# [R] significant anova but no distinct groups ?

Frederic Jean Frederic.Jean at univ-brest.fr
Fri Mar 2 22:52:31 CET 2007

```Dear all,

I am studying a dataset using the aov() function.

The independant variable 'cds' is a factor() with 8 levels and here is
the result in studying the dependant variable 'rta' with aov() :

> summary(aov(rta ~ cds))
Df  Sum Sq Mean Sq F value  Pr(>F)
cds          7 0.34713 0.04959  2.3807 0.02777
Residuals   92 1.91635 0.02083

The dependant variable 'rta' is normally distributed and variances are
homogeneous.
But when studying the result with TukeyHSD, no differences in 'rta'
are seen among groups of 'cds' :

> TukeyHSD(aov(rta ~ cds), which="cds")
Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = rta ~ cds)

\$cds
diff        lwr        upr     p adj
1-0 -0.1046092796 -0.4331100 0.22389141 0.9751178
2-0  0.0359991860 -0.1371359 0.20913425 0.9980970
3-0  0.0261665235 -0.1348524 0.18718540 0.9996165
4-0  0.0004502442 -0.1805448 0.18144531 1.0000000
5-0 -0.1438949939 -0.3104752 0.02268526 0.1422670
[...]
7-5  0.0621598639 -0.1027595 0.22707926 0.9386170
7-6  0.0256519274 -0.1757408 0.22704465 0.9999248

I tried a pairwise.t.test (holm correction) which also was not able to
detect differences in 'rta' among groups of 'cds'
I've never been confronted to such a situation before : is it just a
problem of power of the /a posteriori/ tests used ? Do I miss
something important in basic stats or in R ?
How to highlight differences among 'cds' groups seen with aov() ?

Any help appreciated