# [R] Tukey HSD following lme

From: Christina Schädel <c.schaedel_at_unibas.ch>
Date: Tue, 18 Nov 2008 14:54:37 +0100

I'm using Tukey HSD as post-hoc test following a lme analysis. I'm measuring hemicelluloses in different species treated with three different CO2 concentrations (l=low, m=medium, h=high). The whole experiment is a split-plot design and the Tukey-function from the package multcomp is suitable for lme-analysis with random factors.

The analysis works fine but I get a non significant lme-result and if I do a Tukey afterwards (I know that one usually does a Tukey following a significant anova-result) I get highly significant p-values for two multiple comparisons.

How can this happen? How can the p-values from the Tukey become significant when the lme-model wasn't?

the data are: d

Species Block CO2 hemicell

```  Ps         a     l    9.027363
Ps         b     l    9.647537
Ps         a     m   10.051916
Ps         b     m   10.112294
Ps         a     h   10.342162
Ps         b     h   10.303091

```

my lme model:
anova(hc<-lme(asin(sqrt(0.01*hemicell))~CO2,random=~1|Block/CO2,data=d))

```             numDF denDF   F-value p-value

(Intercept)     1     2 30403.248  <.0001

CO2             2     2     8.051  0.1105

```

Tukey with the lme-object:

summary(glht(hc, linfct=mcp(CO2="Tukey")))

yielding:

Linear Hypotheses:

Estimate Std. Error z value p value

```m - l == 0 0.012616   0.004317   2.922 0.00963 **
h - l == 0 0.016590   0.004317   3.843 < 0.001 ***
h - m == 0 0.003973   0.004317   0.920 0.62738
---
```

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- single-step method)

Thank you very much for your help

Christina

```--
Christina Schädel
Institute of Botany
University of Basel
Schönbeinstrasse 6
CH-4056 Basel
ph. +41 61 267 35 06
fax +41 61 267 29 80
E-Mail C.Schaedel_at_unibas.ch

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