[R] Bonferroni p-value greater than 1

[Peter Dalgaard]

John Fox wrote:
> 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). 
>
>   
Yes, or put differently, the Bonferroni p is an upper bound of the true 
p. It is only accurate at the low end of the p scale. (It works by 
approximating P(A or B) by P(A)+P(B); since P(A and B) gets counted 
twice (make a diagram) that term needs to be small.)

BTW. This was yet another case of someone tacking their mail onto a 
completely different thread (replying to a random mail from r-help). 
Please avoid, since it confuses threading mail programs and the 
archiving system). I was looking for responses, so shifted to threaded 
mode and the post all but disappeared because it got tucked in under 
"multi-level modeling & R?"

> 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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>> PLEASE do read the posting guide 
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>     
>
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>