R help - Oct 2010 - CI using ci.numeric

Hi,

I am trying to calculate confidence intervals using ci.numeric from epicalc
package. If I generate a normal set of data and find the 99% and 95% CI, they
seem too narrow to me. Am I doing something wrong?? The IQR goes from -0.62 to
0.62, so I thought the CI limits should be more extreme than these values.

 x<- rnorm(200,0,1)
ci.numeric(x=mean(x),n=200,sds=sd(x),alpha=0.05)
    n        mean       sd         se  lower95ci upper95ci
1 200 -0.07129813 1.015668 0.07181859 -0.2129213 0.0703250

ci.numeric(x=mean(x),n=200,sds=sd(x),alpha=0.01)
   n        mean       sd         se  lower99ci upper99ci
 200 -0.07129813 1.015668 0.07181859 -0.2580811 0.1154848

quantile(x)
         0%         25%         50%         75%        100% 
-3.23354673 -0.61926758 -0.06672757  0.62000897  2.43763696

Thanks,

D.
 		 	   		  
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2010/10/20 David A. <dasolexa@hotmail.com>
>  I am trying to calculate confidence intervals using ci.numeric from
> epicalc package. If I generate a normal set of data and find the 99% and
95%
> CI, they seem too narrow to me. Am I doing something wrong??

Yes.
set.seed(123)
x<- rnorm(200,0,1)
ci.numeric(x=mean(x),n=length(x),sds=sd(x),alpha=0.05)
#  n                mean            sd              se  lower95ci
 upper95ci
#  200 -0.008570445 0.9431599 0.06669147 -0.1400831 0.1229422
#  Let's compute lower CI of a mean usnig t-distribution as it is in
ci.numeric
 mean(x) - qt(p = (1 - .05/2),df=length(x)-1) * sd(x)/sqrt(length(x))
# [1] -0.1400831
# now using normal distribution
 mean(x) - qnorm(p = (1 - .05/2)) * sd(x)/sqrt(length(x))
# [1] -0.1392833




-- 
Mi³ego dnia

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On Oct 20, 2010, at 4:10 AM, David A. wrote:
>
> Hi,
>
> I am trying to calculate confidence intervals using ci.numeric from  
> epicalc package. If I generate a normal set of data and find the 99%  
> and 95% CI, they seem too narrow to me. Am I doing something wrong??
The next sentence suggests that what you are doing wrong is assuming  
that population parameters like the 0.75 and 0.25 quantiles (the IQR)  
are on the same scale as the confidence intervals around the  
population mean. As the number of samples increases the CI will narrow  
while the expected value of the IQR will remain the same. If you  
wanted to compare two values that remain on the same scale you ought  
to be looking at the SD rather than maen +/- 1.96*se(mean).

> The IQR goes from -0.62 to 0.62, so I thought the CI limits should  
> be more extreme than these values.
>
> x<- rnorm(200,0,1)
> ci.numeric(x=mean(x),n=200,sds=sd(x),alpha=0.05)
>    n        mean       sd         se  lower95ci upper95ci
> 1 200 -0.07129813 1.015668 0.07181859 -0.2129213 0.0703250
>
> ci.numeric(x=mean(x),n=200,sds=sd(x),alpha=0.01)
>   n        mean       sd         se  lower99ci upper99ci
> 200 -0.07129813 1.015668 0.07181859 -0.2580811 0.1154848
>
> quantile(x)
>         0%         25%         50%         75%        100%
> -3.23354673 -0.61926758 -0.06672757  0.62000897  2.43763696
>
> Thanks,
>
> D.
> 		 	   		
> 	[[alternative HTML version deleted]]
>
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David Winsemius, MD
West Hartford, CT