Nils Skotara wrote:
Dear John,
thank you again! You replicated the type III result I got in SPSS! When I
calculate Anova() type II:
Univariate Type II Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
between 4.8000 1 9.0000 8 4.2667 0.07273 .
within 0.2000 1 10.6667 8 0.1500 0.70864
between:within 2.1333 1 10.6667 8 1.6000 0.24150
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I see the exact same values as you had written.
However, and now I am really lost, type III (I did not change anything else)
leads to the following:
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 72.000 1 9.000 8 64.0000 4.367e-05 ***
between 4.800 1 9.000 8 4.2667 0.07273 .
as.factor(within) 2.000 1 10.667 8 1.5000 0.25551
between:as.factor(within) 2.133 1 10.667 8 1.6000 0.24150
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
How is this possible?
This looks like a contrast parametrization issue: If we look at the
per-group mean within-differences and their SE, we get
> summary(lm(within1-within2~between - 1))
..
Coefficients:
Estimate Std. Error t value Pr(>|t|)
between1 -1.0000 0.8165 -1.225 0.256
between2 0.3333 0.6667 0.500 0.631
..
> table(between)
between
1 2
4 6
Now, the type II F test is based on weighting the two means as you would
after testing for no interaction
> (4*-1+6*.3333)^2/(4^2*0.8165^2+6^2*0.6667^2)
[1] 0.1500205
and type III is to weight them as if there had been equal counts
> (5*-1+5*.3333)^2/(5^2*0.8165^2+5^2*0.6667^2)
[1] 0.400022
However, the result above corresponds to looking at group1 only
> (-1)^2/(0.8165^2)
[1] 1.499987
It helps if you choose orhtogonal contrast parametrizations:
> options(contrasts=c("contr.sum","contr.helmert"))
> betweenanova <- lm(values ~ between)> Anova(betweenanova, idata=with,
idesign= ~as.factor(within), type = "III" )
Type III Repeated Measures MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.963 209.067 1 8 5.121e-07 ***
between 1 0.348 4.267 1 8 0.07273 .
as.factor(within) 1 0.048 0.400 1 8 0.54474
between:as.factor(within) 1 0.167 1.600 1 8 0.24150
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907
______________________________________________
R-help@r-project.org 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.
