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PSYB01H3 Study Guide - Final Guide: Internal Validity, Selection Bias, Square Root

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David Nussbaum
Study Guide

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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
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
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
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)

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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,
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
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

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Natural treatment = exposure in the “real world” defines how participants are
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
Individual matching = individual cases in the treatment group are matched with similar
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.
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.
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 ???
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
No comparison group
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