t分布的推导
那我们来写写代码，实践这个过程。我设定一个总体均数为0，标准差=1，样本量为1000的人群（图A是这个总体的概率分布）。图B，也是一次抽取三个人，抽了200个，图C一次抽取6个人。都分别计算t值。我们看到图C，一次抽取6个人，分布更多集中在总体均数为0。 还有一个，问题，图B中画绿框的这一部分，怎么解释呢？课后可以想想。（1.抽样误差、2.开端的，无闭合）
继续写代码实践，。如一次，，，他们分布会有什么特点。从图片可以得出什么规律：发现一次抽取3次和一次抽取6次比。一次抽取3次的曲线更低，向两边散。一次抽取6个样的，更集中。
#生成正态分布的数值,共1000,总体均数为0，标准差为1data <- rnorm(1000, mean = 0, sd = 1)#查看直方图分布hist(data)hist(data,freq = FALSE,,ylim=c(0,0.5))lines(density(data),col="blue",lwd=2)#如果抽取例数n=3的样本k个,假设抽取200个data_n3_k200 = matrix(NA, nrow = 200, ncol = 3)for (i in 1:200) {data_n3_k200[i, ] = sample(data, size = 3)}data_n3_k200 <- as.data.frame(data_n3_k200)data_n3_k200$mean <- apply(data_n3_k200[1:200,1:3],1,mean)data_n3_k200$sd <- apply(data_n3_k200[1:200,1:3],1,sd)data_n3_k200$t <- (data_n3_k200$mean-0)/(data_n3_k200$sd/sqrt(2))hist(data_n3_k200$t,freq = FALSE,ylim=c(0,0.6),xlim=c(-6,6))lines(density(data_n3_k200$t),col="blue",lwd=2)#如果抽取例数n=6的样本k个,假设抽取200个data_n2_k200 = matrix(NA, nrow = 200, ncol = 6)for (i in 1:200) {data_n2_k200[i, ] = sample(data, size = 6)}data_n2_k200 <- as.data.frame(data_n2_k200)data_n2_k200$mean <- apply(data_n2_k200[1:200,1:6],1,mean)data_n2_k200$sd <- apply(data_n2_k200[1:200,1:6],1,sd)data_n2_k200$t <- (data_n2_k200$mean-0)/(data_n2_k200$sd/sqrt(2))hist(data_n2_k200$t,freq = FALSE,ylim=c(0,0.9))lines(density(data_n2_k200$t),col="blue",lwd=2)#如果抽取例数n=3的样本k个,假设抽取10000次data_n3_k10000 = matrix(NA, nrow = 10000, ncol = 3)for (i in 1:10000) {data_n3_k10000[i, ] = sample(data, size = 3)}data_n3_k10000 <- as.data.frame(data_n3_k10000)data_n3_k10000$mean <- apply(data_n3_k10000[1:10000,1:3],1,mean)data_n3_k10000$sd <- apply(data_n3_k10000[1:10000,1:3],1,sd)data_n3_k10000$t <- (data_n3_k10000$mean-0)/(data_n3_k10000$sd/sqrt(2))hist(data_n3_k10000$t,freq = FALSE,ylim=c(0,0.5))lines(density(data_n3_k10000$t),col="blue",lwd=2)zz#如果抽取例数n=6的样本k个,假设抽取1000次data_n2_k10000 = matrix(NA, nrow = 10000, ncol = 6)for (i in 1:10000) {data_n2_k10000[i, ] = sample(data, size = 6)}data_n2_k10000 <- as.data.frame(data_n2_k10000)data_n2_k10000$mean <- apply(data_n2_k10000[1:10000,1:6],1,mean)data_n2_k10000$sd <- apply(data_n2_k10000[1:10000,1:6],1,sd)data_n2_k10000$t <- (data_n2_k10000$mean-0)/(data_n2_k10000$sd/sqrt(2))hist(data_n2_k10000$t,freq = FALSE,ylim=c(0,0.8))lines(density(data_n2_k10000$t),col="blue",lwd=2)z#hist(data_n3_k10000$t,freq = FALSE,ylim=c(0,0.5),xlim = c(-20,20))plot(0,0.5,xlim=c(-1.5,1.5),ylim=c(0,0.7))lines(density(data_n3_k10000$t),col="BLUE",lwd=2)par(new=TRUE)#hist(data_n2_k10000$t,freq = FALSE,axes = FALSE,xlab = "", ylab = "")lines(density(data_n2_k10000$t),col="red",lwd=2)
