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I came by the post "Post-hoc Pairwise Comparisons of Two-way ANOVA" (responding to this post), which shows the following:

dataTwoWayComparisons <- read.csv("http://www.dailyi.org/blogFiles/RTutorialSeries/dataset_ANOVA_TwoWayComparisons.csv")

model1 <- aov(StressReduction~Treatment+Age, data =dataTwoWayComparisons)
summary(model1) # Treatment is signif

pairwise.t.test(dataTwoWayComparisons$StressReduction, dataTwoWayComparisons$Treatment, p.adj = "none")
# no signif pair

TukeyHSD(model1, "Treatment")
# mental-medical   is the signif pair.

(Output is attached bellow)

Could someone please explain why the Tukey HSD is able to find a significant pairing while the paired (unadjusted pvalue) t-test fails in doing so?

Thanks.

Here is the code output

> model1 <- aov(StressReduction~Treatment+Age, data =dataTwoWayComparisons)
> summary(model1) # Treatment is signif
            Df Sum Sq Mean Sq F value    Pr(>F)    
Treatment    2     18   9.000      11 0.0004883 ***
Age          2    162  81.000      99     1e-11 ***
Residuals   22     18   0.818                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> pairwise.t.test(dataTwoWayComparisons$StressReduction, dataTwoWayComparisons$Treatment, p.adj = "none")

        Pairwise comparisons using t tests with pooled SD 

data:  dataTwoWayComparisons$StressReduction and dataTwoWayComparisons$Treatment 

         medical mental
mental   0.13    -     
physical 0.45    0.45  

P value adjustment method: none 
> # no signif pair
> 
> TukeyHSD(model1, "Treatment")
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = StressReduction ~ Treatment + Age, data = dataTwoWayComparisons)

$Treatment
                 diff         lwr        upr     p adj
mental-medical      2  0.92885267 3.07114733 0.0003172
physical-medical    1 -0.07114733 2.07114733 0.0702309
physical-mental    -1 -2.07114733 0.07114733 0.0702309

> # mental-medical   is the signif pair.
Tal Galili
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1 Answers1

10

Because your pairwise $t$-test above is not adjusted for age, and age explains a lot of the variance in StressReduction.

onestop
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    Hi onestop. I imagined this was the case, but couldn't quite see that from the wikipage (http://en.wikipedia.org/wiki/Tukey's_range_test), any suggestions on references for how this is performed? – Tal Galili Feb 05 '11 at 17:54