具有不等方差的参数方差分析 [英] parametric ANOVA with unequal variances

问题描述

我想知道 R 中是否有办法进行方差不等的方差分析?

I was wondering if there is a way in R to do an ANOVA with unequal variances?

想象下面的例子:

x <- c(10,11,15,8,16,12,20)
y <- c(10,14,18,25,28,30,35)

d <- c(x,y)
f <- as.factor(c(rep("a",7), rep("b",7)))

# Unequal variance:

t.test(x,y)$p.value
t.test(d~f)$p.value

# Equal variance:

t.test(x,y, var.equal=TRUE)$p.value
t.test(d~f, var.equal=TRUE)$p.value

anova(lm(d~f))[[5]]
summary(aov(lm(d~f)))[[1]][5]
summary(lm(d~f))[[4]][8]

正如你从这个例子中看到的，在 R 中执行方差分析的不同方法，在只有两个组的情况下，总是导致 p 值与通过 t.test 获得的 p 值相同，具有相同的方差.同样，有没有办法执行方差不等的方差分析?

As you can see from this example the different ways of performing an ANOVA in R, in case of two groups only, always result in a p-value identical to the one obtained by a t.test with equal variances. Again, is there a way to perform an ANOVA with unequal variances?

推荐答案

对于这种情况有 oneway.test()

R> oneway.test(d~f)

    One-way analysis of means (not assuming equal variances)

data:  d and f 
F = 6.631, num df = 1.000, denom df = 8.339, p-value = 0.03179

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