计250025002500250025002500126040012604001251000125100012

26、502501250250标准差标准差50.9950.9915.8115.817.917.912023/2/2339红细红细胞数胞数(1)(1)组组中中值值X X(2)(2)频频数数f f(3)(3)f fi iX Xi i(4)=(2)(3)(4)=(2)(3)f fi iX Xi i2 2(5)=(2)(4)(5)=(2)(4)3.703.703.803.802 27.607.6028.8828.883.903.904.004.004 416.0016.0064.0064.004.104.104.204.209 937.8037.80158.76158.764.304.304.404.401

27、61670.4070.40309.76309.764.504.504.604.602222101.20101.20465.52465.524.704.704.804.802525120.00120.00576.00576.004.904.905.005.002121105.00105.00525.00525.005.105.105.205.20171788.4088.40459.68459.685.305.305.405.409 948.6048.60262.44262.445.505.505.605.604 422.4022.40125.44125.445.705.905.705.905.8

28、05.801 15.805.8033.6433.64合合计计-130130623.0623.03009.123009.12表2 某地区130 名正常成年男子红细胞数（1012/L）的均数和标准差的加权计算2023/2/23405.变异系数(coefficient of variation，CV)适用条件：观察指标单位不同，如身高、体重 同单位资料，但均数相差悬殊均数均数 标准差标准差变异系数变异系数青年男子青年男子 身高身高170 cm170 cm6 cm6 cm3.53.5体重体重60 kg60 kg7 kg7 kg11.711.72023/2/2341【例例】某某地地4040名名7 7岁岁

29、儿儿童童身身高高均均数数为为121.48cm121.48cm，标标准准差差为为4.65cm;4.65cm;体体重重均均数数为为22.18kg22.18kg，标标准准差差2.35kg2.35kg。试试比较其身高和体重的变异程度。比较其身高和体重的变异程度。身高CV=3.83%，体重CV=10.60%2023/2/2342变异指标小结1极差较粗，适合于任何分布2标准差与均数的单位相同，最常用，适合于近似正态分布3变异系数主要用于单位不同或均数相差悬殊资料4平均指标和变异指标分别反映资料的不同特征，常配套使用 如 正态分布：均数、标准差；偏态分布：中位数、四分位半间距2023/2/23431 1、某

30、地某地130130名正常成年男子红细胞数（名正常成年男子红细胞数（10 101212/L/L）测定值如下表所示，请测定值如下表所示，请完成以下问题？完成以下问题？（1 1）编制频数表、绘制直方图？）编制频数表、绘制直方图？（2 2）求均数、中位数、四分位数间距及标准差？）求均数、中位数、四分位数间距及标准差？3.79 3.79 4.574.575.195.194.864.864.284.284.674.675.375.374.984.984.454.455.885.884.534.535.165.164.844.844.154.154.664.665.315.314.974.974.434.4

31、34.774.774.784.785.15.14.834.834.114.114.634.635.285.284.944.944.44.44.744.745.675.675.055.054.814.813.983.984.614.615.235.234.94.94.354.354.74.75.465.465.035.034.494.493.893.894.574.575.215.214.874.874.294.294.674.675.385.384.984.984.464.464.784.784.544.545.165.164.854.854.174.174.664.665.325.324.9

32、74.974.434.434.774.775.075.075.135.134.834.834.134.134.644.645.295.294.954.954.424.424.744.745.695.694.534.534.814.814.014.014.624.625.265.264.914.914.364.364.734.735.495.495.045.044.784.783.943.944.574.575.235.234.94.94.314.314.684.685.395.394.994.994.484.485.085.084.544.545.175.174.864.864.274.274.664.665.365.364.984.984.434.434.774.774.534.535.155.154.844.844.134.134.644.645.295.294.964.964.424.424.754.755.695.694.84.84.824.824.14.14.624.625.265.264.934.934.394.394.744.745.615.615.045.045.15.13.983.984.584.585.235.234.94.94.334.334.684.685.45.45 54.494.494.84.82023/2/2344