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 Thanks in advance, Fred J.
The pairwise tests compare only pairs of means. Plot the means themselves. Chances are you will see some clustering of groups, or a visible contrast of several groups. Rich
Cody_Hamilton at Edwards.com
2007-Mar-02 22:22 UTC
[R] significant anova but no distinct groups ?
Frederic,
You're performing 8*7/2 = 28 multiple comparisons controlling the FWE at
the .05 level. Using a Bonferroni's adjustment (admittedly more
conservative than the Holm's or Tukey's approach), that's testing
each
comparison at the .05/28 = 0.0018 level. With only 100 observations spread
over 8 levels, you won't have much power to detect a difference.
Regards,
-Cody
Frederic Jean
<Frederic.Jean at un
iv-brest.fr> To
Sent by: r-help at r-project.org
r-help-bounces at st cc
at.math.ethz.ch
Subject
[R] significant anova but no
03/02/2007 01:52 distinct groups ?
PM
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
Thanks in advance,
Fred J.
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Mendiburu, Felipe (CIP)
2007-Mar-02 23:51 UTC
[R] significant anova but no distinct groups ?
You can use the LSD.test or waller.test of the package agricolae that less conservatives than tukey. ________________________________ From: r-help-bounces at stat.math.ethz.ch on behalf of Frederic Jean Sent: Fri 3/2/2007 4:52 PM To: r-help at r-project.org Subject: [R] significant anova but no distinct groups ? 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 Thanks in advance, Fred J. ______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Frederic Jean wrote:> 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() ?The apparent paradox is only apparent. This sort of thing can and does happen. One way of thinking about this situation is to envisage a circle (Anova) and a square (multiple comparisons), superimposed, with the corners of the square sticking outside of the circle, and the extremities of the circle protruding beyond the edges of the square. You get a ``significant'' result from the Anova if a point lands outside the circle; you get a ``significant'' result from the multiple comparisons if a point lands outside the square. So if a point lands in the corners of the square that stick out beyond the circle, you have a ``significant'' Anova result, but find no ``significant'' differences in the multiple comparisons. Conversely a point could land in the extremities of the circle that protrude beyond the edges of the square, in which case you would find ``significant'' differences in the multiple comparisons but your Anova test would not be ``significant''. These are rare but not unheard of phenomena. The essence of the situation is that the data are giving you an ambiguous message. There is no real way to resolve the ambiguity except by collecting more data. Note that if there is a significant Anova result there will be at least one ``contrast'' amongst the means that is significantly different from zero on an a posteriori basis. This contrast need not however be a pairwise difference between means. cheers, Rolf Turner rolf at math.unb.ca