9
$\begingroup$

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.
$\endgroup$
9
$\begingroup$

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

$\endgroup$
  • 1
    $\begingroup$ Hi onestop. I imagined this was the case, but couldn't quite see that from the wikipage (en.wikipedia.org/wiki/Tukey's_range_test), any suggestions on references for how this is performed? $\endgroup$ – Tal Galili Feb 5 '11 at 17:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.