# How could a Tukey HSD test be more signif then the uncorrected P value of t.test?

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

> # no signif pair
>
> TukeyHSD(model1, "Treatment")
Tukey multiple comparisons of means
95% family-wise confidence level

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

$Treatment diff lwr upr p adj mental-medical 2 0.92885267 3.07114733 0.0003172 physical-medical 1 -0.07114733 2.07114733 0.0702309 physical-mental -1 -2.07114733 0.07114733 0.0702309 > # mental-medical is the signif pair.  ## 1 Answer Because your pairwise$t\$-test above is not adjusted for age, and age explains a lot of the variance in StressReduction.

• 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? – Tal Galili Feb 5 '11 at 17:54