Statistics for the Behavioral Sciences (5 th ed.)
Gravetter & Wallnau
Chapter 14
Repeated--Measures ANOVA
Repeated
University of Guelph
Psychology 3320 — Dr. K. Hennig
Winter 2003 Term
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Table 1414-1 (p. 444) - Notation
Two sets of data representing typical examples of singlesingle- factor, repeated
measures research designs.
number of scores
Example see text p. 449
in each Tx
“Person totals” =
A1 + A2 …An
total number
of scores Grand total=T + T …
1
2
Step 1: (recall s2 = SS/df
SS/df))
Calculate the SS for each of the partitions:.
2
Calculate:
within treatments
…
between treatments
between subjects
Step 2
Determine the df
df..
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Step 3
Calculation of the variances (MS values)
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MSbetween treatments = SSbetween treatments /df between treatments
=50/3 = 16.67
MSerror = SSerror/dferror= 8/12 = 0.67
F = MSbetween treatments / MSerror = 16.67/ 0.67 = 24.88
F(2, 12) = ?? for α = .05; What about .01?
Hypothesis testing
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E.g., Example 14.1 effectiveness of classroom
control technique on unruly outbursts
H0: µbefore = µ 1 + µ 1 month + µ 6months
H1: at least one mean is different
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Advantages
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For independent measures ANOVA:
l
l
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F= Tx effect + (individual differences + error)
(individual differences + error)
Lets suppose:
F = 10 + 1000 + 1
1000 + 1
Tx effect = 10 units
ind. differences = 1000 units
= 1011 / 1001 = 1.01
For repeated measures ANOVA
l
l
other error = 1 unit
F= Tx effect + error ((- individual differences)
error ((-individual differences )
F = 10 +1/1 = 11/1 = 11
Figure 1414-5 (p. 464)
The effect of amount of reward on running speed.
Treatment means are depicted by the broken line.
Individual scores for each subject at each level of reward
are shown by solid lines.
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Figure 1414-6 (p. 464)
The effect of amount of reward on running speed. The
treatment means are depicted by the broken line. Individual
scores for each subject at each level of reward are shown
by solid lines.
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