方差不等的参数方差分析 [英] parametric ANOVA with unequal variances

问题描述

我想知道R中是否可以做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]

从此示例中可以看到，仅在两个组的情况下，在R中执行ANOVA的不同方法始终会导致p值等于通过t.test获得的p值，且方差相等.再次，有没有一种方法可以执行方差不相等的方差分析?

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

在这种情况下，存在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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