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, , , , , ,*,*,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,*,医学英语写作英文教程,医学英语写作英文教程医学英语写作英文教程趋势性分析公共卫生学院卫生统计教研室,易 静一、涵义一个变量随同另一个变量数量协同变化关系的密切程度、数量规律及方向的统计分析称为趋势分析。,两变量间的关系可以是因果关系,也可为等位伴随关系。,多对一(复相关和多重线性回归、非线性回归)和多对多(典型相关)。,多变量构造结果变量或构造多原因变量(主成份分析、因子分析)。,医学英语写作英文教程医学英语写作英文教程医学英语写作英文教程,1,趋势性分析,公共卫生学院卫生统计教研室,易 静,趋势性分析公共卫生学院卫生统计教研室,2,一、涵义,一个变量随同另一个变量数量协同变化关系的密切程度、数量规律及方向的统计分析称为趋势分析。,两变量间的关系可以是因果关系,也可为等位伴随关系。,多对一(复相关和多重线性回归、非线性回归)和多对多(典型相关)。,多变量构造结果变量或构造多原因变量(主成份分析、因子分析)。,一、涵义一个变量随同另一个变量数量协同变化关系的密切程度、数,3,二、趋势性分析的分类及适用条件,类别,变量分布的要求,资料类型,变量设定形式,直线相关,正态双变量,定量,实测值,直线回归,y,或者,y-,正态变量,定量,实测值,曲线回归,x,或,y,x,与,y,转换值为正态,定量,实测或转换值,秩相关,x,或,y,x,与,y,非正态,定量或等级,秩转换值,定性相关,单向有序行列表,x,为等级,y,非正态,(,二值或等级,),x,为等级,y,为计数或百分率或分两组,x,转换为记分,(-,+),y,为二值,(0,1),双向有序行列表,x,、,y,均为等级,双向有序列联表,均秩差转换值,二、趋势性分析的分类及适用条件类别变量分布的要求资料类型变量,4,三、直线相关,1.,研究和解释两个等位正态随机变量数量协同变,化关系的密切程度和方向的线性统计分析方法。,三、直线相关1. 研究和解释两个等位正态随机变量数量协同变,5,例,1,测得某地,15,名正常成年人的血铅,X(mmol/L),和,24,小时的尿铅,Y(mmol/L),如下表,试分析血铅与,24,小时尿铅之间是否有直线关系?,表,15,例自愿者的血铅和,24,小时尿铅测量值(,mmol/L,),编号,血铅,(X),尿铅,(Y),1,0.11,0.14,2,0.25,0.25,3,0.23,0.28,4,0.24,0.25,5,0.26,0.28,6,0.09,0.1,7,0.25,0.27,8,0.06,0.09,9,0.23,0.24,10,0.33,0.3,11,0.15,0.16,12,0.04,0.05,13,0.2,0.2,14,0.34,0.32,15,0.22,0.24,例1 测得某地15名正常成年人的血铅X(mmol/,6,(,0.2, 0.2,),(0.2, 0.2),7,(,0.2, 0.2,),positive association,(0.2, 0.2)positive association,8,2.,样本直线相关系数,(Pearson),:,总体直线相关系数:,2. 样本直线相关系数(Pearson):,9,表,15,例自愿者的血铅和,24,小时尿铅测量值(,mmol/L,),编号,血铅,(X),尿铅,(Y),XY,X,2,Y,2,1,0.11,0.14,0.0154,0.0121,0.0196,2,0.25,0.25,0.0625,0.0625,0.0625,3,0.23,0.28,0.0644,0.0529,0.0784,4,0.24,0.25,0.0600,0.0576,0.0625,5,0.26,0.28,0.0728,0.0676,0.0784,6,0.09,0.1,0.0090,0.0081,0.0100,7,0.25,0.27,0.0675,0.0625,0.0729,8,0.06,0.09,0.0054,0.0036,0.0081,9,0.23,0.24,0.0552,0.0529,0.0576,10,0.33,0.3,0.0990,0.1089,0.0900,11,0.15,0.16,0.0240,0.0225,0.0256,12,0.04,0.05,0.0020,0.0016,0.0025,13,0.2,0.2,0.0400,0.0400,0.0400,14,0.34,0.32,0.1088,0.1156,0.1024,15,0.22,0.24,0.0524,0.0484,0.0576,合计,3.0,3.17,0.7388,0.7168,0.7681,表 15例自愿者的血铅和24小时尿铅测量值(mm,10,=0,r,0,=0r0,11,3.,t,test,(1),H,0,:,=0,H,1,:,0,=0.05,(2),计算,t,统计量,(3),确定,P,值,做出统计推断,=15-2=13,,,,,t,r,=17.189,,,p,0.05,3. t test(1) H0: =0,12,4.,总体直线相关系数的区间估计,4. 总体直线相关系数的区间估计,13,四、直线回归,1.,研究自变量,X,与应变量,Y,数量协同变化的比,例关系和方向的统计分析方法。通过拟合有,统计学意义的直线回归方程实现统计预测与,控制。,四、直线回归1. 研究自变量X与应变量Y数量协同变化的比,14,例,2,在某地一项膳食调查中,随机抽取了,14,名,4060,岁的健康妇女,测定每人的基础代谢,(kJ/d),与体重,(kg),数据,见下表。,表,14,名中年健康妇女基础代谢与体重测量值,编号,基础代谢,(kJ/d),体重,(kg),1,4175.6,50.7,2,4435.0,53.7,3,3460.2,37.1,4,4020.8,51.7,5,3987.4,47.8,6,4970.6,62.8,7,5359.7,67.3,8,3970.6,48.6,9,3983.2,44.6,10,5050.1,58.6,11,5355.5,71.0,12,4560.6,59.7,13,4874.4,62.1,14,5029.2,61.5,例2 在某地一项膳食调查中,随机抽取了14名40,15,医学英语写作英文教程课件,16,医学英语写作英文教程课件,17,医学英语写作英文教程课件,18,y,=,a,+,bx,y=a+bx,19,2.,样本直线回归系数,总体直线回归系数:,2. 样本直线回归系数,20,.,医学英语写作英文教程课件,21,医学英语写作英文教程课件,22,3.,t,test,H,0,:=,0,H,1,:,0,=,0.05,3. t testH0:=0,23,t,b,=12.584,=14-2=12, ,P,0,时,如,Y,ln,X,,,Y,随,X,上升,先快后慢;,b,0,时,如,Y,1,ln,X,,,Y,随,X,下降,先快后慢,.,(见下图),Y,a,b,ln,X,(,b,0),2.,对数函数,YablnX (X0),32,当以,Y,和,ln,X,绘制的散点图呈直线趋势时,可考虑采用对数函数描述,Y,和,X,间的非线性关系,并且该直线的斜率就是,b,,截距就是,a,。,Y,ln,X,对数函数直线化,更一般的对数函数形如,Y,a,b,ln(,X,c,),c,往往是未知的,绘图时需试用不同数值。,当以Y和lnX绘制的散点图呈直线趋势时,可考,33,或,Y,a,exp(,bX,),,,(,a,0),b,0,时,如 ,,Y,随,X,上升,称正指数函数;,X,时,,Y,0,,故以,X,轴的负侧为渐近线;,b,0,时,如,Y,随,X,下降,称负指数函数;,X,时,,Y,0,,故以,X,轴的正侧为渐近线。,指数函数曲线,3.,指数函数,或Ya exp(bX),34,对公式两边取对数,得,ln,Y,ln,a,bX,当以,ln,Y,和,X,绘制的散点图呈直线趋势时,可考虑采用指数函数描述,Y,和,X,间的非线性关系,并且该直线的斜率就是,b,,截距就是,ln,a,。,ln,Y,ln,a,X,指数函数直线化,对公式两边取对数,得,35,更一般的指数函数形如,(a,0),实践中,需以,1n(,Y,-,c,),和,X,的散点图是否呈直线趋势来识别。,c,也常是未知的, 绘图时需试用不同数值。有的问题中,单个指数项犹嫌不足,需采用多个指数项之和,如,这在药物代谢动力学中尤为多见。,更一般的指数函数形如,36,二次多项式,:,b,0,时,开口向上,有极小值;,b,0,b,0,Logistic,曲线,5. Logistic,函数,(logistic function),38,特别,当,k=1,时,,当以,ln,Y,/(1,Y,),和,X,绘制的散点图呈直线趋势时,可考虑采用,logistic,函数描述,Y,和,X,间的非线性关系,并且,该直线的斜率就是,b,, 截距就是,ln,a,-ln,a,X,Logistic,函数直线化,特别,当k=1时,,39,决定系数:,一般来说,决定系数,R,2,较大时拟合效果较好;注意,为了单纯地得到较大的决定系数,R,2,,模型的形式可能会很复杂,甚至使其中的参数无法解释实际意义,这是不可取的。要充分结合专业知识、实际情况和应用效果来确定最终的曲线。,曲线拟合效果,决定系数:曲线拟合效果,40,判断何种曲线拟合效果好,且有统计学意义:,判断何种曲线拟合效果好,且有统计学意义:,41,六、秩相关,(,等级相关,),资料不满足双变量正态分布条件或等级资料,Spearman,秩(等级)相关系数,六、秩相关(等级相关)资料不满足双变量正态分布条件或等级资料,42,1.,双定量资料秩相关,例,3,:某医生欲了解人群中氟骨症患病率(,%,),与饮水中氟含量(,mg/L,)之间的关系。随机,观察,8,个地区氟骨症患病率与饮水中氟含量,,数据如下表,计算等级相关系数,。,1. 双定量资料秩相关例3:某医生欲了解人群中氟骨症患病率(,43,表 不同地区饮水中氟含量,(mg/L),与氟骨症患病率,(%),饮水中氟含量,X,氟骨症患病率,Y,0.48,22.37,0.64,23.31,1.00,25.32,1.47,22.29,1.60,35.00,2.86,35.00,3.21,46.07,4.71,48.31,表 不同地区饮水中氟含量(mg/L)与氟骨症患病率(%)饮水,44,表 不同地区饮水中氟含量,(mg/L),与氟骨症患病率,(%),饮水中氟含量,氟骨症患病率,d,d,2,X,秩次,Y,秩次,0.48,1,22.37,2,-1,1,0.64,2,23.31,3,-1,1,1.00,3,25.32,4,-1,1,1.47,4,22.29,1,3,9,1.60,5,35.00,5.5,-0.5,0.25,2.86,6,35.00,5.5,0.5,0.25,3.21,7,46.07,7,0,0,4.71,8,48.31,8,0,0,合计,12.5,表 不同地区饮水中氟含量(mg/L)与氟骨症患病率(%)饮,45,Spearman,秩相关系数,:,Spearman秩相关系数:,46,2.,列联表(双向有序变量)秩相关,级,/,度,轻,中,重,合计,秩范围,平均秩次,轻,中,重,I,35(8.5),12(74.5),6(121),53,1-53,27,2528.75,66603,87846,II,15(48),40(18),5(64.5),60,54-113,83.5,34560,12960,20801.25,III,20(103),10(37),20(9.5),50,114-163,138.5,212180,13690,1805,合计,70,62,31,163,249268.75,93253,110452.25,秩范围,1-70,71-132,133-163,平均秩次,35.5,101.5,148,452974,例,4,肺结核,X,片肺门密度与病情的相关分析,2. 列联表(双向有序变量)秩相关级/度轻中重合计秩范围平均,47,七、定性资料,(,率、构成比,),的相关,1.,临床观察慢性病(肿瘤)不同年龄(病情)术后年数死亡情况,问预后与年龄是否有关?,(1),差异性检验,(2),相关性检验,术后年数,20,40,60,合计,校正观察人数,N,ij,实际死亡人数,O,ij,期望死亡人数,E,ij,校正观察人数,N,ij,实际死亡人数,O,ij,期望死亡人数,E,ij,校正观察人数,N,ij,实际死亡人数,O,ij,期望死亡人数,E,ij,校正观察人数,实际死亡人数,0,.,.,.,.,.,.,.,.,.,.,.,1,.,.,.,.,.,.,.,.,.,.,., .,.,.,.,.,.,.,.,.,.,.,.,11,.,.,.,.,.,.,.,.,.,.,.,合计,例,5,七、定性资料(率、构成比)的相关1. 临床观察慢性病(肿瘤),48,(,1,)差异性检验,术后年数,20,40,60,合计,校正观察人数,N,ij,实际死亡人数,O,ij,期望死亡人数,E,ij,校正观察人数,N,ij,实际死亡人数,O,ij,期望死亡人数,E,ij,校正观察人数,N,ij,实际死亡人数,O,ij,期望死亡人数,E,ij,校正观察人数,实际死亡人数,0,.,.,.,.,.,.,.,.,.,.,.,1,.,.,.,.,.,.,.,.,.,.,., .,.,.,.,.,.,.,.,.,.,.,.,11,.,.,.,.,.,.,.,.,.,.,.,合计,(1)差异性检验术后年数204060合计校正观察人数实,49,(,2,)相关性检验,年龄,组号,(,i,),O,E,i,(,O,-,E,),iE,i,2,E,20,1,69,48.022,20.978,48.022,48.022,40,2,67,83.890,-33.780,167.780,325.560,60,3,17,21.088,-12.264,63.264,189.792,合计,153,153,-25.066,279.066,573.374,P,0.05,年龄越小,死亡率越高,预后越差。,(2)相关性检验年龄组号(i)OEi(O-E)iEi2E20,50,2. 2X,C,表的相关,(1),按数量(工龄)分组资料,例,6,工龄(年),合计,工人数(,n,),52,100,224,191,56,113,737(,N,),患病数(,t,),0,5,23,35,16,23,102(,T,),患病率(,%,),0,5,10.3,18.3,28.3,20.2,13.84,组中值,0.5,1.5,3,5,7,10,Z=,组中值,-5,-4.5,-3.5,-2,0,2,7,tZ,0,-17.5,-46,0,32,115,83.5,nZ,-234,-350,-448,0,112,570,-350,nZ,2,1053,1225,896,0,224,2850,6248,P,0.05,计分:,,其中,c,是百分数个数,(2)按性质(轻中重)分组资料性别轻中重合计女(t)3246,52,(3),百分率很小(大)时,使用简化式:,(3)百分率很小(大)时,使用简化式:,53,八、升降趋势检验,(,1,)将时间序列某指标值分两段(奇数舍中间数值)形,成配对( ),对子相减后得(,+,),.0.,(,-,)。,(,2,)将(,+,)个数与(,-,)个数做,n,,以,min,(,+,)个数,(,-,)个数,作,k,,查,k,值表(旧统,计百科全书,P,131,)决定趋势。,八、升降趋势检验(1)将时间序列某指标值分两段(奇数舍中间数,54,End!,医学英语写作英文教程课件,55,1,、最灵繁的人也看不见自己的背脊。,非洲,2,、最困难的事情就是认识自己。,希腊,3,、有勇气承担命运这才是英雄好汉。,黑塞,4,、与肝胆人共事,无字句处读书。,周恩来,5,、阅读使人充实,会谈使人敏捷,写作使人精确。,培根,1、最灵繁的人也看不见自己的背脊。非洲2、最困,56,
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