# R oneway.test with equal and non equal variance

can anybody tell me why the oneway.test() results in a p-value of NA when var.equal is set to FALSE but in a p-value of 0.7173 when it is set to TRUE

Here is my example:

x <- c(3.921973, 5.703782, 3.921973, 3.921973, 3.921973, 6.075346, 3.921973, 3.921973, 3.921973, 3.921973)
y <- c(4.424847, 4.424847, 4.424847, 4.424847, 4.424847, 4.424847, 4.424847, 4.424847)

d <- c(x,y)
f <- c(rep("a", 10), rep("b", 8))

oneway.test(d ~ f, var.equal = FALSE)

oneway.test(d ~ f, var.equal = TRUE)


Thanks for you help!

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The reason is that the sample variance of y is $0$ since all its elements are 4.424847. When var.equal = FALSE you get division by 0 (or some similar problem) at some point. –  MånsT Aug 7 '12 at 12:42

When in doubt, look at the source code (it's one of the interest of R). In that case you can just issue the name of the function at the R prompt. As pointed out by @MånsT, variance for the b group is zero, which makes one of the intermediate computation result in NaN when var.equal = FALSE.(a)

Note that if you only work with two groups, it is probably better to stay with a $t$-test with Welch correction, which in this case does not show any problem.

> t.test(d ~ f, var.equal = FALSE)

Welch Two Sample t-test

data:  d by f
t = -0.4145, df = 9, p-value = 0.6882
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.7061202  0.4874086
sample estimates:
mean in group a mean in group b
4.315491        4.424847


(a) The reference paper cited in the online help is given below:
B. L. Welch (1951), On the comparison of several mean values: an alternative approach. Biometrika, 38, 330-336

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