卡方检验数据是否是正态分布的

参考https://www.zhihu.com/question/356250489一文进行修改注释。

x <- runif(150, 0.7, 85.96)

range(x)

a <- 1.504611 #x最小值

b <- 85.649936 #x最大值

breaks <- seq(a, b, length.out = 13)

xx <- cut(x, breaks = breaks)

freq <-table(xx)

p <- c(0, pnorm(breaks[-c(1, length(breaks))], mean = mean(x), sd = sd(x)), 1) #累积概率

p <- p[-1] - p[-length(p)] #每个点的概率，相当于后一个减去前一个

e <- p*100

chi_square <- sum((freq - e)^2/e)

p_value <- 1 - pchisq(chi_square, length(breaks) - 1 - 3) #对于正态分布来讲，自由度减去3 (https://www.statisticssolutions.com/chi-square-goodness-of-fit-test/)