Outline:
 Definitional Formula
 Computational Formula
 An example
Definitional Formula
Again, the reason is to eliminate individual differences from our hypothesis
testing statistic.
Yesterday with the ttest, we looked at what the within did in terms of the bottom of our conceptual formula
difference b/t groups = difference b/t groups
variability w/i groups = ind. diffs. + measurement error
Allowed us to pull out the ind. diffs.
Let’s turn to what this will mean for a within subjects ANOVA,
We want to be able to do the same thing for the case where we
have more than two groups. The goal is the same and the end result
is the same, but the actual process is different.
WHAT IS AN ANOVA?
1. Partition Variance
2. Compare Variances
For a oneway betweensubjects the parts were: MS_{A} and MS_{E}
How does this apply here, with a within subject design?
1. Still going to have the part due to IV: MS_{A}
But we are going to look more closely at the error component
due to subjects (MS_{S}), due to measurement error (MS_{E})
2. Compare: part due to IV to part due to error (so just
like in ttest, we will remove ind. diffs. from our final statistic).
How do we partition variance?
1. Start at deviations
Dev_{T} = Dev_{A} + Dev_{S} + Dev_{E}
Xia  M_{T} = (M_{A}  M_{T}) + (M_{S}
 M_{T}) + (Xia  M_{A}  M_{S} + M_{T})
Dev_{T} is how far the individual score is from the overall
mean
Dev_{A} is how far the group mean is from the overall mean
 due to IV
Dev_{S} is how far the individual mean is from the overall
mean  due to subject
Dev_{E} is how far the individual score is from what is expected
based on group and subject and total means  thought of as not measuring
accurately
2. Square the deviations and sum across individuals and groups
SS_{T} = SUMaSUMi (Xia  M_{T})2
SS_{A} = SUMaSUMi (M_{A}  M_{T})2
SS_{S} = SUMaSUMi (M_{S}  M_{T})2
SS_{E} = SUMaSUMi (Xia  M_{A}  M_{S} + M_{T})2
3. Divide by the df
df_{T} = N_{T}1
df_{A} = A  1
df_{S} = N_{S} 1
df_{E} = (A  1)(N_{S} 1)
4. Now you have partitioned variance and can fill in the source
table






































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Let’s do the example:
Within Subjects ANOVA
DV  number of hours taken to read chapters of equivilent lengths


























































WithinSubjects ANOVA






































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if BetweenSubjects ANOVA






































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