# [R] very simple repeated measures, newbie questions

Prof Brian D Ripley ripley at stats.ox.ac.uk
Sun Mar 26 17:07:50 CEST 2000

```On Sun, 26 Mar 2000, Jonathan Baron wrote:

> Suppose I do a psychology experiment in which each of six
> subjects does several items in each of five fixed conditions, A,
> B, C, D, and E.  The items are randomized separately for each
> subject, so I can ignore order.  All I want to know is whether
> the five conditions differ.  The data look like this.  Each row
> is a subject, and each number is the score in the given
> condition.
>
> A  B  C  D  E
> 4  1  5 10 10
> 9  2 10  7  7
> 6  3  7  8  8
> 7  4  9  8  9
> 6  3  7  8  9
> 3  2  5  7  7
>
> Question 1:  This is the simplest possible repeated measures
> design.  It should yield F(4,24)=16.033 for the effect of
> condition.  (The example is from the Systat manual, slightly
> changed.)  How do I show this with R?

There are some choices, but the simplest would be
>  score <- scan()
1: 4  1  5 10 10
6: 9  2 10  7  7
11: 6  3  7  8  8
16: 7  4  9  8  9
21: 6  3  7  8  9
26: 3  2  5  7  7
31:
> condition <- rep(LETTERS[1:5], len=30)
> subject <- rep(1:6, rep(5,6))
> df <- data.frame(subject=factor(subject), condition, score)
> summary(aov(score ~ subject + condition, data=df))
Df  Sum Sq Mean Sq F value    Pr(>F)
subject      5  20.567   4.113  1.9618    0.1287
condition    4 134.467  33.617 16.0334 4.969e-06
Residuals   20  41.933   2.097

Technically, I think you might want a random-effects analysis,

> summary(aov(score ~ condition + Error(subject), data=df))

but with such a simple design they are the same analysis.

> Question 2:  I would like a graph in which each line is a
> subject, and the abscissa is labeled A B C D E.  Thus, one line
> would connect the points 4 1 5 10 10.  Another would connect 9 2
> 10 7 7, and so on.  (Systat calls this a parallel plot, and I
> have come to find it very useful for a first look at data.)  Can
> this be done in R?

Yes. (I guess you'd like to know how?)  Here is one way:

plot(c(1,5), range(score), type="n", xaxt="n", xlab="condition",
ylab="score")
axis(1, at=1:5, labels=LETTERS[1:5])
for(i in 1:6) lines(1:5, score[subject==i], type="o")

Perhaps a simpler one is

matplot(matrix(score, 5), type="l", xaxt="n")
axis(1, at=1:5, labels=LETTERS[1:5])

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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