Repeated Measures Analysis of Variance

1
Repeated Measures Analysis of Variance

• Chapter 18

2
Repeated Measures

• With the dependant measures t-test, we defined a
  repeated measure design as one that took multiple
  observations from each subject

3
Repeated Measures ANOVA

• With the one-way ANOVA, we had 2 sources of
  variability
• Variability between groups
• Variability within groups
• With the repeated measures ANOVA, we now have a
  3rd source of variance
• individual differences between subjects
• SStotal SSbetween SSerror SSsubjects

4
Formulas

• SSTOTAL ?X2total - (?Xtotal)2
• Ntotal
• SSBetween (?X1)2 (?X2)2 .. (?Xk)2 -
  (?Xtotal)2
• n1
  n2 nk Ntotal
• SSSubjects ? (?XS)2 - (?Xtotal)2
• k Ntotal
• SSERROR SSTOTAL - SSBetween - SSSubjects

5
Formulas

• dftotal N-1
• dfbetween k - 1
• k is the number of conditions
• dfsubjects s-1
• s is the number of subjects
• dferror (k-1)(s-1)

6
Sums of Squares Example

• We are interested in the effect of mediation on
  individuals stress levels. We measure the stress
  levels of 4 people 1 week before mediation
  training, during the week long mediation
  training, and 1 week after.
• Compute SStotal SSbetween SSerror SSsubjects

7
Assumptions

• Normality
• Homogeneity of Variance
• The relationship between the different conditions
  is constant
• This is a often violated assumption
• Use the Geisser-Greenhouse correction
• We adjust our degrees of freedom, so we use a
  more conservative critical value
• Use F?(1, n-1) to look up the critical value
  where n is the number of observations in a group

8
Advantages Disadvantages

• Advantages
• It separates subject differences from error which
  gives us a more powerful test
• Disadvantages
• Carry over effects from one condition to the next
• We can potentially alleviate this concern by
  counterbalancing the order in which we present
  the conditions

9
Example

• We are interested in whether wearing a uniform
  affects students school satisfaction. We measured
  the school satisfaction of individuals 3 months
  before a dress code was enacted, while the dress
  code was in effect and 3 moths after it was
  repealed.
• Conduct a repeated measures ANOVA (? .05) and
  Tukeys HSD test

10
EXAM 3

• Exam 3 is Monday 2/26 at 600pm in Morton 235
• The help session is Sunday 2/25 from 600pm to
  730pm in Porter 102