# Paired t-tests

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## Paired t-tests

 Hello List, I'm trying to do a paired t-test, and I'm wondering if it's consistent with equations.  I have a dataset that has a response and two treatments (here's an example):    ID trt order          resp 17  1   0     1  0.0037513592 18  2   0     1  0.0118723051 19  4   0     1  0.0002610251 20  5   0     1 -0.0077951450 21  6   0     1  0.0022339952 22  7   0     2  0.0235195453 The subjects were randomized and assigned to receive either the treatment or the placebo first, then the other.  I know I'll eventually have to move on to a GLM or something that incorporates the order, but for now I wanted to start with a simple t.test.  My problem is that, if I get the responses into two vectors x and y (sorted by ID) and do a t.test, and then compare that to a formula t.test, they aren't the same. > t.test(x,y,paired=TRUE)         Paired t-test data:  x and y t = -0.3492, df = 15, p-value = 0.7318 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:  -0.010446921  0.007505966 sample estimates: mean of the differences            -0.001470477 > t.test(resp~trt,data=dat1[[3]],paired=TRUE)         Paired t-test data:  resp by trt t = -0.3182, df = 15, p-value = 0.7547 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:  -0.007096678  0.005253173 sample estimates: mean of the differences           -0.0009217521 What I'm assuming is that the equation isn't retaining the inherent order of the dataset, so the pairing isn't matching up (even though the dataset is ordered by ID).  Is there a way to make the t.test retain the correct ordering? Thanks, Sam ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Paired t-tests

 On Aug 15, 2010, at 9:05 AM, R Help wrote: > Hello List, > > I'm trying to do a paired t-test, and I'm wondering if it's consistent > with equations.  I have a dataset that has a response and two > treatments (here's an example): > >   ID trt order          resp > 17  1   0     1  0.0037513592 > 18  2   0     1  0.0118723051 > 19  4   0     1  0.0002610251 > 20  5   0     1 -0.0077951450 > 21  6   0     1  0.0022339952 > 22  7   0     2  0.0235195453 > > The subjects were randomized and assigned to receive either the > treatment or the placebo first, then the other.  I know I'll > eventually have to move on to a GLM or something that incorporates the > order, but for now I wanted to start with a simple t.test.  My problem > is that, if I get the responses into two vectors x and y (sorted by > ID) and do a t.test, and then compare that to a formula t.test, they > aren't the same. > >> t.test(x,y,paired=TRUE) > > Paired t-test > > data:  x and y > t = -0.3492, df = 15, p-value = 0.7318 > alternative hypothesis: true difference in means is not equal to 0 > 95 percent confidence interval: > -0.010446921  0.007505966 > sample estimates: > mean of the differences >           -0.001470477 > >> t.test(resp~trt,data=dat1[[3]],paired=TRUE) > > Paired t-test > > data:  resp by trt > t = -0.3182, df = 15, p-value = 0.7547 > alternative hypothesis: true difference in means is not equal to 0 > 95 percent confidence interval: > -0.007096678  0.005253173 > sample estimates: > mean of the differences >          -0.0009217521 > > What I'm assuming is that the equation isn't retaining the inherent > order of the dataset, so the pairing isn't matching up (even though > the dataset is ordered by ID).  Is there a way to make the t.test > retain the correct ordering? > > Thanks, > Sam See this thread from just 2 days ago:   https://stat.ethz.ch/pipermail/r-help/2010-August/249068.htmlperhaps focusing on Thomas' reply, which is the next post in the thread. Bottom line, don't use the formula method for a paired t test. HTH, Marc Schwartz ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Paired t-tests

 Marc Schwartz wrote: > On Aug 15, 2010, at 9:05 AM, R Help wrote: > >> Hello List, >> >> I'm trying to do a paired t-test, and I'm wondering if it's consistent >> with equations.  I have a dataset that has a response and two >> treatments (here's an example): >> >>   ID trt order          resp >> 17  1   0     1  0.0037513592 >> 18  2   0     1  0.0118723051 >> 19  4   0     1  0.0002610251 >> 20  5   0     1 -0.0077951450 >> 21  6   0     1  0.0022339952 >> 22  7   0     2  0.0235195453 >> >> The subjects were randomized and assigned to receive either the >> treatment or the placebo first, then the other.  I know I'll >> eventually have to move on to a GLM or something that incorporates the >> order, but for now I wanted to start with a simple t.test.  My problem >> is that, if I get the responses into two vectors x and y (sorted by >> ID) and do a t.test, and then compare that to a formula t.test, they >> aren't the same. >> >>> t.test(x,y,paired=TRUE) >> Paired t-test >> >> data:  x and y >> t = -0.3492, df = 15, p-value = 0.7318 >> alternative hypothesis: true difference in means is not equal to 0 >> 95 percent confidence interval: >> -0.010446921  0.007505966 >> sample estimates: >> mean of the differences >>           -0.001470477 >> >>> t.test(resp~trt,data=dat1[[3]],paired=TRUE) >> Paired t-test >> >> data:  resp by trt >> t = -0.3182, df = 15, p-value = 0.7547 >> alternative hypothesis: true difference in means is not equal to 0 >> 95 percent confidence interval: >> -0.007096678  0.005253173 >> sample estimates: >> mean of the differences >>          -0.0009217521 >> >> What I'm assuming is that the equation isn't retaining the inherent >> order of the dataset, so the pairing isn't matching up (even though >> the dataset is ordered by ID).  Is there a way to make the t.test >> retain the correct ordering? >> >> Thanks, >> Sam > > > See this thread from just 2 days ago: > >   https://stat.ethz.ch/pipermail/r-help/2010-August/249068.html> > perhaps focusing on Thomas' reply, which is the next post in the thread. > > Bottom line, don't use the formula method for a paired t test. Yes. I'm not sure the same problem is afoot here, though. In particular, I'm puzzled by the fact that there are 15DF in both cases, but different average difference. This kind of suggests to me that maybe the x and y are not computed correctly. (If only the ordering was scrambled, the average difference should be the same, but the variance typically inflated.) -- Peter Dalgaard Center for Statistics, Copenhagen Business School Phone: (+45)38153501 Email: [hidden email]  Priv: [hidden email] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.