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**preview**shows pages 1-3. to view the full**20 pages of the document.**True Experiments II: Multifactorial Designs Chapter 7

Multifactorial Designs

Also called factorial designs

Two or more independent variables that are qualitatively different

Each has two or more levels

Can be within- or between-subjects

Efficient design

Good for understanding complex phenomena

Multifactorial Design Example-in book chart

Notation

Multifactorial designs are identified by a numbering notation

Number of numbers = how many independent variables

Number of values = how many levels of each independent variable

Number of conditions = product of the numbering notation

A Complex Within-Subjects Experiment

Adams and Kleck (2003)

Two independent variables: gaze direction (direct / indirect), facial muscle

contraction (anger / fear)

Numbering Nomenclature: A “2 by 2 Within” Design

Within-subjects design

Participants made anger / fear judgments of faces and reaction time was

recorded

Adams and Kleck (2003) Results-in book

Main Effects

The effects of each independent variable on the dependent variable

Row means = the averages across levels of one independent variable

Column means = the averages across levels of the other independent

variable

Interactions

When the effects of one level of the independent variable depend on the particular level of

the other independent variable

A significant interaction should be interpreted before the main effects

Graphing the Interaction

A line graph of the simple main effects is useful for examining the interaction

Simple main effect = the value of each cell (or possible combination of

levels of the independent variables)

Interaction Types

Crossover interaction

Lines cross over one another

Antagonistic interaction

Independent variables show opposite effects

Parallel lines indicate no interaction (additivity)

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Additivity: No Interaction-in book

Antagonistic Interaction- in book

Crossover Interaction- in book

A Complex Between-Subjects 2x3 Experiment

Baumeister, Twenge, & Nuss (2002)

Can feelings of social isolation influence our cognitive abilities?

Manipulated participants‟ “future forecast” (alone, rich relationships,

accident-prone)

Also manipulated the point at which the participant was told the forecast

was bogus (after test/recall, before test/encoding)

Nomenclature: A “3 by 2 Between (groups)” Design

Baumeister et al. (2002) Study Design- in book

Results: Baumeister et al. (2002) - in book

Analyzing Multifactorial Designs

ANOVA (or F-test) = statistical procedure that compares two or more levels of independent

variable(s)

Simple ANOVA = only one IV

Factorial ANOVA = more than one IV

Allows comparison of all effects simultaneously

Ratio of systematic variance to error variance

Analyzing Multifactorial Designs

Ratio of systematic variance to error variance… Basic idea:

1. Calculate the variance using the entire sample

2. Calculate the variance within each group

3. Under the Null Hypothesis (i.e., grouping the sample for each treatment group),

there is no difference between the overall variance and sum of the individual

grouped/within variances because under the Null hypothesis, the various group

means is equal to the overall mean.

4. We then look at the ratio between the sum of the grouped (systematic) variances

and the overall (random or error)variance.

5. The greater the ratio, the less likely the results can be attributed to “chance’

More Complex “Hybrid” Designs

It is possible to combine Between and Within factors in a single study:

Example: Looking at Male-Female differences in self-esteem at ages 5, 7 and 12.

This would be classified as a “2 Between, 3 Within” design.

Quasi-Experimental & Non-Experimental Designs Chapter 8

Quasiexperimental Design

Often, we cannot manipulate a variable of interest

Quasi-independent variables:

Subject variable = individual characteristic used to select participants to

groups

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Natural treatment = exposure in the “real world” defines how participants are

selected

Types of Quasiexperimental Design

Nonequivalent-control-group designs

Experimental and comparison groups that are designated before the

treatment occurs and are not created by random assignment

Before-and-after designs

Pretest and posttest but no comparison group

Nonequivalent-Control-Group Designs

Random assignment cannot be used to create groups

Confounds related to equivalency of groups cannot be eliminated

Often high in external validity

Particularly ecological validity

Matching

Individual matching = individual cases in the treatment group are matched with similar

individuals

Aggregate matching = identifying a comparison group that matches the treatment group in

the aggregate rather than trying to match individual cases

Regression to the mean can be a problem

What is Regression to the Mean ???

Int J Epidemiol. 2005 Feb;34(1):215-20. Epub 2004 Aug 27.

Regression to the mean: what it is and how to deal with it.

Barnett AG, van der Pols JC, Dobson AJ.

Abstract

BACKGROUND:

Regression to the mean (RTM) is a statistical phenomenon that can make natural variation

in repeated data look like real change. It happens when unusually large or small

measurements tend to be followed by measurements that are closer to the mean.

RESULTS:

The effect of RTM in a sample becomes more noticeable with increasing measurement

error and when follow-up measurements are only examined on a sub-sample selected

using a baseline value.

How to reduce the effects of RTM at the study design stage

1. Random allocation to comparison groups

2. Selection of subjects based on multiple measurements

What is Regression to the Mean ???

CONCLUSIONS:

RTM is a ubiquitous phenomenon in repeated data and should always be considered as a

possible cause of an observed change. Its effect can be alleviated through better study

design and use of suitable statistical methods

Before-and-After Designs aka Pre-Post Designs

Useful for studies of interventions that are experienced by virtually every case in some

population

No comparison group

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