[R] Bonferroni p-value greater than 1

[John Fox]

Dear Horace,

The Bonferonni p-value is obtained from the "unadjusted" p-value by
multiplying the latter by the number of observations, and provides a
conservative (although usually quite accurate) outlier test. When the
adjusted p-value exceeds 1 you can take that as an indication that there are
no unusually large studentized residuals (and indeed that the largest
studentized residual is smaller than one would expect under the standard
linear-model assumptions). 

I hope this helps,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Horace Tso
> Sent: Wednesday, March 28, 2007 6:36 PM
> To: 'R R-help'
> Subject: [R] Bonferroni p-value greater than 1
> 
> Hi folks,
> 
> I use the outlier.test in package car to test a lm model and 
> the bonferroni p value returned is shown as NA. When the 
> object is typed it indicates the p value is greater than 1. 
> I'm not sure how to interpret it. 
> 
> Thanks in advance.
> 
> Horace W. Tso
> 
> 
> > outlier.test(mod)$test
> max|rstudent|            df  unadjusted p  Bonferroni p
>    2.04106376   18.00000000    0.05618628            NA 
> 
> > outlier.test(mod)
> 
> max|rstudent| = 2.041064, degrees of freedom = 18,
> unadjusted p = 0.05618628, Bonferroni p > 1
> 
> Observation: 1 
> 
> The lm model looks fine to me,
> 
> > summary(mod)
> 
> Call:
> lm(formula = x ~ ind, na.action = na.fail)
> 
> Residuals:
>     Min      1Q  Median      3Q     Max 
> -1.2082 -0.5200  0.1309  0.5725  0.9593 
> 
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|)    
> (Intercept) 59.84586    0.31900   187.6  < 2e-16 ***
> ind         -0.16768    0.02541    -6.6 2.57e-06 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> Residual standard error: 0.705 on 19 degrees of freedom
> Multiple R-Squared: 0.6963,     Adjusted R-squared: 0.6803 
> F-statistic: 43.56 on 1 and 19 DF,  p-value: 2.57
> 
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