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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

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Outline

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### Outline

1. Definition of Complex Designs

2. Some important terms

• Testing theories

• 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

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.’

### Definition of Complex Design

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.

### Some important terms

A1

A2

B1

A1B1

A2B1

B2

A2B2

A1B2

The basic 2 X 2 factorial design

Training duration

ShortLong

Motor - Short

Motor - Long

Motor

Abstract - Short

Abstract - Long

Abstract

The basic 2 X 2 factorial design

Factorial design

Main effect

The effect of one variable in a multi-variable design, ignoring all other variables

### Some Important Terms

A1

A2

B1

B1

A1B1

A2B1

B2

B2

A2B2

A1B2

Comparing these two means gives us the main effect of B

A1

A2

Comparing these two means gives us the main effect of A

The basic 2 X 2 factorial design

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.

### Some Important Terms

A1

A2

B1

A1B1

A2B1

B2

A2B2

A1B2

Here, A1B1 – A1B2 gives the SME of B at A1

SME = simple main effect

A1

A2

B1

A1B1

A2B1

B2

A2B2

A1B2

Here, A2B1 – A2B2 gives the SME of B at A2

SME = simple main effect

A1

A2

Here, A1B1 - A2B1 gives the SME of A at B1

B1

A1B1

A2B1

B2

A2B2

A1B2

SME = simple main effect

A1

A2

B1

A1B1

A2B1

Here, A1B2 – A2B2 gives the SME of A at B2

B2

A2B2

A1B2

SME = simple main effect

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).

### Some important terms

A1

A2

B1

400

500

B2

575

425

25

75

SME of B at A2

SME of B at A1

These numbers show observations on some dimension (such as reaction time in milliseconds)

The SME of B is much smaller for A1 than for A2 – that’s an interaction of variables A and B

Coffee

No Coffee

Cereal

40

100

60

10

50

60

40

10

SME of Cereal with

Coffee

No Cereal

SME of Coffee is larger with Cereal than without

SME of Cereal

Without Coffee

The SME of Cereal is larger with Coffee than without.

DV = a measure of mood quality

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.

### Interaction – an example

Learning

On deck

In pool

On deck

Recall

13.5

8.6

In pool

11.4

8.4

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.

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

### Some important terms

Testing theories

Complex Designs allow tests that are:

more powerful

more economical, and

less likely to be correct by chance

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

More powerful

More economical

Better use made of subjects’ time – test several hypotheses at once.

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.

Testing theories

More powerful

More economical

Less likely to be correct by chance

Testing theories

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.

Arousal

High

Low

High

Difficulty

60

40

Low

50

80

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.

Testing theories

Establishing external validity of a result

When no interaction is found, it’s safer to generalize effects of eachvariable across levels of the other variable.

But don’t generalize the effect of A beyond the levels of B used in the experiment.

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.

We don’t know what’s going on in this region – so we shouldn’t say anything about it

2 4 10

7

20

Clear

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 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.

### Analysis when no interaction occurs

Simple comparisons

Yes

More than 2 means?

Yes

No

Finished

SME of A at B1?

No

SME of A at B2?

Yes

Does A interact with B?

Simple comparisons

Yes

More than 2 means?

Yes

No

Main effect of A?

No

Finished

No

Finished

Main effect of B?

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

### Complex design example

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)

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

15

10

5

0

-5

06 wks

### Pratkanis et al. (1988)

There’s no main effect of the variable order (discounting cue given before or after persuasive message during original session)

15

10

5

0

-5

BeforeAfter

### 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

15

10

5

0

-5

06 wks

cue before message

cue 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.

### Pratkanis et al. (1988)

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?

### Natural groups designs

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

### Halpern & Bower example

%

Structured

Unstructured

Musicians

Non-musicians

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.

### Halpern & Bower example

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.

### CAUTION! Ceiling & Floor Effects

100

0

A1 A2 A3

B1

B2

Why do these lines have different slopes? We cannot say. Might be a real interaction of A and B. Might be a ceiling effect.

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).

### CAUTION! Ceiling & Floor Effects

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.