# [R] output from multcomp and lm

John Fox jfox at mcmaster.ca
Tue Feb 3 14:04:00 CET 2004

```Dear Hiroto,

The anova() function reports a sequential analysis of variance, so the test
for Cond ignores the covariate. A good guess is that the effect of Cond
isn't significant controlling for the covariate. You could instead use
drop1() or Anova() in the car package.

I hope that this helps,
John

At 10:46 AM 2/3/2004 +0900, Hiroto Miyoshi wrote:

>Dear R-users
>
>I analysed the same data set by two different ways;
>analysis of covariance by using lm and anova functions
>and multiple comparison by using simtest function in
>the multcomp library.
>
>The output from the analysis of covariance is;
>
> >   y<-lm(D~Cond+Q1,data=x)
> > anova(y)
>Analysis of Variance Table
>
>Response: D
>              Df Sum Sq Mean Sq F value    Pr(>F)
>Cond        2 1017.8   508.9   4.7548  0.0135041 *
>Q1           1 1652.7  1652.7 15.4417  0.0002969 ***
>Residuals 44 4709.2   107.0
>---
>Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
>
>where Cond is a factor with three levels (A,B,C)
>and Q1 is a covariate.
>
>
>
>Now, simtest showed the following output
>
> >   o5<-summary(simtest(D~Cond+Q1,conf.level=0.95,data=x,type="Tukey"))
> >   o5
>
>   Simultaneous tests: Tukey contrasts
>
>Call:
>simtest.formula(formula = D ~ Cond + Q1, data = x, conf.level = 0.95,
>     type = "Tukey")
>
>   Tukey contrasts for factor Cond, covariable:  Q1
>
>Contrast matrix:
>               CondA CondB CondC
>CondB-CondA 0    -1     1     0 0
>CondC-CondA 0    -1     0     1 0
>CondC-CondB 0     0    -1     1 0
>
>
>Absolute Error Tolerance:  0.001
>
>Coefficients:
>                     Estimate t value Std.Err. p raw  p Bonf  p adj
>CondB-CondA    5.555  -1.461    3.802  0.151   0.453   0.319
>CondC-CondB   -5.248  -1.365    3.661 0.179   0.453   0.319
>CondC-CondA    0.306  -0.084    3.844  0.934   0.934   0.934
>
>The results from two analyses seem so different that I am
>wondering why.  I do understand that multiple comparison may
>not show any significant difference even when the overall analysis
>of (co)variance shows the statistical significance of a factor.
>
>However, in my analysis, overall analysis showed statistical significance of
>1.4% level and mutiple comparison showed significance of 32% level
>Could this happen? and why?  Please enlighten me.
]
-----------------------------------------------------
John Fox
Department of Sociology
McMaster University