R help - Mar 2008 - relationship between t-test CI and SEM?

Hi,

I have what is probably a stupid question but I'm confused so here goes:

- I have a distribution (n=100) and want to determine if the mean is 
significantly different from 0.5.
- When I plot the 2-tailed 95% confidence limits for the standard error 
of the mean I find that the upper one just overlaps with 0.5. I was 
under the impression that this would lead me to conclude that there was 
no significant difference between the sample mean and 0.5.
- However, when I perform a t-test it tells me that my mean /is/ 
significantly different from 0.5. The confidence intervals returned by 
the t-test don't seem to match with the SEM I calculated (lm does return 
the same intervals).

I have tried this in both R and matlab with the same results. So I think 
I'm calculating things right. Am I misinformed about the interpretation 
of the SEM? What are the confidence limits returned by the t-test (they 
bear no relationship to the SEM)?


Thanks!

Rob

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at
r-project.org] On Behalf
> Of Rob Campbell
> Sent: Sunday, March 09, 2008 9:19 PM
> To: r-help at r-project.org
> Subject: [R] relationship between t-test CI and SEM?
> 
> Hi,
> 
> I have what is probably a stupid question but I'm confused so here
goes:
> 
> - I have a distribution (n=100) and want to determine if the mean is
> significantly different from 0.5.
> - When I plot the 2-tailed 95% confidence limits for the standard error
> of the mean I find that the upper one just overlaps with 0.5. I was
> under the impression that this would lead me to conclude that there was
> no significant difference between the sample mean and 0.5.
> - However, when I perform a t-test it tells me that my mean /is/
> significantly different from 0.5. The confidence intervals returned by
> the t-test don't seem to match with the SEM I calculated (lm does
return
> the same intervals).
> 
> I have tried this in both R and matlab with the same results. So I think
> I'm calculating things right. Am I misinformed about the interpretation
> of the SEM? What are the confidence limits returned by the t-test (they
> bear no relationship to the SEM)?
> 
> 
> Thanks!
> 
> Rob
> 
Rob,

It would help if you showed how you were computing the SEM, rather than telling
us you are doing it correctly (the posting guide does ask you to provide
commented, minimal, self-contained, reproducible code).  When I calculate the
SEM I get the same value produced by t.test().

Dan

Daniel Nordlund
Bothell, WA