# [R] Discrepancy between R and SPSS in 2-way, repeated measures ANOVA

John Maindonald john.maindonald at anu.edu.au
Sat Sep 10 14:17:01 CEST 2005

```There are 20 distinct individuals, right? expno breaks the 20
individuals into five groups of 4, right? Is this a blocking factor?

If expno is treated as a blocking factor, the following is what you get:

> xy <- expand.grid(expno=letters[1:5],cond=letters[1:4],
+                                    time=factor(paste(1:2)))
> xy\$subj <- factor(paste(xy\$expno, xy\$cond, sep=":"))
> xy\$cond <- factor(xy\$cond)
> xy\$expno <- factor(xy\$expno)
> xy\$y <- rnorm(40)
> summary(aov(y~cond*time+Error(expno/cond), data=xy))

Error: expno
Df Sum Sq Mean Sq F value Pr(>F)
Residuals  4   3.59    0.90

Error: expno:cond
Df Sum Sq Mean Sq F value Pr(>F)
cond       3   1.06    0.35    0.36   0.78
Residuals 12  11.86    0.99

Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
time       1   2.27    2.27    1.38   0.26
cond:time  3   3.27    1.09    0.67   0.59
Residuals 16  26.19    1.64

If on the other hand this is analyzed as for a complete
randomized design, the following is the output:

> summary(aov(y~cond*time+Error(subj), data=xy))

Error: subj
Df Sum Sq Mean Sq F value Pr(>F)
cond       3   1.06    0.35    0.37   0.78
Residuals 16  15.46    0.97

Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
time       1   2.27    2.27    1.38   0.26
cond:time  3   3.27    1.09    0.67   0.59
Residuals 16  26.19    1.64

On 10 Sep 2005, at 8:00 PM, Larry A Sonna wrote:

> From: "Larry A Sonna" <larry_sonna at hotmail.com>
> Date: 10 September 2005 12:10:06 AM
> To: <r-help at stat.math.ethz.ch>
> Subject: [R] Discrepancy between R and SPSS in 2-way, repeated
> measures ANOVA
>
>
> Dear R community,
>
> I am trying to resolve a discrepancy between the way SPSS and R
> handle 2-way, repeated measures ANOVA.
>
> An experiment was performed in which samples were drawn before and
> after treatment of four groups of subjects (control and disease
> states 1, 2 and 3).  Each group contained five subjects.  An
> experimental measurement was performed on each sample to yield a
> "signal".  The before and after treatment signals for each subject
> were treated as repeated measures.  We desire to obtain P values
> for disease state ("CONDITION"), and the interaction between signal
> over time and disease state ("CONDITION*TIME").
>
> Using SPSS, the following output was obtained:
>                      DF        SumSq (Type 3)    Mean Sq    F
> value     P=
>
> COND              3                 42861            14287
> 3.645 0.0355
>
> TIME                1                     473
> 473       0.175 0.681
>
> COND*TIME     3                     975               325
> 0.120 0.947
>
> Error                16                43219             2701
>
>
>
> By contrast, using the following R command:
>
> summary(aov(SIGNAL~(COND+TIME+COND*TIME)+Error(EXPNO/COND),
> Type="III"))
>
> the output was as follows:
>
>                  Df     Sum Sq     Mean Sq     F value  Pr(>F)
>
> COND          3          26516       8839      3.2517     0.03651 *
>
> TIME            1            473         473      0.1739     0.67986
>
> COND:TIME  3            975         325      0.1195     0.94785
>
> Residuals     28        76107      2718
>
>
>
> I don't understand why the two results are discrepant.  In
> particular, I'm not sure why R is yielding 28 DF for the residuals
> whereas SPSS only yields 16.  Can anyone help?
>
>

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Bioinformation Science, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.

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