Complex Design

Two group Designs

• One independent variable with 2 levels:– IV: color of walls

• Two levels: white walls vs. baby blue– DV: anxiety

White walls Baby blue wallsBaby blue walls

Two group Designs – within subjects

• One independent variable with 2 levels:– IV: color of walls

• Two levels: white walls vs. baby blue– DV: anxiety

– All participants are tested in both white classroom and baby blue classroom

White walls Baby blue wallsBaby blue walls

Two group Designs – between subjects

• One independent variable with 2 levels:– IV: color of walls

• Two levels: white walls vs. baby blue– DV: anxiety

– Some participants are tested in white classroom and another set of participants are tested in baby blue classroom.

White walls Baby blue wallsBaby blue walls

More than two groups

• One independent variable with 3 levels:– IV: color of walls

• 3 levels: white walls vs. baby blue vs. red– DV: anxiety

– Can use within-subjects design or between-subjects design.

White walls Baby blue wallsBaby blue walls Red wallsRed walls

Why conduct studies with more than two groups? Can answer more sophisticated questions with a multiple

group design—more efficient.

Compare more than 2 kinds of treatment in one study. Compare 2 kinds of treatment and a control group. Compare a treatment vs. placebo vs. control group.

To go from a two groups design to a multiple groups design, you add another level to your IV.

Analysis of variance: One-way Randomized ANOVA

One-way Repeated Measures ANOVA

Factorial Designs• Experiments with more than 1 independent variable.

• Factorial designs– More than 1 factor (or IV) is being manipulated in the study.– IV 1: gender (male vs. female)– IV 2: color of walls (white vs. baby blue) – DV: anxiety

• Benefits:– Assess how variables interact with each other. – Increases generalizability of results because we are measuring how

multiple variables affect behavior, at the same time.

Factorial Designs

• 2 X 2 factorial design– The number of digits tells us how many independent

variables are being manipulated. – The value of digits tells us the number of levels of each IV.

• 3 X 3 ?• 2 X 3?• 2 X 2 X 3?• __ X __ X __ ?

2 X 2: simplest factorial design

The simplest Factorial Design

DV: speed of salesclerk to respond to customer.

2 X 2 factorial design• Clerks (male & female) responded

faster to hearing customers.

• Overall speed for males and females was the same. – Average 2 dots on male line and

2 dots on female line.

• Hearing customer: male clerks responded faster.

• Deaf customer: female clerks responded faster.

• The effects of customer hearing seemed to vary according to sex of salesclerk.

4 min

3

3.7

Factorial designs

• Provides information about each factor separately. – Gender of clerks– Hearing of customers

• Saves time to run 1 factorial design versus 2 separate experiments (i.e., gender; hearing ability).

• Provides information about how the 2 factors interact.

• Main effects: – The effect of each

independent variable separately.

– Main effect for factor A– Main effect for factor B

• Interaction– Joint effect of

independent variables on the DV.

Interaction

• An interaction is present when the effects of one independent variable change as the levels of the other independent variable changes.

• An interaction is present when the effects of one independent variable depend on the level of the other independent variable.

2 x 2 design

Clothing style of customer

Resp

onse

tim

e of

cle

rk (i

n se

c)

• Main effect of A?

• Main effect of B?

• AB interaction?

• NO

• Yes

• NO

• Main effect of A?

• Main effect of B?

• AB interaction?

• Yes

• Yes

• NO

• Main effect of A?

• Main effect of B?

• AB interaction?

• Yes

• NO

• Yes

• Main effect of A?

• Main effect of B?

• AB interaction?

• No

• No

• Yes

Statistical Analysis

• Two-way ANOVA– 2 independent variables

• ANOVA for each type of design: – Two-way Randomized ANOVA (both variables are

between- subjects)

– Two-way Repeated measures ANOVA (both variables are within-subjects)

– Two-way mixed ANOVA (one variable within-subjects and the other variable between subjects)

Rationale of ANOVA

• F = between-groups variance within-groups variance

• F = systematic variance + error variance error variance

IV has an effect: F > 1; must pass a cutoff for statistical significance.

IV has no effect or small effect: F ≤ 1

Two-way Randomized ANOVA

• 3 F-ratios– F-ratio for factor A– F-ratio for factor B – F-ratio for interaction

• F-ratios obtained by dividing each MS (variance) by Mserror (within-groups variance)

• Table 11.8 11.9, pg 254

Two-way Repeated measures & Mixed ANOVAs

• 3 F-ratios– F-ratio for factor A– F-ratio for factor B – F-ratio for interaction

• More complex statistical procedures