04c可信区间.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,柏建岭讲稿,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,Medical statistics,医学统计学,参数估计,Parameter Estimation,2026/10/24,2,主要内容,可信区间的概念,均数的可信区间,率的可信区间,事件数的可信区间,基本概念回顾,总体,个体、个体变异,总体参数,未知,样本,代表性、抽样误差,随机,抽样,样本统计量,已知,统计推断,风 险,2026/10/24,4,统计推断的内容,参数估计,(parameter estimation),假设检验,(hypothesis test),2026/10/24,5,参数估计,由样本统计量估计总体参数,点估计,(point estimation),区间估计,(interval estimation),2026/10/24,6,参数估计之一：点估计,用样本统计量作为总体参数的估计,例如,：,用样本均数作为总体均数的一个估计,2026/10/24,7,点估计的缺陷,m,=?cm,s,=?cm,x1,x2,x3,x4,N,=143.37,s,=5.23,x1,x2,x3x10,=144.07,s,=4.72,x1,x2,x3x10,=142.72,s,=9.2473,x1,x2,x3x10,样本含量,n,=10,2026/10/24,8,点估计,直接用样本统计量作为总体参数的估计值,方法简单，但未考虑抽样误差的大小,在实际问题中，总体参数往往是未知的，但它们是固定的值，并不是随机变量值。而样本统计量随样本的不同而不同，属随机的。,2026/10/24,11,4.2,均数的可信区间,基础：抽样误差理论,从正态分布总体中随机抽取一个样本，则,t,值接近于,0,的可能性较大，远离,0,的可能性较小，出现太大的,t,值和太小的,t,值的可能性更小，根据,t,分布的性质，,2026/10/24,12,均数的可信区间,总体均数的,(1-,),可信区间定义为：,2026/10/24,13,影响可信区间大小的因素,可信度,可信度越大，区间越宽,个体变异,变异越大，区间越宽,样本含量,样本含量越大，区间越窄,2026/10/24,14,当样本含量较大时，例如,n,100,，,t,分布近似标准正态分布，此时可用标准正态分布代替,t,分布，作为可信区间的近似计算。相应的,100(1-,)%,可信区间为：,2026/10/24,15,例,4.1,随机抽取,12,名口腔癌患者，检测其发锌含量，得均数为,253.05,g/g,，标准误为,27.18,g/g,，求发锌含量总体均数,95%,的可信区间。,2026/10/24,16,-t,t,0,自由度,n,概 率，,P,单侧,0.25,0.20,0.10,0.05,0.025,0.01,0.005,0.0025,0.001,0.0005,双侧,0.50,0.40,0.20,0.10,0.05,0.02,0.01,0.005,0.002,0.001,1,1.000,1.376,3.078,6.314,12.706,31.821,63.657,127.321,318.309,636.619,2,0.816,1.061,1.886,2.920,4.303,6.965,9.925,14.089,22.327,31.599,3,0.765,0.978,1.638,2.353,3.182,4.541,5.841,7.453,10.215,12.924,4,0.741,0.941,1.533,2.132,2.776,3.747,4.604,5.598,7.173,8.610,5,0.727,0.920,1.476,2.015,2.571,3.365,4.032,4.773,5.893,6.869,6,0.718,0.906,1.440,1.943,2.447,3.143,3.707,4.317,5.208,5.959,7,0.711,0.896,1.415,1.895,2.365,2.998,3.499,4.029,4.785,5.408,8,0.706,0.889,1.397,1.860,2.306,2.896,3.355,3.833,4.501,5.041,9,0.703,0.883,1.383,1.833,2.262,2.821,3.250,3.690,4.297,4.781,10,0.700,0.879,1.372,1.812,2.228,2.764,3.169,3.581,4.144,4.587,11,0.697,0.876,1.363,1.796,2.201,2.718,3.106,3.497,4.025,4.437,12,0.695,0.873,1.356,1.782,2.179,2.681,3.055,3.428,3.930,4.318,13,0.694,0.870,1.350,1.771,2.160,2.650,3.012,3.372,3.852,4.221,14,0.692,0.868,1.345,1.761,2.145,2.624,2.977,3.326,3.787,4.140,15,0.691,0.866,1.341,1.753,2.131,2.602,2.947,3.286,3.733,4.073,附表,2,t,界值表,2026/10/24,柏建岭讲稿,17,本例自由度,n,=12-1=11,，经查表得,t,0.05,11,=2.201,，则,即口腔癌患者发锌含量总体均数的,95%,可信区间为：,193.23,321.87(,g/g),。用该区间估计口腔癌患者发锌含量总体均数的可信度为,95%,。,例,4.1,2026/10/24,18,例,4.2,某地,120,名,12,岁男孩身高均数为,142.67cm,，标准误为,0.5477cm,，计算该地,12,岁男孩身高总体均数,90%,的可信区间。,2026/10/24,19,-t,t,0,自由度,n,概 率，,P,单侧,0.25,0.20,0.10,0.05,0.025,0.01,0.005,0.0025,0.001,0.0005,双侧,0.50,0.40,0.20,0.10,0.05,0.02,0.01,0.005,0.002,0.001,1,1.000,1.376,3.078,6.314,12.706,31.821,63.657,127.321,318.309,636.619,2,0.816,1.061,1.886,2.920,4.303,6.965,9.925,14.089,22.327,31.599,3,0.765,0.978,1.638,2.353,3.182,4.541,5.841,7.453,10.215,12.924,4,0.741,0.941,1.533,2.132,2.776,3.747,4.604,5.598,7.173,8.610,5,0.727,0.920,1.476,2.015,2.571,3.365,4.032,4.773,5.893,6.869,6,0.718,0.906,1.440,1.943,2.447,3.143,3.707,4.317,5.208,5.959,7,0.711,0.896,1.415,1.895,2.365,2.998,3.499,4.029,4.785,5.408,8,0.706,0.889,1.397,1.860,2.306,2.896,3.355,3.833,4.501,5.041,9,0.703,0.883,1.383,1.833,2.262,2.821,3.250,3.690,4.297,4.781,10,0.700,0.879,1.372,1.812,2.228,2.764,3.169,3.581,4.144,4.587,11,0.697,0.876,1.363,1.796,2.201,2.718,3.106,3.497,4.025,4.437,12,0.695,0.873,1.356,1.782,2.179,2.681,3.055,3.428,3.930,4.318,13,0.694,0.870,1.350,1.771,2.160,2.650,3.012,3.372,3.852,4.221,14,0.692,0.868,1.345,1.761,2.145,2.624,2.977,3.326,3.787,4.140,15,0.691,0.866,1.341,1.753,2.131,2.602,2.947,3.286,3.733,4.073,1.6449,1.9600,2.5758,附表,2,t,界值表,2026/10/24,20,例,4.2,n,=120100,，标准正态分布代替,t,分布，,u,0.10,=1.64,即该地,12,岁男孩平均身高的,90,可信区间为：,141.77143.57(cm),，可认为该地,12,岁男孩平均身高在,141.77143.57(cm),之间。,2026/10/24,21,4.2.2,均数之差可信区间的计算,正常组 肝炎组,2,=,？,均 数,:235.21,ug/dL,标准差,:14.39,ug/dL,1,=,？,均 数,:271.89,ug,/dL,标准差,:10.38,ug/dL,1,-,2,？,2026/10/24,22,与均数之差有关的抽样分布,“,均数之差”与“均数之差的标准误”之比，,服从自由度,=,n,1,+,n,2,-2,的,t,分布。,样本含量较大时，服从,标准正态分布,。,2026/10/24,23,合并方差与均数之差的标准误,合并方差,(,方差的加权平均,),均数之差的标准误,2026/10/24,24,计算,4.3,率的可信区间,1,、率的抽样误差及标准误,2,、总体率,的区间估计,3,、两总体率之差,1,-,2,的区间估计,总体率,的区间估计,正态近似法 当样本例数,n,足够大，且样本率,p,和,(1-,p,),都不太小时，即,np,和,n,(1-,p,),均大于,5,时，,样本率,p,的抽样分布近似正态分布。,例,4.4,从某地人群中随机抽取,144,人，检查乙型肝炎表面抗原携带状况，阳性率为,9.20,，求该地人群的乙型肝炎表面抗原阳性率的,95,可信区间。,本例,n,=144,，,p,=9.20,，可用近似正态法计算可信区间。先计算：,95,可信限为：,9.20%1.962.41%,，,4.48%,13.92%,。,精确概率法 当样本例数,n,较小时，特别是当,p,接近,0,或,1,时，应根据二项分布的原理确定总体率的可,信区间。,查表法（附表,6,）,back7,两总体率之差,1,-,2,的区间估计,如果,n,1,p,1,，,n,1,(1-,p,1,),，,n,2,p,2,，,n,2,(1-,p,2,),均大于,5,，则正态,近似的方法可用于求总体率之差的可信区间：,2026/10/24,30,4.6,正确理解可信区间的涵义,可信区间一旦形成，它要么包含总体参数，要么不包含总体参数，二者必居其一，无概率可言。所谓,95,的可信度是针对可信区间的构建方法而言的。,以均数的可信区间为例，其涵义是：如果重复,100,次抽样，每次样本含量均为,n,，每个样本均按 构建可信区间，则在此,100,个可信区间内，理论上有,95,个包含总体均数，而有,5,个不包含总体均数。,2026/10/24,31,95%,可信区间的含义,按这种方法构建的可信区间，理论上平均每,100,次，有,95,次可以估计到总体参数。,2026/10/24,32,正确理解可信区间的涵义,在区间估计中，总体参数虽未知，但却是固定的值（,且只有一个），,而不是随机变量值,。,2026/10/24,33,下列说法正确吗？,算得某,95%,的可信区间，则：,总体参数有,95%,的可能落在该区间。,有,95%,的总体参数在该区间内。,该区间包含,95%,的总体参数。,该区间有,95%,的可能包含总体参数。,该区间包含总体参数，可信度为,95%,。,2026/10/24,34,可信区间与参考值范围的区别,可信区间用于估计总体参数，总体参数只有一个。,参考值范围用于估计变量值的分布范围，变量值可能很多甚至无限。,95%,的可信区间中的,95%,是,可信度,，即所求可信区间包含总体参数的可信程度为,95%,95%,的参考值范围中的,95%,是一个,比例,，即所求参考值范围包含了,95%,的正常人。,2026/10/24,35,标准差与标准误的联系,都是变异指标。,当,n,不变时，标准差，标准误,2026/10/24,36,标准差与标准误的区别,标准差描述原始数据的,离散程度,；,标准误反映均数的,抽样误差,大小。,2026/10/24,37,标准差与标准误的区别,标准差衡量样本均数对原始数据的,代表性,，标准差越小，样本均数对原始数据的代表性越好；,标准误衡量样本均数估计总体均数的,精确性,，标准误越小，样本均数估计总体均数精度越高。,2026/10/24,38,标准差与标准误的区别,当,n,N,时,，样本标准差总体标准差,当,n,N,时,，标准误,0,2026/10/24,39,标准差与标准误的区别,结合样本均数和正态分布的规律，标准差估计,参考值范围,；,结合样本均数和,t,分布的规律，标准误估计总体均数的,可信区间,。,2026/10/24,40,概念辨析,标准差,标准误,个体变异,抽样误差,参考值范围,可信区间,变量分布,抽样分布,2026/10/24,41,Homework,简述标准差和标准误的区别和联系,简述参考值范围与均数的可信区间的区别和联系,2026/10/24,42,Thank you,