R oneway.test with equal and non equal variance

Question

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!

Answer 1

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}