单尾检验和双尾检验
library(BSDA) # 问题： 比较两个城市 人的IQ是否相等 cityA = c(82, 84, 85, 89, 91, 91, 92, 94, 99, 99, 105, 109, 109, 109, 110, 112, 112, 113, 114, 114) cityB = c(90, 91, 91, 91, 95, 95, 99, 99, 108, 109, 109, 114, 115, 116, 117, 117, 128, 129, 130, 133) # 执行两样本的Z检验 z.test(x=cityA, y=cityB, mu=0, sigma.x=15, sigma.y=15) # Z 统计量为 -1.7182 z.test(x=cityB, y=cityA, mu=0, sigma.x=15, sigma.y=15 )# Z 统计量为 -1.7182 # 计算p值, 由于是双尾检验，所有乘以2 pnorm(-1.7182,mean=0,sd=1)*2 (1-pnorm(1.7182,mean=0,sd=1))*2 # 检验结果可视化 ##################################### x <- seq(-5,5,length.out = 100) # 随机变量X的可能取值，这里是IQ的可能取值 y <- dnorm(x,0,1) # 正态分布密度概率函数的高度 plot(x,y,type = "l") ##################################### Z.5 <- qnorm(0.05/2,mean=0,sd = 1) # 计算p值为0.05时的Z统计量 abline(v = Z.5,col="red") abline(v = -Z.5,col="red") abline(v = -1.7182) abline(v = 1.7182)
Two-sample z-Test data: cityA and cityB z = -1.7182, p-value = 0.08577 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -17.446925 1.146925 sample estimates: mean of x mean of y 100.65 108.80 Two-sample z-Test data: cityB and cityA z = 1.7182, p-value = 0.08577 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -1.146925 17.446925 sample estimates: mean of x mean of y 108.80 100.65 0.0857601415480858 0.0857601415480858