R help - Feb 2013 - On p-values presented in the summary of Linear Models

Dear list members

I have a doubt on how p-values for t-statistics are calculated in the
summary of Linear Models.

Here goes an example:

x <- rnorm(100,50,10)
y <- rnorm(100,0,5)
fit1<-lm(y~x)
summary(fit1)
summary(fit1)$coef[2] # b
summary(fit1)$coef[4] # Std. Error
summary(fit1)$coef[6] # t-statistic
summary(fit1)$coef[8] # Pr(>|t|
summary(fit1)$df [2] # degrees of freedom

# t-statistic can be calculated as:
t<-(summary(fit1)$coef[2])/summary(fit1)$coef[4]
t # t-statistic

# the critical value for t0.05(2)df can be obtained in a t distribuition
table
# http://www.math.unb.ca/~knight/utility/t-table.htm or with
qt(0.975,summary(fit1)$df[2])

# Two-sided p-value should be estimated with
dt(t,summary(fit1)$df[2]) # isn't it?

But this value is different from summary(fit1)$coef[8]

My question is: how to reach to the same p-value indicated in Pr(>|t|) or
summary(fit1)$coef[8]?

Thanks in advance,

Antonio Olinto

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On 02/07/2013 08:22 PM, Antonio Silva wrote:
> Dear list members
>
> I have a doubt on how p-values for t-statistics are calculated in the
> summary of Linear Models.
>
> Here goes an example:
>
> x <- rnorm(100,50,10)
> y <- rnorm(100,0,5)
> fit1<-lm(y~x)
> summary(fit1)
> summary(fit1)$coef[2] # b
> summary(fit1)$coef[4] # Std. Error
> summary(fit1)$coef[6] # t-statistic
> summary(fit1)$coef[8] # Pr(>|t|
> summary(fit1)$df [2] # degrees of freedom
>
> # t-statistic can be calculated as:
> t<-(summary(fit1)$coef[2])/summary(fit1)$coef[4]
> t # t-statistic
>
> # the critical value for t0.05(2)df can be obtained in a t distribuition
> table
> # http://www.math.unb.ca/~knight/utility/t-table.htm or with
> qt(0.975,summary(fit1)$df[2])
>
> # Two-sided p-value should be estimated with
> dt(t,summary(fit1)$df[2]) # isn't it?
>
The dt() function is giving you the value from the density function, not 
the probability.  Use pt() to obtain probabilities.

> But this value is different from summary(fit1)$coef[8]
>
> My question is: how to reach to the same p-value indicated in Pr(>|t|)
or
> summary(fit1)$coef[8]?
>
> Thanks in advance,
>
> Antonio Olinto
>
> 	[[alternative HTML version deleted]]
>
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>

-- 
Kevin E. Thorpe
Head of Biostatistics,  Applied Health Research Centre (AHRC)
Li Ka Shing Knowledge Institute of St. Michael's
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.3016

OK, I found the answer:

2*pt(t,summary(fit1)$df[2])

Thanks anyway ...


2013/2/7 Antonio Silva <aolinto.lst@gmail.com>
> Dear list members
>
> I have a doubt on how p-values for t-statistics are calculated in the
> summary of Linear Models.
>
> Here goes an example:
>
> x <- rnorm(100,50,10)
> y <- rnorm(100,0,5)
> fit1<-lm(y~x)
> summary(fit1)
> summary(fit1)$coef[2] # b
> summary(fit1)$coef[4] # Std. Error
> summary(fit1)$coef[6] # t-statistic
> summary(fit1)$coef[8] # Pr(>|t|
> summary(fit1)$df [2] # degrees of freedom
>
> # t-statistic can be calculated as:
> t<-(summary(fit1)$coef[2])/summary(fit1)$coef[4]
> t # t-statistic
>
> # the critical value for t0.05(2)df can be obtained in a t distribuition
> table
> # http://www.math.unb.ca/~knight/utility/t-table.htm or with
> qt(0.975,summary(fit1)$df[2])
>
> # Two-sided p-value should be estimated with
> dt(t,summary(fit1)$df[2]) # isn't it?
>
> But this value is different from summary(fit1)$coef[8]
>
> My question is: how to reach to the same p-value indicated in Pr(>|t|)
or
> summary(fit1)$coef[8]?
>
> Thanks in advance,
>
> Antonio Olinto
>


-- 
Antônio Olinto Ávila da Silva
Biólogo / Oceanógrafo
Instituto de Pesca (Fisheries Institute)
São Paulo, Brasil

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On 8 Feb 2013, at 01:24, "Antonio Silva" <aolinto.lst at
gmail.com> wrote:
> # Two-sided p-value should be estimated with
> dt(t,summary(fit1)$df[2]) # isn't it?
No, on two counts.
> 
First, dt is the density; you need pt, the cumulative probability, not dt.
Second, pt(t, ...) would calculate the one sided lower tail probability. You
need twice the upper tail probability for a two-sided p-value. Try 2*pt(t, ...,
lower.tail=FALSE) (and if thats wrong by a factor of four i've multiplied
instead of dividing ... again ....)

S

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