# [R] Question about interpretation of paired t-tests

Beat Meier meierbeat at gmx.ch
Mon Feb 1 10:36:47 CET 2010

```hi there,

i have a few questions about the correct interpretation of a paired t-test.
(i don't think that this matters, but I'm using R 2.10.1 on Windows).

to my questions:

you can help me...

I use one- and two-sided t-tests. My questons are on one side about how
R uses the hypothesis' and the second one is about p-vaues. First the
one-sided:

> t.test(var1,var2,paired=T,alternative="g")

Paired t-test

data:  var1 and var2
t = 4.3456, df = 50, p-value = 3.401e-05
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
0.00825842        Inf
sample estimates:
mean of the differences
0.01344257

This tests (H0-Hypothesis), whether the difference in means is smaller
or equal to 0? Here, the p-value is smaller than 0.05, which should mean
that at a level of 95% one can't reject the H0-hypothesis? there is no
strong evidence for rejecting the hypothesis, that the difference in
means is smaller or equal to 0?
(Question is, if I write "alternative="g"", if this defines my
alternative hypothesis (difference in means > 0) which I couldn't reject
if the p-value was >0.05?)

The two-sided:
> t.test(var1,var2,paired=T,alternative="t")

Paired t-test

data:  var1 and var2
t = 4.3456, df = 50, p-value = 6.801e-05
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.007229405 0.019655737
sample estimates:
mean of the differences
0.01344257

This tests, whether the difference in means is 0. p-value is smaller
than 0.025 (alpha/2) at a level of 95%, so the hypothesis that the
difference in means is 0 can't be rejected?

Thanks a lot,
B. Meier

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