R help - Apr 2008 - p-values always identical for t.test of certain group of samples, why ?

Hi,

Given the following,

a <- rnorm(5)
b <- rnorm(5)
c <- rnorm(5)
a.1g.scale <- scale(c(a,b,c))[1:5]
b.1g.scale <- scale(c(a,b,c))[6:10]
c.1g.scale <- scale(c(a,b,c))[11:15]
a.2g.scale <- scale(c(a,b))[1:5]
b.2g.scale <- scale(c(a,b))[6:10]
c.2g.scale <- scale(c)
a.3g.scale <- scale(a)
b.3g.scale <- scale(b)
c.3g.scale <- scale(c)

I am puzzled why the p-values are identical for t.test(a.1g.scale,
b.1g.scale), t.test(a.2g.scale, b.2g.scale), and t.test(a, b); similarly for
t.test(a.3g.scale, b.3g.scale) and t.test(b.3g.scale, c.3g.scale); similarly
for t.test(b.1g.scale, c.1g.scale) and t.test(b, c)
> t.test(a.1g.scale, b.1g.scale)$p.value
[1] 0.7462252
> t.test(a.2g.scale, b.2g.scale)$p.value
[1] 0.7462252
> t.test(a.3g.scale, b.3g.scale)$p.value
[1] 1
> t.test(b.1g.scale, c.1g.scale)$p.value
[1] 0.4995508
> t.test(b.2g.scale, c.2g.scale)$p.value
[1] 0.885622
> t.test(b.3g.scale, c.3g.scale)$p.value
[1] 1
> t.test(a, b)$p.value
[1] 0.7462252
> t.test(b, c)$p.value
[1] 0.4995508

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Why should it not be the same? Its the same dataset (up to scaling) you 
are testing on. Your effect (mean difference) will be different, but not 
your (standardized) t-statistic and df and therefore not your p-value.
You will get the same result for the first if you simply test
t.test(a,b)

hth.

Ng Stanley schrieb:
> Hi,
>
> Given the following,
>
> a <- rnorm(5)
> b <- rnorm(5)
> c <- rnorm(5)
> a.1g.scale <- scale(c(a,b,c))[1:5]
> b.1g.scale <- scale(c(a,b,c))[6:10]
> c.1g.scale <- scale(c(a,b,c))[11:15]
> a.2g.scale <- scale(c(a,b))[1:5]
> b.2g.scale <- scale(c(a,b))[6:10]
> c.2g.scale <- scale(c)
> a.3g.scale <- scale(a)
> b.3g.scale <- scale(b)
> c.3g.scale <- scale(c)
>
> I am puzzled why the p-values are identical for t.test(a.1g.scale,
> b.1g.scale), t.test(a.2g.scale, b.2g.scale), and t.test(a, b); similarly
for
> t.test(a.3g.scale, b.3g.scale) and t.test(b.3g.scale, c.3g.scale);
similarly
> for t.test(b.1g.scale, c.1g.scale) and t.test(b, c)
>
>   
>> t.test(a.1g.scale, b.1g.scale)$p.value
>>     
> [1] 0.7462252
>   
>> t.test(a.2g.scale, b.2g.scale)$p.value
>>     
> [1] 0.7462252
>   
>> t.test(a.3g.scale, b.3g.scale)$p.value
>>     
> [1] 1
>   
>> t.test(b.1g.scale, c.1g.scale)$p.value
>>     
> [1] 0.4995508
>   
>> t.test(b.2g.scale, c.2g.scale)$p.value
>>     
> [1] 0.885622
>   
>> t.test(b.3g.scale, c.3g.scale)$p.value
>>     
> [1] 1
>   
>> t.test(a, b)$p.value
>>     
> [1] 0.7462252
>   
>> t.test(b, c)$p.value
>>     
> [1] 0.4995508
>
> 	[[alternative HTML version deleted]]
>
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-- 
Eik Vettorazzi
Institut f?r Medizinische Biometrie und Epidemiologie
Universit?tsklinikum Hamburg-Eppendorf

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