[R] Calculation of extremely low p-values (in lm)

[Sindri]

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 "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



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Sindri Traustason
Glostrup Hospital Ophthalmology Research Dept.
Copenhagen, Demark

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