Factorial Designs

• So far: basic designs (one IV, one DV)

• Now: more than one IV (still one DV)

2 x 3 Factorial Design

Independent Variable A A1

A2 A3

A1 B1Cell mean

A2 B1 A3 B1

A1 B2 A2 B2 A3 B2IV B

B1

B2

B1Marginalmean

B2Marginalmean

A1Marginal

mean

A3Marginal

mean

A2Marginal

mean

2 types of effects

• Main Effect - The influence of one Independent variable in a factorial design

• Interaction Effect - joint influence of two or more IVs on the DV– The effect of one IV depends on the level of

another IV.

Example

• Study examining gender (M-F) and intervention to improve test-taking skills

• 3 IV levels– control (no intervention)– reading material (instructional booklet)– personalized tutoring

Intervention Control Booklet Tutoring

A1 B1 A2 B1 A3 B1

A1 B2 A2 B2 A3 B2

Male

Female

What would a main effect of gender look like?

Control Reading Tutoring0

102030

405060

708090100

MaleFemale

What would a main effect of intervention look like?

What would an interaction look like?

What should we interpret?

• If one main effect - report it• 2 main effects – report both• BUT if there’s an interaction…

– Only interpret/report the interaction– Because the effect of test-taking intervention

depends on gender

Interaction

Combining Between and Within Participant Designs

• Factorial design based on a mixed model• -or- mixed model design• IVs can be either between-groups (e.g.,

gender) or within-groups (a.k.a. repeated)

Advantages of Factorial Designs

• Can test more than 1 hypothesis at a time • Able to deal with extraneous variables

– Build into design and test outright

• Increases precision b/c it evaluates more variables at once

• Allows researcher to understand interactive effects of variables

Disadvantages of Factorial Designs

• Gets messy with more than 2 IVs

• Requires more participants (N per cell)

• More difficult to simultaneously manipulate all IVs when you have more of them

Choosing an Experimental Design

• Depends on…• Research question• Nature of variables you are investigating• We have discussed design building blocks

• Page 255: guiding questions

Chapter 7

Control Techniques in Experimental Research

Overview

• Control at the beginning of experiment– Random assignment– Matching

• Control during the experiment– Counterbalancing– Controlling for participant effects– Controlling for experimenter effects

Create equivalent experimental groups

Treat groups the same during the experiment

Random Assignment

• Not to be confused with random sampling!

• In reality, random sampling is rarely used in experimental research

• Generalize on the basis of multiple studies• With different kinds of samples/settings

Random Assignment

• a.k.a randomization– Most important of all control methods– Only technique for controlling both known

and unknown extraneous variables

In experimental

design

Random Assignment

• Quiz time:• How does randomization eliminate systematic

bias in experiments (produce control)?

– All variables distributed in approximately the same manner in all groups

– Influence of extraneous variables is held constant

Random Assignment

• Sample Size– It is possible for random assignment to fail – rare with a large enough sample size (N > 30)

Random Assignment

• Ways of achieving randomization– Table of random numbers– Randomizer.org– Draw out of a hat– Be creative – flip a coin/lottery/etc

• www.Randomizer.org

Text pp. 203-207

Matching

• Equate participants on one or more selected variables

• Matching Variable: The extraneous variable used in matching

• Useful when random assignment is not possible

Methods for Matching Participants

• Holding variables constant• Building the extraneous variable into the

design• Yoked control• Equating participants

Matching by Holding Variables Constant

• Hold extraneous variable constant for all groups in the experiment

• All participants in each treatment group will have same degree or type of extraneous variable

• Requires selection criteria for participant sample

Build Extraneous Variable into the Research Design

• Especially useful if you are interested in:– Differences produced by the levels of the

extraneous variable– Interaction between levels of IV and levels of

extraneous variable

• Sound familiar?– What kind of research design would this be?

Example: Effect of a study skills intervention on college grades in a Quantitative Methods

course…Intensive tutoring program Study packets (usual)

But the literature suggests that learning style may affect how students respond to different study skills training methods.

Learning style is a potential confounding extraneous variable….but we can build it in to the design!

Learning Style

Visual Auditory Kinesthetic

Intensive tutoring program

Study packets

Inte

rven

tion

A

B

Matching by Yoked Control

• Match participants on the basis of the sequence of administering an event

• Each control participant is “yoked” to an experimental participant

• Controls for the possible influence of participant-controlled events

• Example: Sklar & Anisan (1979)– stress and immune response

Matching by Equating Participants

Precision control• Match each participant in experimental group

with a participant in control group on variable(s) of concern

• Example: Scholtz (1973) compared defense styles in suicide attempt vs. no attempt

Matching by Equating Participants

• Precision Control Advantage– Groups are equated on matching variables

• Precision Control Disadvantages– How do you know which variables are critical?– Difficulty of finding matched participants increases

exponentially as number of matching variables increases– Matching limits generalizability of results– Some variables are difficult to match

• Example: prior psychotherapy

– Matching can only be as accurate as the available measurement of the matching variable