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.