On 12/3/2012 6:20 AM, Sindri wrote:
Dear R-users
Please excuse me if this topic has been covered before, but I was unable to
find anything relevant by searching
I am currently doing a comparison of two biological variables that have a
highly significant linear relationship. I know that the p-value of linear
regression is not so interesting in itself, but this particular value does
raise a question.
How does R calculate (extremely low) p-values for linear regression?
For my data I got a p-value on the order of 10^-9 and a reviewer commented
on this. I tried to run the same analysis in both SAS and Sigmastat to be
sure that I was doing it right, but both these programs only return a
p-value of p < 0.0001
Since I am unable to reproduce my results in another statistics program, it
would be nice to be able to explain this unusally low p-value to the
reviewers.
This is a matter of you understanding that the p-value is an area under
a probability density curve. R is simply printing out the actual area
in a tail of some distribution. The other statistical program is making
the assumption that you are using the p-value to compare to a cutoff
alpha value that is (in most fields) never set much below p<0.001. If p
< alpha the "hypothesis test crowd" , would choose to reject NULL
hypothesis, so the other statistics programs take the attitude -- "why
provide more detail?". R chooses to give you the actual number and let
you do what you will with it. You could probably benefit from reviewing
hypothesis testing in a basic statistics book if this is not clear.
Note that 10e-9 is indeed less than 0.0001, so the programs don't
disagree. R just provides more detail.
This "problem" can be illustrated with the following made-up data:
x_var<-c(0.149,0.178,0.3474,0.167,0.121,0.182,0.176,0.448,0.091,0.083,0.090,0.407,0.378,0.132,0.227,0.172,0.088,0.392,0.425,0.150,0.319,0.190,0.171,0.290,0.214,0.431,0.193)
y_var<-c(0.918,0.394,0.131,0.9084,0.916,0.934,0.928,0.279,0.830,0.927,0.964,0.323,0.097,0.914,0.614,0.790,0.984,0.530,0.207,0.858,0.408,0.919,0.869,0.347,0.834,0.276,0.940)
fit<-lm(y_var~x_var)
summary(fit)
Call:
lm(formula = y_var ~ x_var)
Residuals:
Min 1Q Median 3Q Max
-0.39152 -0.06027 0.00933 0.10024 0.22711
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.18696 0.06394 18.562 3.90e-16 ***
x_var -2.25529 0.24788 -9.098 2.08e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1503 on 25 degrees of freedom
Multiple R-squared: 0.768, Adjusted R-squared: 0.7588
F-statistic: 82.78 on 1 and 25 DF, p-value: 2.083e-09
With kind regards,
Sindri Traustason
-----
-----------------------------------------
Sindri Traustason
Glostrup Hospital Ophthalmology Research Dept.
Copenhagen, Demark
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__________________
Robert W. Baer, Ph.D.
Professor of Physiology
Kirksille College of Osteopathic Medicine
A. T. Still University of Health Sciences
Kirksville, MO 63501 USA
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