# Chapter 13 Matched Pairs, Within-Subjects and Mixed Designs

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### Simple Experiment: Independent Groups Design

- Has internal validity (due to random
assignment)
- Each P provides only one score per condition
▪ Requires large # of Ps
- Individual differences may hide a small
treatment effect

### Match Pair Design:

PROCEDURE
Form matched pairs
▪ Randomly assign one member of each
pair to the treatment condition, the other
to the control condition
CONSIDERATIONS
Finding an effective matching variable
- Must create pairs that are very similar to each
other in terms of your DV
▪ External Validity
population (i.e., can have heterogeneous
group)
- Disadvantage: Results may not generalize to
participants who haven't done the matching
Construct Validity may be weakened
because matching may tip off
▪ Power: Can be a BIG plus
- Reduced random error (AS LONG AS
EFFECTIVE IN MATCHING VARIABLES) results
in larger t-values
- However, have fewer r df (pairs - 1), which may
cause reduced power

### The bigger the t-value the______

more likely the effect is statistically significant

### Avantages of Within Subject Designs

▪ Increase Power (two factors)
- Tries to ELIMINATE random error due to
individual differences
▪ More observations (the more you have,
the greater opportunity you have for
random error to balance out)
- More observations = more power

### Disadvantages of Within Subject Designs

▪Construct validity threatened
- P, who receives at least two levels of IV and
performs DV task at least twice, has multiple
opportunities to figure out hypothesis
▪ Internal Validity may be weakened due
to order effects (4 of them - KNOW
THESE)
- Testing (i.e., practice) effects -> get better on
DV
- Fatigue effects -> get worse on DV
▪ Can be considered a negative practice effect
- Treatment carryover effects
▪ Effect of an earlier treatment lingers
- E.g., drug given earlier may affect performance on
later trial
- Sensitization
▪ Threatens internal validity because they behave
different AFTER they figure out what the hyp is.

### Within-Subjects Design: Dealing with order Effects

▪ Minimize each individual threat
- Testing (i.e., practice) effect
▪ Give Ps extensive practice before beginning
- Fatigue/boredom (i.e., negative practice effect)
▪ Make it interesting, undemanding, and short
- Carryover effect
▪ Lengthen times between different treatments
- Sensitization
▪ Hide what you are varying and use unobtrusive DV
▪ Use as few levels as possible to reduce
opportunities for each individual threat

### Counterbalanced Within Subjects Designs:Procedure

▪ Devise set of sequences such that:
- Every condition appears in every position the
same number of times
▪ e.g., C1 is first as many times as it is last
- Every condition precedes every other condition
as many times as it follows that condition
▪ e.g., # C1 comes before C2 = # C2 comes before
C1
▪ Randomly assign Ps to your sequences

- Ensures that routine order effects are balanced
across conditions
▪ e.g., 2 trx and 8 Ps
4 Ps will get A then B
4 Ps will get B then A
- Opportunity to learn about effect of the withinsubjects variable of order (e.g., trials,
positions, etc.)
- Opportunity to learn about the effect of the
between-subjects variable of sequence

May require more subjects
- Therefore, more resources (e.g., time, money,
etc)
▪ Analysis becomes much more
sophisticated
- May be quite difficult for the beginner to
understand

### Possible Results from 2x2 Counterbalanced Design

Main effect of Trx
- Between-Groups comparison
▪ Main effect of counterbalancing sequence
(CB)
- Between-Groups comparison
▪ Trx x CB interaction`

### Counterbalanced WithinSubjects Designs: Summary

▪ Balances out routine order effects
▪ Provides info not only about the effect of
the treatment, but also about the effect
of order and sequence

### Four approaches to the order problem

▪AVOID the problem by using betweensubjects designs instead
▪ Randomize sequence of treatments
▪ Randomly assign Ps to
counterbalanced sequences
▪ Reduce sources of order effects (i.e.,
practice, fatigue, carry-over,
sensitization)

### Within-Subjects Design: Dealing with Order Effects

▪ Minimize each individual threat
- Testing (i.e., practice) effect
▪ Give Ps extensive practice before beginning
- Fatigue/boredom (i.e., negative practice effect)
▪ Make it interesting, undemanding, and short
- Carryover effect
▪ Lengthen times between different treatments
- Sensitization
▪ Hide what you are varying and use unobtrusive DV
▪ Use as few levels as possible to reduce
opportunities for each individual threat

### Mixed Designs

▪Combining between-subjects and withinsubjects design
- One (or more) factors varied BETWEEN groups
- One (or more) factors varied WITHIN groups
▪ Allows for both internal validity, power,
and possibly external validity

### Choosing an Experimental Design: General Considerations

▪ Pure between-subjects designs may:
- Have more construct validity because harder
for participants to guess the hypothesis
- Have more internal validity because they are
not vulnerable to order effects
- Easier to analyze
▪ Within-subjects designs have more
power
▪ External validity depends on whether the
variable is "within-subjects" or "betweensubjects" in real life

### Choosing Designs: The Two Conditions Case

▪Pure between-subjects design
▪ Matched-pairs design
▪ Randomized within-subjects designs
▪ Counterbalanced designs

### Choosing Designs:Multiple IVs

▪ Use a within-subjects factorial design
▪ Use a between-subjects factorial design
▪ Use a mixed design (both within- and
between-subjects design)

Example:

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