Solved – How to report t statistic from R

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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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