[R] interpreting one-way anova tables

[David Winsemius]

On Sep 20, 2010, at 11:53 AM, Jabez Wilson wrote:

> Hi, I am trying to reconcile anova table in R (summary(lm)) with  
> individual t.test.
> datafilename="http://personality-project.org/R/datasets/R.appendix1.data 
> "
> data.ex1=read.table(datafilename,header=T)   #read the data into a  
> table
> summary(lm(Alertness~Dosage,data=data.ex1))

The quick answer is that in the ANOVA situation where you are  
interpreting individual level parameters, you are testing for the  
difference of a particular group from a shared mean (the intercept)  
across all three groups, whereas with the t-test you are only  
considering two groups at a time. (The default treatment contrasts do  
not actually result in the intercept estimate being a global mean,  
however.)

-- 
David.

>
> gives:
>
> Call:
> lm(formula = Alertness ~ Dosage, data = data.ex1)
>
> Residuals:
>    Min     1Q Median     3Q    Max
> -8.500 -2.437  0.250  2.687  8.500
>
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|)
> (Intercept)   32.500      2.010  16.166 6.72e-11 ***
> Dosageb       -4.250      2.659  -1.598 0.130880
> Dosagec      -13.250      3.179  -4.168 0.000824 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 4.924 on 15 degrees of freedom
> Multiple R-squared: 0.5396,     Adjusted R-squared: 0.4782
> F-statistic: 8.789 on 2 and 15 DF,  p-value: 0.002977
>
> As far as I understand it the lines "Dosageb" and "DosageC"  
> represent the difference between DosageA and the other two dosages.
> My question is this: are these differences and the p-values  
> associated with them the same as a t.test or pairwise.t.test on  
> these groups? If I do t.tests, I get different values for t and p- 
> value from those in the anova table above.
> Can someone please explain what the discrepancy is?
> Thanks
>
>
>
>
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>
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David Winsemius, MD
West Hartford, CT