Transcript PP 8 - Personal Web Pages

Repeated Measures ANOVA
factorial within-subjects designs
One-Way Repeated Measures

One-way Repeated Measures Designs are used
when:
– the same subjects are measured on 3 or more
occasions (TIME)
– the same subjects are exposed to 3 or more
treatments (TREATMENT)
– the same subjects provide three or more ratings
that are measured on the same scale (MEASURE)
Examples

The same subjects are assessed on pre,
mid, and post treatment occasions.

The same subjects are given three
different types of medication.

The same subjects rate three different
aspects of school climate.
Factorial Designs

Between-subjects terms can be completely
crossed with within-subjects terms to form
factorial designs.

All three uses of within-subjects terms, TIME,
TREATMENT, and MEASURE, can be
combined with between-subjects terms to form
a variety of completely crossed factorial
designs.
Examples - TIME

Subjects are assessed on pre, mid,
and post treatment occasions,
AND are randomly assigned to two
different treatments.
Pre
Textbook I
Textbook II
Mid
Post
Examples - TREATMENT

Male and female participants each receive
three different treatment conditions.
Participants are randomly assigned to
receive the treatments in different orders.
Drug I
Male
Female
Drug II
Placebo
Examples - MEASURE

Teachers rate three different aspects of
school climate, AND are randomly
assigned to a treatment or control group.
The treatment group gets a particular
model of administrator support.
Communication
Treatment
Control
Support
Policu Clarity
Examples - MEASURE
 Subjects
are randomly assigned to
three different types of medication,
AND asked to rate two different
aspects of the effects of the drug.
Pain
Drug A
Drug B
Placebo
Swelling
Educational Evaluation

Factorial designs with multiple
completely crossed within-subjects terms
can also be used but are relatively rare in
educational research.

“Split plot” designs are very common,
with one within-subjects term (time) and
one between-subjects term (group). Why?
Examples

Suppose you are charged with evaluating
different delivery models for staff
development in your school district.

The question is whether some use of
computer based instruction would be
helpful.
Examples

You are interested in evaluating knowledge, job
satisfaction, and teaching effectiveness gains over
time.

You consider the following three specific delivery
models for staff development in your school district:
– Traditional format
– Computer-based tutorials
– The combination of the two
Examples

A possible research design:
Pre
Post
Computer Tutorial
Traditional Delivery
Trad + Tutorial

What are some of the potential issues with
this design?
Examples

What are some of the potential issues with
this design?
–
–
–
–
Randomization of schools, teachers, classes, etc.
Difficulty of content
Time of the year the instruction takes place
Availability of computer technology
Pre
Computer Tutorial
Traditional Delivery
Trad + Tutorial
Post
Our Research Design
Fall
Winter
Spring
48-50
Child
Age in
Months
51-53
at First
Assessment
54-56
Outcomes:
Social-Emotional
Literacy
Cognitive
Language
Physical
Mathematics
Factorial Designs

Just like the One-way ANOVA is
analogous to the One-Way
Repeated Measures procedure,
Split plot factorial designs share
many of the same properties with
completely crossed BetweenSubjects Factorial designs.
Similarities

Null and Alternative Hypotheses for Multiple
Main Effects

Null and Alternative Hypotheses for
Interaction Terms

Graphing the data and post-hoc comparisons
are essential as interpretation aids.
Hypotheses

Main Effect for Time (MEASURE or

Main Effect for Group

TREATMENT)
Interaction Effects – different patterns of
growth or rates of growth between the groups
Our Research Design
Fall
Winter
Spring
48-50
Child
Age in
Months
51-53
at First
Assessment
54-56
Outcomes:
Social-Emotional
Literacy
Cognitive
Language
Physical
Mathematics
Differences

Sphericity Assumption with the Univariate
case.

Homogeneity of Variance-Covariance
Matrices in the Multivariate case.

Data from individual subjects occurs in
multiple cells rather than only one cell.
Special Considerations

Additional potential threats to the
validity of this type of design:
–
–
–
–
practice effects
order effects
fatigue effects
carry-over effects
Interpretation

Follow the same steps we used for
factorial designs with only betweensubjects terms
 Consider the interactions first
 Graph the results
 Look at Height, Slope, Parallelism
 Use Tukey Post Hoc test to help explain
the results
Interpretation



Height = difference between
groups
Slope = growth over time
Parallelism = differential rates of
growth between the groups
Graphs
Social Development by Schedule
4.000
3.500
3.000
2.500
2.000
1.500
Split Day
Fall
Winter
Spring
Split Week