Wilcoxon-Mann-Whitney秩和检验ranksumtest（或testU）
⽐较两个独⽴样本群组的平均值，这⾥不需要假设总体为Gaussian类型分布；这也称作Mann-Whitney U-test
抹茶千层蛋糕你想要看看两个⾜球队在⼀年进球数均值是否⼀样。以下为每个队在⼀年6场⽐赛中的进球数：
一级期刊Team A: 6, 8, 2, 4, 4, 5
Team B: 7, 10, 4, 3, 5, 6
Wilcoxon-Matt-Whitney test (or Wilcoxon rank sum test, orMann-Whitney U-test) ⽤于⽐较两个并不满⾜正态分布群组的均值⽐较：这是⼀个⾮参数检验（non-parametrical test）。其与应⽤于独⽴样本的t-test相当。光大水墨风景
让我们看看如何在R中解决这个我问题：
a = c(6, 8, 2, 4, 4, 5)
b = c(7, 10, 4, 3, 5, 6)
Wilcoxon rank sum test
data: a and b
径字组词
W = 14, p-value = 0.5174
alternative hypothesis: true location shift is not equal to 0
p-value⼤于0.05，因此我们可接受null hypothesis H0，即两个群组的均值统计相等。如果你运⾏ st(b, a, correct = FALSE)，p-value在逻辑上将会是⼀样的：
a = c(6, 8, 2, 4, 4, 5)
b = c(7, 10, 4, 3, 5, 6)
Wilcoxon rank sum test
data: b and a
鲍鱼怎么做最简便最好吃呢W = 22, p-value = 0.5174
alternative hypothesis: true location shift is not equal to 0
⽽值W的计算如下：
sum.rank.a = sum(rank(c(a,b))[1:6]) #sum of ranks assigned to the group a
W = sum.rank.a – (length(a)*(length(a)+1)) / 2
W
[1] 14
sum.rank.b = sum(rank(c(a,b))[7:12]) #sum of ranks assigned to the group b
W = sum.rank.b – (length(b)*(length(b)+1)) / 2
W
[1] 22
最后我们⽐较对独⽴样本Wilcoxon的表上查表得到的区间。对两个6个样本群组查表得到的区间是(26,52)，⽽我们样本的区间为：秋处露秋寒霜降是指哪六个节气
sum(rank(c(a,b))[1:6]) #sum of ranks assigned to the group a
[1] 35
sum(rank(c(a,b))[7:12]) #sum of ranks assigned to the group b
[1] 43
因为计算的区间(35, 43)包含在查表区间(26,52)，我们论断接受null hypothesis H0，即均值相等
过年日记100字=========================================================
在使⽤函数st，以下的输⼊参数形式才是使⽤了rank sum检验⽅法：
Wilcoxon rank sum test with continuity correction
data: a and b
W = 14, p-value = 0.5711
alternative hypothesis: true location shift is not equal to 0
#------------------------------------------
Wilcoxon rank sum test with continuity correction
data: b and a
甜蜜暴君W = 22, p-value = 0.5711
alternative hypothesis: true location shift is not equal to 0
这⾥求得的两个W值分别是低尾部值和⾼尾部值，我们可以⽤以下函数获得接受区间：
qwilcox(0.025, length(a), length(b), lower.tail=T)
[1] 6
qwilcox(0.025, length(a), length(b), lower.tail=F)
[1] 30
之前计算的W值区间(14, 22)在[6,30]范围内，所以我们接受null hypothesis，即a和b的均值显著相等。
