I'm wondering how to report the result of a t-test from R given that the degrees of freedom change when the lengths of the vectors are the same.

For example

`set.seed(1) n = 500 x = rnorm(n, 6, 1) y = rnorm(n, 6, 2) t = t.test(x,y) t t$parameter `

Gives the output

`> t Welch Two Sample t-test data: x and y t = 1.0924, df = 716.16, p-value = 0.275 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.09130295 0.32035262 sample estimates: mean of x mean of y 6.022644 5.908119 > t$parameter df 716.156 `

Whereas

`set.seed(2) n = 500 x = rnorm(n, 6, 1) y = rnorm(n, 6, 2) t = t.test(x,y) t t$parameter `

Gives the output

`> t Welch Two Sample t-test data: x and y t = -0.62595, df = 748.05, p-value = 0.5315 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.2602459 0.1344099 sample estimates: mean of x mean of y 6.061692 6.124610 > t$parameter df 748.0475 `

I'm not sure if it would be typical to report the first as $t(716.15), p = 0.275$ and the second as $t(748.05), p = 0.53$

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#### Best Answer

If you have to report all the details then you should also report the actual t-value, not just degrees of freedom.

About the degrees of freedom: your degrees of freedom changes because you are using t-test with Welch correction for pooling the variances of the two groups. If your context permits to assume equal variances in both groups you could call the `t.test()`

in the following way:

`t.test(x, y, var.equal=TRUE) `

then you would get the same degrees of freedom for both cases – a whole number dependant on the number of observations. However don't do this just to get a round degrees of freedom value.

And if Welch t-test is more appropriate in your case consider stating that Welch t-test was used in your report as well.

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