数学选修2-3-列联表独立性分析.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,*,世博会英国馆,2026/10/25,郑平正 制作,8.4,列联表独立性分析案例,1,（一）,独立性检验,第一步：,H,0,：假设,吸烟,和,患病,之间没有关系,通过数据和图表分析，得到结论是：,吸烟与患病有关,结论的可靠程度如何？,患病,不患病,总计,吸烟,a,b,a+b,不吸烟,c,d,c+d,总计,a+c,b+d,a+b+c+d,第二步：列出,2,2,列联表,用,2,统计量研究这类问题的方法,步骤,第三步：引入一个随机变量：,卡方统计量,第四步：查对临界值表，作出判断。,P(,c,2,x,0,),0.50,0.40,0.25,0.15,0.10,0.05,0.025,0.010,0.005,0.001,x,0,0.455,0.708,1.323,2.072,2.706,3.841,5.024,6.635,7.879,10.828,P(,c,2,x,0,),0.50,0.40,0.25,0.15,0.10,0.05,0.025,0.010,0.005,0.001,x,0,0.455,0.708,1.323,2.072,2.706,3.841,5.024,6.635,7.879,10.828,0.1%,把握认为,A,与,B,无关,1%,把握为,A,与,B,无关,99.9%,把握认,为,A,与,B,有关,99%,把握认,为,A,与,B,有关,90%,把握认,为,A,与,B,有关,10%,把握认为,A,与,B,无关,没有充分的依据显示,A,与,B,有关，但也不能显示,A,与,B,无关,例如,独立性检验,通过公式计算,患病,不患病,总计,吸烟,39,15,54,不吸烟,21,25,46,总计,60,40,100,H,0,：,吸烟,和,患病,之间没有关系,解,：,已知在 成立的情况下，,故有,99%,的把握认为,H,0,不成立，即有,99%,的把握认为,“,患病与吸烟有关系,”,。,即在 成立的情况下，大于,6.635,概率非常小，近似为,0.010,现在的,=7.307,的观测值远大于,6.635,，出现这样的观测值的概率不超过,0.010,。,例,1.,在,500,人身上试验某种血清预防感冒作用，把他们一年中的感冒记录与另外,500,名未用血清的人的感冒记录作比较，结果如表所示。问：该种血清能否起到预防感冒的作用？,未感冒,感冒,合计,使用血清,258,242,500,未使用血清,216,284,500,合计,474,526,1000,解：设,H,0,：感冒与是否使用该血清没有关系。,因当,H,0,成立时，,2,6.635,的概率约为,0.01,，故有,99%,的把握认为该血清能起到预防感冒的作用。,P(,c,2,x,0,),0.50,0.40,0.25,0.15,0.10,0.05,0.025,0.010,0.005,0.001,x,0,0.455,0.708,1.323,2.072,2.706,3.841,5.024,6.635,7.879,10.828,P(x,0,),0.50,0.40,0.25,0.15,0.10,0.05,0.025,0.010,0.005,0.001,x,0,0.455,0.708,1.323,2.072,2.706,3.841,5.024,6.635,7.879,10.828,有效,无效,合计,口服,58,40,98,注射,64,31,95,合计,122,71,193,解：设,H,0,：药的效果与给药方式没有关系。,因当,H,0,成立时，,2,1.3896,的概率大于,15%,，故不能否定假设,H,0,，即不能作出药的效果与给药方式有关的结论。,2.072,例,2,：为研究不同的给药方式（口服与注射）和药的效果（有效与无效）是否有关，进行了相应的抽样调查，调查的结果列在表中，根据所选择的,193,个病人的数据，能否作出药的效果和给药方式有关的结论？,P(x,0,),0.50,0.40,0.25,0.15,0.10,0.05,0.025,0.010,0.005,0.001,x,0,0.455,0.708,1.323,2.072,2.706,3.841,5.024,6.635,7.879,10.828,例,3,：气管炎是一种常见的呼吸道疾病，医药研究人员对两种中草药治疗慢性气管炎的疗效进行对比，所得数据如表所示，问：它们的疗效有无差异？,有效,无效,合计,复方江剪刀草,184,61,245,胆黄片,91,9,100,合计,275,70,345,解：设,H,0,：两种中草药的治疗效果没有差异。,因当,H,0,成立时，,2,10.828,的概率为,0.001,，故有,99.9%,的把握认为，两种药物的疗效有差异。,P(,c,2,x,0,),0.50,0.40,0.25,0.15,0.10,0.05,0.025,0.010,0.005,0.001,x,0,0.455,0.708,1.323,2.072,2.706,3.841,5.024,6.635,7.879,10.828,作业,P87,习题？,