Repeated measure ANOVA; how it works, F statistic, assumptions and its pros and cons

1. Presented to
Ms Maryium Gul
Presented by
Aamna Haneef
Roll no: 05
MS (2012-2014)
Lahore College for Women
University

2. Repeated Measures ANOVA

4. Repeated measures ANOVA is
also referred to as a
• “within-subjects ANOVA”,
• “Dependent groups” or
• “ANOVA for correlated
samples”
Other Names

5. Why the repeated factor is
called a “within” subjects factor?
Because comparisons are
made multiple times
("repeated") “within” the
same subject rather than
across ("between") different
subjects

6. In within subject design
• Each participant is measured more
than once
• Same subjects across the levels of the
IV
• Levels can be ordered like time or
treatment
• Or levels can be un-ordered (e.g. cases
take three different types of
depression inventories)

7. What RM ANOVA does?
Like T-Tests, repeated measures
ANOVA gives the statistic tools
to determine whether or not
change has occurred over time
T-Tests compare
average scores at
two different time
periods
RM ANOVA
compared the
average score at
multiple time
periods

8. The logic of RM ANOVA
Any differences that are found
between treatments can be
explained by only two factors:
1. Treatment effect
2. Error or Chance

9. Cont…
A particular subject’s scores will be
more alike than scores collected from
multiple subjects
Less variability decrease in
sampling error

10. Cont…
Subject A B C
Each row
represents
one
subject
measured
under
each of k
conditions.
1
subj1 under
condition A
subj1 under
condition B
subj1 under
condition C
2
subj2 under
condition A
subj2 under
condition B
subj2 under
condition C
3
subj3 under
condition A
subj3 under
condition B
subj3 under
condition C
And so on…

11. Assumptions
Dependent variable
It should be measured at the
interval or ratio level (continuous),
such as
• revision time
• Intelligence
• exam performance
• weight

12. Assumptions Cont…
Independent variable
It should consist of at least two
categorical, "related groups" or
"matched pairs“
• 10 individuals' performance in a
spelling test before and after new form
of computerized teaching method
• measuring changes in blood pressure
due to an exercise-training program

13. Assumptions Cont…
No significant outliers differences
Data values that are "far away" from
the main group of data
• Distorting the differences
between the related groups
• Reduces the accuracy of
results

14. Assumptions Cont…
Normally distributed Dependent
variable
• The dependent variable between the
two or more related groups should be
approximately normally distributed
• It is quite "robust" to violations of
normality
• The Shapiro-Wilk test of normality
can test for normality

15. Assumptions Cont…
Sphericity
• Refers to differences between
variances in levels of the repeated-
measures factor (Time)
• Violation of the assumption of
sphericity, causes the test to become
too liberal (leads to an increase in the
Type I error)
• Mauchly's Test of Sphericity can help
to test for its violation

16. Hypothesis for RM ANOVA
The repeated measures ANOVA tests for
whether there are any differences
between related population means
H0: µ1 = µ2 = µ3 = … = µk
H0: There are no differences between
population means.
HA: At least one treatment or
observation mean is significantly
different

17. Sources of Variability
• In repeated measure ANOVA, there are
three potential sources of variability:
1. Treatment variability: between columns,
2. Within subjects variability: between
rows, and
3. Random variability: residual(chance
factor or experimental error beyond the
control of a researcher) .
• A repeated measure design is powerful, as
it controls for all potential sources of
variability.

18. FORMULA
variance between treatments
F = ------------------------------------------
Error variance
• A large F value indicates that the
differences between
treatments/observations are
greater than would be expected by
chance or error alone.

19. Approaches to RM ANOVA
SPSS conducts 3 types of tests if the
within-subject factor has more than 2
levels
• The standard univariate ANOVA test
• The alternative univariate tests
• The multivariate test

20. Advantages
• Using the same participants in
different experimental manipulations
• Exclude the effects of individual
differences
• This design is also very economical
• Removing variance due to differences
between subjects from the error
variance greatly increases the power
(probability of correctly rejecting a
false null hypothesis)

21. Disadvantages
• Practice effects causing participants’
results to improve
• Carry-over effects (bias)
• Demand characteristics (more
exposure, more time to think about
meaning of the experiment).
• Boredom and lack of concentration

22. Tidbits
Why it is always called F statistic?
The F statistic was named after
Ronald A. Fisher, who mainly
developed ANOVA