Slides to accompany Weathington,
Cunningham & Pittenger (2010),
Chapter 14: Correlated Groups
Designs
1
Objectives
• Correlated groups
• Repeated-measures designs
• Carryover effects
• Matched-group designs
• Mixed-model designs
2
Why Correlated-Groups?
• Sometimes the treatment groups in a
study are not independent
– This is an assumption underlying betweengroups designs
3
Correlated-Groups Logic
• Minimizing within-group variance is a
constant goal (increases our power)
–Homogeneous groups can help
–Subject variables can also be used
–Correlated-groups is another good
design strategy
4
Correlated-Groups Logic
• Figure 14.1
• We can partition out variance due to
individual differences
• This reduces MSwithin and increases the F
• Two options:
– Repeated measures design
– Matched-participants design
5
Figure 14.1
6
Repeated-Measures Design
• Data collected over multiple conditions, using
the same set of participants
• Testing same person over multiple levels of
the IV
– Could be manipulated or could be time
• Figure 14.2
7
Figure 14.2
8
Repeated-Measures Results
• Summary table e.g., Table 14.3
• Notice that you are able to partition out an
additional chunk of the variance in the DV
– Compare with Table 14.2
– This reduces MSwithin
• For this type of design the groups are not
independent
9
Table 14.2 vs. Table 14.3
Between
Within
Total
Between
Participants
Within
Total
SS
22.4286
36.2500
58.6786
df
6
21
27
MS
3.7381
1.7262
F
2.166
p
0.088
SS
22.43
26.11
10.14
58.68
df
6
3
18
27
MS
3.74
8.70
0.56
F
6.63
p
0.00
10
Repeated-Measures Pros/Cons
• Advantages
– Increased power
• Each participant is his/her own control
– Smaller required sample size
• Disadvantages
– Several forms of potential carryover effects
• Table 14.4
11
Reducing Carryover Effects
• Several design options exist
– Use between-subjects design
• Especially if experiment cause irreversible
change
– Use a special design modification:
• Solomon four-group design
• Counterbalancing
• Latin square design
12
Solomon Four-Group Design
• Incorporates 3 control groups to account
for sequence-related events
• Use a 2 x 2 factorial (b-g) ANOVA
• Table 14.5 and Figure 14.4 illustrate
Group 1
Group 2
Pretest
O1
Treatment
Treatment
O3
Group 3
Treatment
Group 4
Note: O x represents an observation or test score
Posttest
O2
O4
O5
O6
13
Counterbalancing
• Requires random shuffling of the sequence
of testing for each participant
• Total # of possible arrangements = k!
• Sample size must allow you to have
enough people to adequately test each of
the possible arrangements
14
Latin Square Design
• Alternative to full counterbalancing
• Ensures that
a. Each condition occurs once in each
position of the sequence
b. Sequence is random
• Table 14.7
• Complex analysis though…
15
Matched-Group Design
• Retains power of repeated-measures, but
tests each participant in only 1 condition
• Used when an important subject variable
correlates with the DV
– Each condition is a separate group of
participants
– Matched across conditions to control for
variance due to this subject variable
16
Matched-Groups Design
• Table 14.8 shows steps
– Ordered pairs of participants have similar
scores on the pretest
• A.K.A. randomized block design
• Sometimes matching is done on several
subject variables at once
• Because groups are matched, they are not
independent
17
Table 14.8
18
Matched-Groups Pros/Cons
• Advantage
– Potential for high power
• Disadvantage
– Potential for low power if matching
technique fails to match on an important
subject variable
• Important = significantly linked to DV
19
Yoked-Control Group
• Researcher randomly pairs control
participant with active participant
• Both participants experience exactly the
same sequence of study procedures, except
the control participant is not exposed to
the IV
• Figure 14.6
20
Figure 14.6
21
Mixed-Model Designs
• Between- and within-subjects elements
combined
– Between-subjects: Experimental vs. Control
– Within-subjects: Multiple trials
• Somewhat more complicated in terms of design,
but analysis is based on same principles as we
have already discussed
• This chapter’s Research in Action section
provides a good illustration
22
What is Next?
• **instructor to provide details
23