review memory scores for subjects given three different study sequences: find the sum of squares...
DESCRIPTION
Review Memory scores for subjects given three different study sequences: SS treatment = 84 SS residual = 30 df treatment = 2 df residual = 7 Calculate F, for testing whether the group means are reliably different A.0.8 B.1.25 C.9.8 D.180 ABC M = 14M = 11M = 7TRANSCRIPT
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ReviewMemory scores for subjects given three different study sequences:
Find the sum of squares between groups, SStreatment
A. 24B. 25C. 42D. 84
A B C
17 12 8
14 10 9
12 11 4
13
M = 14 M = 11 M = 7
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ReviewMemory scores for subjects given three different study sequences:
Find the sum of squares within groups, SSresidual
A. 14B. 30C. 104D. 114
A B C
17 12 8
14 10 9
12 11 4
13
M = 14 M = 11 M = 7
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ReviewMemory scores for subjects given three different study sequences:
SStreatment = 84SSresidual = 30dftreatment = 2 dfresidual = 7
Calculate F, for testing whether the group means are reliably different
A. 0.8B. 1.25C. 9.8D. 180
A B C
17 12 8
14 10 9
12 11 4
13
M = 14 M = 11 M = 7
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Repeated-Measures ANOVA
11/11
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Repeated-Measures Design
• Multiple measurements for each subject– Different stimulus types, conditions, times, etc.– All measurements are of the same variable, but in
different situations– Generalizes paired-samples design
• Is there an effect of the treatment?– Variation due to condition, time, stimulus, etc.– Do the means of the measurements vary?
• Same null hypothesis as simple ANOVA– m1 = m2 = … = mk
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Repeated-Measures Data
• Individual differences – Variation from one subject to another– Affects all the scores of any given subject
Measurement
Subject 1 2 3 4
1 78 73 82 75
2 108 105 113 106
3 84 79 89 80
4 94 88 98 92
5 121 115 123 117
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Accounting for Individual Differences
• Individual differences complicate hypothesis testing– Inflate variability of scores– Don’t affect random variability of treatment means
• Contribute to all measurements equally
• Basic idea– Subtract subject mean for each score– Do simple ANOVA on these differences (dfresidual changes)
Measurement Difference Score
Subject 1 2 3 4 Ms 1 2 3 4
1 78 73 82 75 77 1 -4 5 -2
2 108 105 113 106 108 0 -3 5 -2
3 84 79 89 80 83 1 -4 6 -3
4 94 88 98 92 93 1 -5 5 -1
5 121 115 123 117 119 2 -4 4 -2
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Partitioning Variability• Break total variability into treatment, subjects, and residual error
• Total variability– Same as before:
• Variability due to treatment
– Same as before:
• Variability due to individual differences– Same idea as SStreatment
– Variability of subject means:• Residual variability
– Remaining variability– Can calculate directly, but not intuitive
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Partitioning Variability
Measurement
Subject 1 2 3 4 Ms
1 78 73 82 75 77
2 108 105 113 106 108
3 84 79 89 80 83
4 94 88 98 92 93
5 121 115 123 117 119Mi 97 92 101 94 96
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Repeated-Measures ANOVA• Does treatment explain significant portion of variability?
– Don't want to penalize for variability due to individual differences– Removing SSsubject reduces SSresidual and makes it a fair comparison
• Hypothesis test for repeated-measures ANOVA:
– Same as regular ANOVA, except we first remove SSsubject
– (SSsubject not meaningful with simple ANOVA because each subject is only in one group)
SStotal
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Degrees of Freedom
dftotal = nk – 1
dftreatment = k – 1
dfresidual = nk – 1 – (k–1) – (n–1)= nk – n – k + 1 .
SStotal
dfsubject = n – 1
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ReviewCoffee drinkers are given arithmetic tests on 3 different days: one after drinking coffee, one after decaf, and one with nothing.
Find the sum of squares for individual differences, SSsubject
A. 152B. 558C. 1674D. 2232
Condition
Subject C D N Ms
1 79 73 82 78
2 64 57 59 60
3 83 75 85 81
4 94 87 98 93Mi 80 73 81 78
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ReviewCoffee drinkers are given arithmetic tests on 3 different days: one after drinking coffee, one after decaf, and one with nothing.
SStotal = 1860SStreatment = 152SSsubject = 1674SSresidual = 34
What would SSresidual be if these were 12 unrelated subjects?
A. 34B. 186C. 1708D. 1826
Condition
Subject C D N Ms
1 79 73 82 78
2 64 57 59 60
3 83 75 85 81
4 94 87 98 93Mi 80 73 81 78
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ReviewCoffee drinkers are given arithmetic tests on 3 different days: one after drinking coffee, one after decaf, and one with nothing.
SStotal = 1860SStreatment = 152 dftreatment = 2SSsubject = 1674 dfsubject = 3SSresidual = 34 dfresidual = 6
Find the F statistic for testingdifferences across conditions
A. 0.14B. 13.41C. 98.47D. 111.88
Condition
Subject C D N Ms
1 79 73 82 78
2 64 57 59 60
3 83 75 85 81
4 94 87 98 93Mi 80 73 81 78