Chapter 14: Repeated Measures Analysis of Variance (ANOVA)
First of all, you need to recognize the difference between a repeated measures (or dependent
groups) design and the between groups (or independent groups) design. In an independent groups
design, each participant is exposed to only one of the treatment levels and then provides one
response on the dependent variable. However, in a repeated measures design, each participant is
exposed to every treatment level and provides a response on the dependent variable after each
treatment. Thus, if a participant has provided more than one score on the dependent variable, you
know that you're dealing with a repeated measures design.
Comparing the Independent Groups ANOVA and the Repeated Measures ANOVA
The fact that the scores in each treatment condition come from the same participants has an
important impact on the between-treatment variability found in the MSBetween (MSTreatment). In an
independent groups design, the variability in the MSBetween arises from three sources: treatment
effects, individual differences, and random variability. Imagine, for instance, a single-factor
independent groups design with three levels of the factor. As seen below, the three group means
vary.
Mean
a1
3
5
2
6
4
3
3.83
a2
7
6
9
7
8
7
7.33
a3
9
8
9
7
9
8
8.33
As you should recall, the variability among the group means determines the MSBetween. In this
case, MSBetween = 33.5, which is the variance of the group means (5.583) times the sample size
(6). Why do the group means differ? One source of variability — individual differences —
emerges because the scores in each group come from different people. Thus, even with random
assignment to conditions, the group means could differ from one another because of individual
differences. And the more variability due to individual differences in the population, the greater
the variability both within groups and between groups. Another source of variability — random
effects — should play a fairly small role. Nonetheless, because there will be some random
variability, it could influence the three group means. Finally, you should imagine that your
treatment will have an impact on the means, which is the treatment effect that you set out to
examine in your experiment.
Given the sources of variability in the MSBetween, you need to construct a MSError that
involves individual differences and random variability. Thus, your F ratio would be:
F =
Treatment Effect + Individual Differences +Random Variability
Individual Differences +Random Variability
Ch. 14 Repeated Measures ANOVA - 1
When treatment effects are absent, your F ratio would be roughly 1.0. As the treatment effects
increased, your F ratio would grow larger than 1.0.
In the case of these data, the F-ratio would be fairly large, as seen in the StatView source
table below:
ANOVA Table for Score
A
Residual
DF
Sum of Squares
Mean Square
F-Value
P-Value
Lambda
Power
2
67.000
33.500
25.769
<.0001
51.538
1.000
15
19.500
1.300
Means Table for Score
Effect: A
Count
Mean
Std. Dev.
Std. Err.
a1
6
3.833
1.472
.601
a2
6
7.333
1.033
.422
a3
6
8.333
.816
.333
Imagine, now, that you have the same three conditions and the same 18 scores,
but now presume that they come from only 6 participants in a repeated measures design. Even
though the MSBetween would be identical, in a repeated measures design that variability is not
influenced by individual differences. Thus, the MSBetween of 33.5 would come from treatment
effects and random effects.
In order to construct an appropriate F ratio, you now need to develop an error term that
contains only random variability. The logic of the procedure we will use is to take the error term
that would be constructed were these data from an independent groups design (and would
include individual differences and random variability) and remove the portion due to individual
differences, which leaves behind the random variability that we want in our error term.
Conceptually, then, our F ratio would be comprised of the components seen below:
F =
Treatment Effect + Random Variability
Random Variability
Remember, however, that even though the components in the numerator of the F ratio differ in
the independent groups and repeated measures ANOVAs, the computations are identical. That is,
regardless of the nature of the design, the formula for SSBetween is:
SSTreatment = Â
T 2 G2
n
N
Ch. 14 Repeated Measures ANOVA - 2
And the formula for dfBetween is:
dfTreatment = k -1
Furthermore, you’ll still need to compute the SSError for the independent groups ANOVA
(which is just the sum of the SS for each condition) and the dfError for the independent groups
ANOVA (which is just n-1 for each condition times the number of conditions). However,
because this “old” error term contains both individual differences and random variability, we
need to estimate and remove the contribution of individual differences.
We estimate the contribution of individual differences using the same logic as we use
when computing the variability among treatments. That is, we treat each participant as the level
of a factor (think of the factor as “Subject” or “Participant”). If you think of the computation this
way, you’ll immediately notice that the formulas for SSBetween and SSSubject are identical, with the
SSBetween working on columns while the SSSubject works on rows. The actual formula would be:
SSSubject = Â
P 2 G2
k
N
If you’ll look at our data again, to complete your computation you would need to sum
across each of the participants and then square those sums before adding them and dividing by
the number of treatments.
Mean
a1
3
5
2
6
4
3
3.83
a2
7
6
9
7
8
7
7.33
a3
9
8
9
7
9
8
8.33
P
19
19
20
20
21
18
Your computation of SSSubject would be:
SSSubject =
19 2 + 19 2 + 20 2 + 20 2 + 212 + 18 2 117 2 2287
=
- 760.5 = 1.83
3
18
3
You would then enter the SSSubject into the source table and subtract it from the SSWithin (which is
the error term from the independent groups design). As seen in the source table below, when you
subtract that SSSubject, you are left with SSError = 17.67. The SS in the denominator of the repeated
measures design will always be less than that found in an independent groups design for the
same scores.
Ch. 14 Repeated Measures ANOVA - 3
Source
Between
Within Groups
Subject
Error
Total
SS
67
19.5
1.83
17.67
86.5
df
2
15
5
10
17
MS
33.5
F
18.93
1.77
Of course, you need to apply the same procedure to the degrees of freedom. The
dfWithinGroups for the independent groups design must be reduced by the dfSubject. The dfSubject is
simply:
df Subjects = n -1
Just as you should note the parallel between the SSBetween and the SSSubject, you should also note the
parallel between the dfBetween and the dfSubject. Because you remove the dfSubject, the df in the error
term for the repeated measures design will always be less than the df in the error term for an
independent groups design for the same scores. Furthermore, it will always be true that the dfError
in a repeated measures design is the product of the dfBetween and the dfSubject.
For completeness, below is the source table that StatView would generate for these data
using a repeated measures ANOVA:
ANOVA Table for A
DF
Sum of Squares
Mean Square
Subject
5
1.833
.367
Category for A
2
67.000
33.500
10
17.667
1.767
Category for A * Subject
F-Value
P-Value
Lambda
Power
18.962
.0004
37.925
.999
Means Table for A
Effect: Category for A
Count
Mean
Std. Dev.
Std. Err.
a1
6
3.833
1.472
.601
a2
6
7.333
1.033
.422
a3
6
8.333
.816
.333
You should note the differences between the source tables that you would generate doing
the analyses as shown in your Gravetter & Wallnau textbook and that generated by StatView.
First of all, the SS and df columns are reversed. But more important, you need to note that the
first row is the Subject effect, the second row is the Treatment Effect (called Category for A) and
the third row is the Error Effect (Random), which appears as Category for A * Subject. Thus, the
F ratio appears in the second row, but is the expected ratio of the MSBetween and the MSError.
Ch. 14 Repeated Measures ANOVA - 4
You should also note a perplexing result. Generally speaking, the repeated measures
design is more powerful than the independent groups design. Thus, you should expect that the F
ratio would be larger for the repeated measures design than it is for the independent groups
design. For these data, however, that’s not the case. Note that for the independent groups
ANOVA, F = 25.8 and for the repeated measures ANOVA, F = 18.9. (For the repeated measures
analysis, the difference between the StatView F and the calculator-computed F is due to
rounding error.)
What happened? Think, first of all, of the formula for the F ratio. The numerator is
identical, whether the analysis is for an independent groups design or a repeated measures
design. So for any difference in the F ratio to emerge, it has to come from the denominator.
Generally speaking, as seen in the formula below, larger F ratios would come from larger dfError
and smaller SSError.
F=
MSTreatment
SSError
df Error
But, for identical data, the dfError will always be smaller for a repeated measures analysis! So,
how does the increased power emerge? Again, for identical data, it’s also true that the SSError will
always be smaller for a repeated measures analysis. As long as the SSSubject is substantial, the F
ratio will be larger for the repeated measures analysis. For these data, however, the SSSubject is
actually fairly small, resulting in a smaller F ratio. Thus, the power of the repeated measures
design emerges from the presumption that people will vary. That is, you’re betting on substantial
individual differences. As you look at the people around you, that presumption is not all that
unreasonable.
Use the source table below to determine the break-even point for this data set. What
SSSubject would need to be present to give you the exact same F ratio as for the independent groups
ANOVA?
Source
Between
Within Groups
Subject
Error
Total
SS
67
19.5
86.5
df
2
15
5
10
17
MS
33.5
F
25.8
So, as long as you had more than that level of SSSubject you would achieve a larger F ratio using
the repeated measures design.
Testing the Null Hypothesis and Post Hoc Tests for Repeated Measures ANOVAs
You would set up and test the null hypothesis for a repeated measures design just as you
would for an independent groups design. That is, for this example, the null and alternative
hypotheses would be identical for the two designs:
Ch. 14 Repeated Measures ANOVA - 5
H0: m1 = m2 = m3
H1: Not H0
To test the null hypothesis for a repeated measures design, you would look up the FCritical with the
dfBetween and the dfError found in your source table. That is, for this example, FCrit(2,10) = 4.10.
If you reject H0, as you would in this case, you would then need to compute a post hoc
test to determine exactly which of the conditions differed. Again, the computation of Tukey’s
HSD would parallel the procedure you used for an independent groups analysis. In this case, for
the independent groups design, your Tukey’s HSD would be:
HSD = 3.67
1.3
= 1.71
6
For the repeated measures design, your Tukey’s HSD would be:
HSD = 3.88
1.77
= 2.1
6
Ordinarily, of course, your HSD would be smaller for the repeated measures design, due to the
typical reduction in the MSError. For this particular data set, given the lack of individual
differences, that’s not the case.
A Computational Example
RESEARCH QUESTION: Does behavior modification (response-cost technique) reduce the
outbursts of unruly children?
EXPERIMENT:
Randomly select 6 participants, who are tested before treatment, then one
week, one month, and six months after treatment. The IV is the duration of
the treatment. The DV is the number of unruly acts observed.
STATISTICAL HYPOTHESES:
DECISION RULE:
H0: mBefore = m1Week = m1Month = m6Months
H1: Not H0
If FObt ≥ FCrit, Reject H0. FCrit(3,15) = 3.29
Ch. 14 Repeated Measures ANOVA - 6
DATA:
P1
P2
P3
P4
P5
P6
X
T (SX)
SX2
SS
Before
8
4
6
8
7
6
6.5
39
265
11.5
1 Week
2
1
1
3
4
2
2.3
14
1 Month
1
1
0
4
3
1
1.5
10
6 Months
1
0
2
1
2
1
1
7
38
28
11
5.3
11.3
P
12
6
10
16
16
10
SUM
70
342
2.8
30.9
SOURCE TABLE:
SOURCE
SS Formula
T
G2
Ân N
SS
2
Between
Within grps
SSS in each group
Between subjs
P 2 G2
Âk-N
Error
(SSWithin Groups – SSBetween subjects)
Total
ÂX2 -
G2
N
DECISION:
POST HOC TEST:
INTERPRETATION:
EFFECT SIZE:
Ch. 14 Repeated Measures ANOVA - 7
df
MS
F
Suppose that you continued to assess the amount of unruly behavior in the children after the
treatment was withdrawn. You assess the number of unruly acts after 12 months, 18 months, 24
months and 30 months. Suppose that you obtain the following data. What could you conclude?
P1
P2
P3
P4
P5
P6
T (SX)
SX
12 Months
1
2
1
3
2
1
10
2
20
SOURCE
18 Months
2
2
3
4
2
2
15
24 Months
2
3
3
4
3
4
19
30 Months
5
4
4
6
5
4
28
41
63
134
SS Formula
T
G2
Ân-N
SS
2
Between
Within grps
SSS in each group
P 2 G2
k
N
Between subjs
Â
Error
(SSWithin Groups – SSBetween subjects)
Total
ÂX
2
-
G2
N
DECISION:
POST HOC TEST:
INTERPRETATION:
EFFECT SIZE:
Ch. 14 Repeated Measures ANOVA - 8
df
P
10
11
11
17
12
11
72
MS
F
An Example to Compare Independent Groups and Repeated Measures ANOVAs
Independent Groups ANOVA
T (SX)
SX
2
A2
2
3
3
3
11
A3
3
4
4
5
16
A4
4
5
6
6
21
22
31
66
113
6
2
SS
s
A1
1
1
2
4
8
2
SOURCE
.75
.25
2
2.75
.92
.67
SS
56 (G)
df
MS
11.5
F
Between
Error
Total
Repeated Measures ANOVA
A1
SOURCE
A2
A3
Exactly the same as above
SS
A4
df
Between
Within Groups
Between Subjs
Error
Total
Ch. 14 Repeated Measures ANOVA - 9
MS
F
Repeated Measures Analyses: The Error Term
In a repeated measures analysis, the MSError is actually the interaction between
participants and treatment. However, that won't make much sense to you until we've talked about
two-factor ANOVA. For now, we'll simply look at the data that would produce different kinds of
error terms in a repeated measures analysis, to give you a clearer understanding of the factors
that influence the error term.
These examples are derived from the example in your textbook (G&W, p. 464). Imagine
a study in which rats are given each of three types of food rewards (2, 4, or 6 grams) when they
complete a maze. The DV is the time to complete the maze. As you can see in the graph below,
Participant1 is the fastest and Participant6 is the slowest. The differences in average performance
represent individual differences. If the 6 lines were absolutely parallel, the MSError would be 0, so
an F ratio could not be computed. So, I've tweaked the data to be sure that the lines were not
perfectly parallel. Nonetheless, if performance was as illustrated below, the MSError would be
quite small. The data are seen below in tabular form and then in graphical form.
P1
P2
P3
P4
P5
P6
Mean
2
s
2 grams
1.0
2.0
3.0
4.0
5.0
6.0
3.5
3.5
4 grams
1.5
2.5
3.5
5.0
6.5
7.5
4.42
5.44
6 grams
2.0
3.5
5.0
6.0
7.0
9.0
5.42
6.24
P
4.5
8.0
11.5
15.0
18.5
22.5
Participant1
Participant2
Participant3
Participant4
Participant5
Participant6
Small MSError
10
Speed of Response
8
6
4
2
0
2
4
6
Amount of Reward (grams)
The ANOVA on these data would be as seen below. Note that the F-ratio would be significant.
Ch. 14 Repeated Measures ANOVA - 10
ANOVA Table for Reward
Subject
Category for Reward
Category for Reward * Subject
DF
Sum of Squares
Mean Square
5
74.444
14.889
2
11.028
5.514
10
1.472
.147
F-Value
P-Value
Lambda
Power
37.453
<.0001
74.906
1.000
Means Table for Reward
Effect: Category for Reward
Count
Mean
Std. Dev.
Std. Err.
Reward 2g
6
3.500
1.871
.764
Reward 4g
6
4.417
2.333
.952
Reward 6g
6
5.417
2.498
1.020
Moderate MSError
Next, keeping all the data the same (so SSTotal would be unchanged), and only rearranging
data within a treatment (so that the s2 for each treatment would be unchanged), I've created
greater interaction between participants and treatment. Note that the participant means would
now be closer together, which means that the SSSubject is smaller. In the data table below, you'll
note that the sums across participants (P) are more similar than in the earlier example.
P1
P2
P3
P4
P5
P6
Mean
2
s
2 grams
1.0
2.0
3.0
4.0
5.0
6.0
3.5
3.5
4 grams
1.5
3.5
2.5
6.5
5.0
7.5
4.42
5.44
6 grams
3.5
5.0
2.0
6.0
9.0
7.0
5.42
6.24
P
6.0
10.5
7.5
16.5
19.0
20.5
Participant1
Participant2
Participant3
Participant4
Participant5
Participant6
Moderate MSError
10
Speed of Response
8
6
4
2
0
2
4
6
Amount of Reward
Note that the F-ratio is still significant, though it is much reduced. Note, also, that the MSTreatment
is the same as in the earlier example.
Ch. 14 Repeated Measures ANOVA - 11
ANOVA Table for Reward
DF
Sum of Squares
Mean Square
5
63.111
12.622
2
11.028
5.514
10
12.806
1.281
Subject
Category for Reward
Category for Reward * Subject
F-Value
P-Value
Lambda
Power
4.306
.0448
8.612
.606
Means Table for Reward
Effect: Category for Reward
Count
Mean
Std. Dev.
Std. Err.
Reward 2g
6
3.500
1.871
.764
Reward 4g
6
4.417
2.333
.952
Reward 6g
6
5.417
2.498
1.020
Large MSError
Next, using the same procedure, I'll rearrange the scores even more, which will produce an even
larger MSError. Note, again, that the SSSubject grows smaller (as the Participant means grow closer
to one another) and the SSError grows larger.
4 grams
3.5
6.5
7.5
1.5
2.5
5.0
4.42
5.44
6 grams
6.0
9.0
3.5
5.0
7.0
2.0
5.42
6.24
Participant1
Participant2
Participant3
Participant4
Participant5
Participant6
Large MSError
10
8
Speed of Response
P1
P2
P3
P4
P5
P6
Mean
2
s
2 grams
1.0
2.0
3.0
4.0
5.0
6.0
3.5
3.5
6
4
2
0
2
4
6
Amount of Reward
Ch. 14 Repeated Measures ANOVA - 12
P
10.5
17.5
14.0
10.5
14.5
13.0
ANOVA Table for Reward
DF
Sum of Squares
Mean Square
5
11.778
2.356
2
11.028
5.514
10
64.139
6.414
Subject
Category for Reward
Category for Reward * Subject
F-Value
P-Value
Lambda
Power
.860
.4524
1.719
.155
Means Table for Reward
Effect: Category for Reward
Count
Mean
Std. Dev.
Std. Err.
Reward 2g
6
3.500
1.871
.764
Reward 4g
6
4.417
2.333
.952
Reward 6g
6
5.417
2.498
1.020
Varying Individual Differences
It is possible to keep the MSError constant, while increasing the MSSubject, as the two examples
below illustrate. As you see in the first example, the SSSubject is fairly small and the MSError is quite
small.
Small Individual Differences
Participant1
Participant2
Participant3
Participant4
Participant5
Participant6
10
Speed of Response
8
6
4
2
0
2
4
6
Amount of Reward (grams)
ANOVA Table for Reward
Subject
Category for Reward
Category for Reward * Subject
DF
Sum of Squares
Mean Square
5
54.125
10.825
2
15.250
7.625
10
.250
.025
F-Value
P-Value
Lambda
Power
305.000
<.0001
610.000
1.000
Means Table for Reward
Effect: Category for Reward
Count
Mean
Std. Dev.
Std. Err.
Reward 2g
6
4.500
1.871
.764
Reward 4g
6
5.500
1.871
.764
Reward 6g
6
6.750
1.969
.804
Next, I've decreased the first two participants' scores by a constant amount and increased the last
two participants' scores by a constant amount. Because the interaction between participant and
treatment is the same, the MSError is unchanged. However, because the means for the 6
participants are more different than before, the SSSubject increases.
Ch. 14 Repeated Measures ANOVA - 13
Moderate Individual Differences
Participant1
Participant2
Participant3
Participant4
Participant5
Participant6
12
10
Speed of Response
8
6
4
2
0
2
4
6
Amount of Reward (grams)
ANOVA Table for Reward
Subject
Category for Reward
Category for Reward * Subject
DF
Sum of Squares
Mean Square
5
114.125
22.825
2
15.250
7.625
10
.250
.025
F-Value
P-Value
Lambda
Power
305.000
<.0001
610.000
1.000
Means Table for Reward
Effect: Category for Reward
Count
Mean
Std. Dev.
Std. Err.
Reward 2g
6
4.500
2.739
1.118
Reward 4g
6
5.500
2.739
1.118
Reward 6g
6
6.750
2.806
1.146
Ch. 14 Repeated Measures ANOVA - 14
StatView for Repeated Measures ANOVA: G&W 465
First, enter as many columns (variables) as you have levels of your independent variable. Below
left are the data, with each column containing scores for a particular level of the IV. The next
step is to highlight all 3 columns and then click on the Compact button. You’ll then get the
window seen below on the right, which allows you to name the IV (as a compact variable). Note
that your data window will now reflect the compacting process, with Stimulus appearing above
the 3 columns.
To produce the analysis, choose Repeated Measures ANOVA from the Analyze menu. Move
your compacted variable to the Repeated measure box on the left, as seen below left. Then, click
on OK to produce the actual analysis, seen below right.
ANOVA Table for Stimulus
DF
Sum of Squares
Mean Square
Subject
4
6.000
1.500
Category for Stimulus
2
30.000
15.000
Category for Stimulus * Subject
8
28.000
3.500
F-Value
P-Value
Lambda
Power
4.286
.0543
8.571
.568
Means Table for Stimulus
Effect: Category for Stimulus
Count
Mean
Std. Dev.
Std. Err.
Neutral
5
3.000
.707
.316
Pleasant
5
6.000
2.121
.949
Aversive
5
3.000
1.871
.837
Note that these results are not quite significant, so you would not ordinarily compute a post hoc
test. Nonetheless, just to show you how to compute a post hoc test, choose Tukey/Kramer from
the Post-hoc tests found on the left, under ANOVA. That will produce the table seen below. It’s
no surprise that none of the comparisons are significant, given that the overall ANOVA did not
produce any significant results.
Tukey/Kramer for Stimulus
Effect: Category for Stimulus
Significance Level: 5 %
Mean Diff.
Crit. Diff.
Neutral, Pleasant
-3.000
3.380
Neutral, Aversive
0.000
3.380
Pleasant, Aversive
3.000
3.380
Ch. 14 Repeated Measures ANOVA - 15
Practice Problems
Drs. Dewey, Stink, & Howe were interested in memory for various odors. They conducted a
study in which 6 participants were exposed to 10 common food odors (orange, onion, etc.) and
10 common non-food odors (motor oil, skunk, etc.) to see if people are better at identifying one
type of odorant or the other. The 20 odors were presented in a random fashion, so that both
classes of odors occurred equally often at the beginning of the list, at the end of the list, etc.
(Thus, this randomization is a strategy that serves the same function as counterbalancing.) The
dependent variable is the number of odors of each class correctly identified by each participant.
The data are seen below. Analyze the data and fully interpret the results of this study.
SX (T)
SX
SS
2
Food Odors
7
8
6
9
7
5
42
304
Non-Food Odors
4
6
4
7
5
3
29
151
10
Ch. 14 Repeated Measures ANOVA - 16
10.8
Suppose that Dr. Belfry was interested in conducting a study about the auditory capabilities of
bats, looking at bats’ abilities to avoid wires of varying thickness as they traverse a maze. The
DV is the number of times that the bat touches the wires. (Thus, higher numbers indicate an
inability to detect the wire.) Complete the source table below and fully interpret the results.
Ch. 14 Repeated Measures ANOVA - 17
Dr. Richard Noggin is interested in the effect of different types of persuasive messages on a
person’s willingness to engage in socially conscious behaviors. To that end, he asks his
participants to listen to each of four different types of messages (Fear Invoking, Appeal to
Conscience, Guilt, and Information Laden). After listening to each message, the participant rates
how effective the message was on a scale of 1-7 (1 = very ineffective and 7 = very effective).
Complete the source table and analyze the data as completely as you can.
Ch. 14 Repeated Measures ANOVA - 18
Dr. Beau Peep believes that pupil size increases during emotional arousal. He was interested in
testing if the increase in pupil size was a function of the type of arousal (pleasant vs. aversive). A
random sample of 5 participants is selected for the study. Each participant views all three stimuli:
neutral, pleasant, and aversive photographs. The neutral photograph portrays a plain brick
building. The pleasant photograph consists of a young man and woman sharing a large ice cream
cone. Finally, the aversive stimulus is a graphic photograph of an automobile accident. Upon
viewing each photograph, the pupil size is measured in millimeters. An incomplete source table
resulting from analysis of these data is seen below. Complete the source table and analyze the
data as completely as possible.
Means Table for Stimulus
Effect: Category for Stimulus
Count
Mean
Std. Dev.
Std. Err.
Neutral
5
2.600
.548
.245
Pleasant
5
6.400
1.517
.678
Aversive
5
4.400
1.140
.510
Ch. 14 Repeated Measures ANOVA - 19
Suppose you are interested in studying the impact of duration of exposure to faces on the ability
of people to recognize faces. To finesse the issue of the actual durations used, I'll call them
Short, Medium, and Long durations. Participants are first exposed to a set of 30 faces for one
duration and then tested on their memory for those faces. Then they are exposed to another set of
30 faces for a different duration and then tested. Finally, they are given a final set of 30 faces for
the final duration and then tested. The DV for this analysis is the percent Hits (saying Old to an
Old item). Suppose that the results of the experiment come out as seen below. Complete the
analysis and interpret the results as completely as you can. If the results turned out as seen
below, what would they mean to you? [15 pts]
Means Table for Duration
Effect: Category for Duration
Count
Mean
Std. Dev.
Std. Err.
Short
24
43.833
7.257
1.481
Medium
24
47.792
7.342
1.499
Long
24
49.917
6.978
1.424
Ch. 14 Repeated Measures ANOVA - 20