Outline 1. Definition of Complex Designs 2. Some important terms 3. Advantages of complex designs...
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Transcript of Outline 1. Definition of Complex Designs 2. Some important terms 3. Advantages of complex designs...
Outline
1. Definition of Complex Designs
2. Some important terms
3. Advantages of complex designs Testing theories Resolving contradictions Establishing the external validity of a result
4. Analysis in the presence of an interaction
5. Analysis when there is no interaction
6. Natural Groups designs
7. Ceiling effects
Definition of Complex Design
A complex design is one in which more than one variable is manipulated at the same time.
‘Complex’ here does not mean ‘difficult to understand.’
Some important terms
Factorial design The most useful kind of complex design is the factorial experiment, in which each variable is manipulated at all levels of each other variable.
The basic 2 X 2 factorial design
A1B1
A1B2
A2B1
A2B2
A1
B1
B2
A2
The basic 2 X 2 factorial design
Motor - Short
Abstract - Short
Motor - Long
Abstract - Long
Training durationShort Long
Motor
Abstract
Task
Some Important Terms
Factorial design Main effect
The effect of one variable in a multi-variable design, ignoring all other variables
The basic 2 X 2 factorial design
A1 A2
Comparing these two means gives us the main effect of A
B1
B2
Comparing these two means gives us the main effect of B
A1B1
A1B2
A2B1
A2B2
A1
B1
B2
A2
Some Important Terms
Factorial design Main effect Simple main effect
The effect of one variable in a multi-variable design, observed at one level of a second variable.
A1B1
A1B2
A2B1
A2B2
A2
B1
Here, A1B1 – A1B2 gives the SME of B at A1
SME = simple main effect
B2
A1
A1B1
A1B2
A2B1
A2B2
A2
B1
Here, A2B1 – A2B2 gives the SME of B at A2
SME = simple main effect
B2
A1
A1B1
A1B2
A2B1
A2B2
A2
B1Here, A1B1 - A2B1 gives the SME of A at B1
SME = simple main effect
B2
A1
A1B1
A1B2
A2B1
A2B2
A2
B1
Here, A1B2 – A2B2 gives the SME of A at B2
SME = simple main effect
B2
A1
Some important terms
Factorial design Main effect Simple main effect Interaction
an interaction occurs when the effect of one variable varies at levels of another variable.
thus, when there is an interaction between A and B, the SME of A will vary across levels of B (and vice versa).
400
425
500
575
A2
B1
B2
A1
25 75
The SME of B is much smaller for A1 than for A2 – that’s an interaction of variables A and B
SME of B at A1 SME of B at A2
These numbers show observations on some dimension (such as reaction time in milliseconds)
The SME of Cereal is larger with Coffee than without.
SME of Cereal withCoffee
SME of CerealWithout Coffee
No Cereal
100
60
60
50
No Coffee
Cereal
Coffee
40 10
40
10 SME of Coffee is larger with Cereal than without
DV = a measure of mood quality
Interaction – an example
Godden & Baddeley (1975)
Wanted to test context-dependent learning hypothesis
Divers learned a list of words, then recalled the list.
Each step could be either on land or under the water.
Godden & Baddeley (1975)
13.5
8.4
8.6
11.4
On deck
On deck
In pool
In pool
Recall
Learning
DV = # words recalled out of 15
Is it better to learn on deck or in the pool? It depends upon whether you will have to recall on deck or in the pool.
Some important terms
Factorial design Main effect Simple main effect Interaction Analytical comparisons
Tests that determine what is producing a main effect
E.g., is B1 different from B2? Is it different from B3?
Some important terms
Factorial designs Main effect Simple main effect Interaction Analytical comparisons Simple comparisons
tests that determine what is producing a simple main effect
E.g., is B1 different from B2 at level A1? Is B2 different from B3 at A2?
Some important terms
Analytical comparisons:
Tests that determine what is producing a main effect
Simple comparisons:
tests that determine what is producing a simple main effect
Advantages of complex designs
Testing theories Complex Designs allow tests that are: more powerful more economical, and less likely to be correct
by chance
Advantage: Testing theories
More powerful Variability in your data is either random (E) or associated with a systematic source (T)
In a factorial design, associating some variance with the interaction reduces the random error.
A systematic source
Advantage: Testing theories
More powerful More economical
Better use made of subjects’ time – test several hypotheses at once.
Advantage: Testing theories
More powerful More economical Less likely to be correct
by chance
More complex predictions are less likely to be correct by chance, since there are more ways they can go wrong.
Advantages of complex designs
Testing theories More powerful More economical Less likely to be correct by
chance Resolving contradictions
Advantages of complex designs
Testing theories Resolving contradictions
Results from different labs sometimes conflict because different researchers unwittingly choose different levels of variables they are not manipulating.
If those variables can be identified, they can be manipulated in a new study with a factorial design.
40
80
60
50
High
High
Low
Low
Difficulty
Arousal
DV = accuracy (% correct)
If one lab used a difficult task and another used an easy task, researchers would draw opposite conclusions about the effect of arousal.
Advantages of Complex Designs
Testing theories Resolving contradictions Establishing external
validity of a result
When no interaction is found, it’s safer to generalize effects of each variable across levels of the other variable.
But don’t generalize the effect of A beyond the levels of B used in the experiment.
Advantages of complex designs
Don’t generalize effect of A beyond levels of B.
E.g., if A = stimulus quality and B = stimulus size
Levels of B = 2, 4 and 10 cm in our experiment
We find no interaction We can generalize the
effect of A to 7 cm stimuli, but not to 20 cm stimuli.
2 4 10
Clear Degraded
We don’t know what’s going on in this region – so we shouldn’t say anything about it
7 20
Analysis when interaction occurs
Once we detect an interaction, the next step is to ‘decompose’ the interaction.
That is, compare SMEs of A at levels of B (or vice versa).
Which SMEs we examine should be dictated by theory.
Analysis when no interaction occurs
When a variable A does not interact with other variables in the design, you analyze the main effects of A.
As before, use simple comparisons to test for differences between pairs of means for levels of A.
Does A interact with B?
No
Main effect of A?
NoFinished
Yes
Yes
Simple comparisons
SME of A at B1?
SME of A at B2?No
Yes
More than 2 means?
Finished
Simple comparisonsMore than
2 means?
FinishedNo
Yes
Yes
No
Main effect of B?
Complex design example
Pratkanis et al. (JPSP 1988)
The ‘sleeper effect’
The passage of time improves the effect of a persuasive message
This occurs only if message is accompanied by a discounting cue – a cue that causes you to distrust the persuasive message
Pratkanis et al. (1988)
Persuasive message:
“Dr. Smith’s research shows that orange juice consumption can reduce cholesterol.”
Discounting cue:
“This research was funded by Tropicana.”
Pratkanis et al. (1988)
Why does sleeper effect occur?
One model: it’s caused by dissociation – over time, link in memory between persuasive message and discounting cue gets weaker.
Pratkanis et al. tested this idea
Pratkanis et al. (1988)
Basic paradigm: People are given a persuasive message about an object or product + a discounting cue
Later, they are asked to rate the object or product
Pratkanis et al. (1988)
Pratkanis et al. used two independent variables
Delay
Was opinion rating given immediately or six weeks later?
Pratkanis et al. (1988)
Pratkanis et al. used two independent variables
Delay Order
Was discounting cue presented before or after persuasive message during original session?
Pratkanis et al. (1988)
This is the sleeper effect – found when we look at only the variable delay
Message is rated more persuasive (higher score) after delay of 6 weeks
0 6 wks
15
10
5
0
-5
Pratkanis et al. (1988)
There’s no main effect of the variable order (discounting cue given before or after persuasive message during original session)
Before After
15
10
5
0
-5
Pratkanis et al. (1988)
This interaction shows that we get the sleeper effect only when the cue is presented after the persuasive message
Dissociation model can’t explain this
0 6 wks
15
10
5
0
-5
cue before messagecue after message
Pratkanis et al. (1988)
The design of this experiment allowed Pratkanis et al. to test the interaction hypothesis
The interaction observed – sleeper effect occurred only when discounting cue came after persuasive message – is strong evidence against the dissociation theory of the sleeper effect.
Natural groups designs
Natural groups designs
Designs in which experimenter does not assign subjects to groups
Groups are naturally occurring
It is very risky to draw conclusions about why such groups differ in performance on some task.
Natural groups designs
For example: people who are mentally active into their later years are less likely than people who are not mentally active to suffer Alzheimer’s Type Dementia (ATD).
Why?
Having a healthy brain makes you active?
Being active gives you a healthy brain?
Natural groups designs
A natural groups design is really a correlational study, not an experiment!
Thus, in the ATD case, severity of the disease is correlated with mental activity.
Dividing the subjects into two groups (With and Without ATD) doesn’t change this.
But you can still make an argument for cause…
Natural groups designs
Halpern & Bower (1982)
Studied memory for musical notation
People with musical training recall notation better than people without musical training.
Is this because of the training?
Or are people with better memories drawn to musical training?
Halpern & Bower example
Theory: musical training gives musicians the ability to “chunk” notation.
A chunk is a unit formed from several smaller pieces, on the basis of knowledge.
Examples of “chunks:”
BMW
CBC
IBM
NHL
SOA
ISI
JND
Halpern & Bower example
Halpern & Bower compared natural groups: people with and without musical training
used two sets of musical notation:
one with structure (so notation stimuli could be chunked)
one without structure
Halpern & Bower example
Note that this design allows us to test the prediction of an interaction:
Group by structure
Structured Unstructured
MusiciansNon-musicians
%
Halpern & Bower example
Result: Musicians’ recall superiority was greater for musical notation stimuli that had structure (so could be chunked).
Conclusion: musical training gave musicians better memory.
Halpern & Bower example
Reasoning: other accounts don’t explain the importance of structure in producing the musicians’ advantage.
Caveat: This is a sensible argument – but it is just an argument. H & B can invite us to share their conclusion, but we don’t have to.
CAUTION! Ceiling & Floor Effects
Some interactions are spurious. They can be produced by “ceiling” or “floor” effects.
When performance reaches a theoretical maximum (e.g., 100%) or minimum (e.g., 0%) at one level of one treatment condition, subjects cannot get any better (or worse) at other levels of that condition.
Why do these lines have different slopes? We cannot say. Might be a real interaction of A and B. Might be a ceiling effect.
A1 A2 A3
100
B1B2
0
CAUTION! Ceiling & Floor Effects
An interaction produced by running up against a ceiling or floor cannot be interpreted.
Only solution is to run the study again, trying to eliminate the ceiling or floor effect (e.g., make the stimuli harder to perceive).
Complex Designs – Review
A complex design is one in which more than one variable is manipulated at the same time.
In factorial designs, each IV is manipulated at all levels of the other IVs.
A significant F is followed by tests of simple main effects and simple comparisons
Complex Designs – Review
Complex designs allow us to:
Test theories, using precise hypotheses.
Explain contradictory findings across labs.
Establish external validity (or its limits).
Complex Designs – Review
Interactions help us: Decide whether a variable is relevant to investigation of some topic.
Test theories about why natural groups differ in performance on some task.