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 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 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 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 walls Red 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 Response time of clerk (in sec)

Main effect of A? Main effect of B? AB interaction? NO Yes NO

Main effect of A? Main effect of B? AB interaction? 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 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 , 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