Dear Nils,
I don't currently have a copy of SAS on my computer, so I asked Michael
Friendly to run the problem in SAS and he kindly supplied the following
results:
----------- snip ------------
The SAS System
1
12:32 Saturday, January 24,
2009
The GLM Procedure
Class Level Information
Class Levels Values
between 2 1 2
Number of Observations Read 10
Number of Observations Used 10
The SAS System
2
12:32 Saturday, January 24,
2009
The GLM Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information
Dependent Variable w1 w2
Level of within 1 2
MANOVA Test Criteria and Exact F Statistics
for the Hypothesis of no within Effect
H = Type III SSCP Matrix for within
E = Error SSCP Matrix
S=1 M=-0.5 N=3
Statistic Value F Value Num DF Den DF Pr
Wilks' Lambda 0.95238095 0.40 1 8
0.5447
Pillai's Trace 0.04761905 0.40 1 8
0.5447
Hotelling-Lawley Trace 0.05000000 0.40 1 8
0.5447
Roy's Greatest Root 0.05000000 0.40 1 8
0.5447
MANOVA Test Criteria and Exact F Statistics for
the Hypothesis of no within*between Effect
H = Type III SSCP Matrix for within*between
E = Error SSCP Matrix
S=1 M=-0.5 N=3
Statistic Value F Value Num DF Den DF Pr
Wilks' Lambda 0.83333333 1.60 1 8
0.2415
Pillai's Trace 0.16666667 1.60 1 8
0.2415
Hotelling-Lawley Trace 0.20000000 1.60 1 8
0.2415
Roy's Greatest Root 0.20000000 1.60 1 8
0.2415
The SAS System
3
12:32 Saturday, January 24,
2009
The GLM Procedure
Repeated Measures Analysis of Variance
Tests of Hypotheses for Between Subjects Effects
Source DF Type III SS Mean Square F Value Pr
between 1 4.80000000 4.80000000 4.27
0.0727
Error 8 9.00000000 1.12500000
The SAS System
4
12:32 Saturday, January 24,
2009
The GLM Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects
Source DF Type III SS Mean Square F Value Pr
within 1 0.53333333 0.53333333 0.40
0.5447
within*between 1 2.13333333 2.13333333 1.60
0.2415
Error(within) 8 10.66666667 1.33333333
----------- snip ------------
As you can see, these agree with Anova():
----------- snip ------------
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 .
within 1 0.048 0.400 1 8 0.54474
between:within 1 0.167 1.600 1 8 0.24150
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 235.200 1 9.000 8 209.0667 5.121e-07 ***
between 4.800 1 9.000 8 4.2667 0.07273 .
within 0.533 1 10.667 8 0.4000 0.54474
between:within 2.133 1 10.667 8 1.6000 0.24150
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
----------- snip ------------
So, unless Anova() and SAS are making the same error, I guess SPSS is doing
something strange (or perhaps you didn't do what you intended in SPSS). As I
said before, this problem is so simple, that I find it hard to understand
where there's room for error, but I wanted to check against SAS to test my
sanity (a procedure that will likely get a rise out of some list members).
Maybe you should send a message to the SPSS help list.
Regards,
John
------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox
-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
Behalf Of Skotara
Sent: January-24-09 6:30 AM
To: John Fox
Cc: r-help at r-project.org
Subject: Re: [R] Anova and unbalanced designs
Dear John,
thank you for your answer. You are right, I also would not have expected
a divergent result.
I have double-checked it again. No, I got type-III tests.
When I use type II, I get the same results in SPSS as in 'Anova' (using
also type-II tests).
My guess was that the somehow weighted means SPSS shows could be
responsible for this difference.
Or that using 'Anova' would not be correct for unequal group n's, which
was not the case I think.
Do you have any further ideas?
Thank you!
Nils
John Fox schrieb:
Dear Nils,
This is a pretty simple design, and I wouldn't have thought that there
much room for getting different results. More generally, but not here
there's only one between-subject factor), one shouldn't use
contr.treatment() with "type-III" tests, as you did. Is it possible that
got "type-II" tests from SPSS:
------ snip ----------
summary(Anova(betweenanova, idata=with, idesign= ~within, type = "II"
Type II Repeated Measures MANOVA Tests:
------------------------------------------
Term: between
Response transformation matrix:
(Intercept)
w1 1
w2 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 9.6
Sum of squares and products for error:
(Intercept)
(Intercept) 18
Multivariate Tests: between
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.347826 4.266667 1 8 0.072726 .
Wilks 1 0.652174 4.266667 1 8 0.072726 .
Hotelling-Lawley 1 0.533333 4.266667 1 8 0.072726 .
Roy 1 0.533333 4.266667 1 8 0.072726 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: within
Response transformation matrix:
within1
w1 1
w2 -1
Sum of squares and products for the hypothesis:
within1
within1 0.4
Sum of squares and products for error:
within1
within1 21.33333
Multivariate Tests: within
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0184049 0.1500000 1 8 0.70864
Wilks 1 0.9815951 0.1500000 1 8 0.70864
Hotelling-Lawley 1 0.0187500 0.1500000 1 8 0.70864
Roy 1 0.0187500 0.1500000 1 8 0.70864
------------------------------------------
Term: between:within
Response transformation matrix:
within1
w1 1
w2 -1
Sum of squares and products for the hypothesis:
within1
within1 4.266667
Sum of squares and products for error:
within1
within1 21.33333
Multivariate Tests: between:within
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.1666667 1.6000000 1 8 0.24150
Wilks 1 0.8333333 1.6000000 1 8 0.24150
Hotelling-Lawley 1 0.2000000 1.6000000 1 8 0.24150
Roy 1 0.2000000 1.6000000 1 8 0.24150
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
------ snip ----------
I hope this helps,
John
------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox
-----Original Message-----
From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org]
Behalf Of Skotara
Sent: January-23-09 12:16 PM
To: r-help at r-project.org
Subject: [R] Anova and unbalanced designs
Dear R-list!
My question is related to an Anova including within and between subject
factors and unequal group sizes.
Here is a minimal example of what I did:
library(car)
within1 <- c(1,2,3,4,5,6,4,5,3,2); within2 <- c(3,4,3,4,3,4,3,4,5,4)
values <- data.frame(w1 = within1, w2 = within2)
values <- as.matrix(values)
between <- factor(c(rep(1,4), rep(2,6)))
betweenanova <- lm(values ~ between)
with <- expand.grid(within = factor(1:2))
withinanova <- Anova(betweenanova, idata=with, idesign=
~as.factor(within), type = "III" )
I do not know if this is the appropriate method to deal with unbalanced
designs.
I observed, that SPSS calculates everything identically except the main
effect of the within factor, here, the SSQ and F-value are very
If selecting the option "show means", the means for the levels of the
within factor in SPSS are the same as:
mean(c(mean(values$w1[1:4]),mean(values$w1[5:10]))) and
mean(c(mean(values$w2[1:4]),mean(values$w2[5:10]))).
In other words, they are calculated as if both groups would have the
same size.
I wonder if this is a good solution and if so, how could I do the same
thing in R?
However, I think if this is treated in SPSS as if the group sizes are
identical,
then why not the interaction, which yields to the same result as using
Anova()?
Many thanks in advance for your time and help!