R help - Feb 2010 - Question about interpretation of paired t-tests

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:

i've been using a lot of time about this minor concerns now and I hope 
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

I appears that you have the logic backwards.  P-values less than alpha (0.05 in
your example) mean that you can reject the null hypothesis that the true mean
difference is 0.

Also, for the 2 sided test you either compare the 1-tail p-value to alpha/2 or
double the 1-tail p-value (what R does if you specify 2 tails) and compare that
to alpha.  It looks like you are comparing 2*p-value to alpha/2 which is over
correcting (doing a 4-tailed test, hmm, need to think of an example where that
makes sense).

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Beat Meier
> Sent: Monday, February 01, 2010 2:37 AM
> To: r-help at r-project.org
> Subject: [R] Question about interpretation of paired t-tests
> 
> 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:
> 
> i've been using a lot of time about this minor concerns now and I hope
> 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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