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Factorial Designs (two or more factors [IV's]) - Coggle Diagram
Factorial Designs
(two or more factors [IV's])
Notation
single factor design
two factor design
Y x Y
three factor design
2 x 3 x 2
12 conditions
factor 1 has 2 levels
factor 2 has 3 levels
factor 3 has 2 levels
... factor design
Advantages
more realistic situation
observable:
individual factors
group factors
Data
Matrix
each cell corresponds to a seperate treatment condition (specific combination of the factors)
provides three seperate
and distinct sets of info
how factors affect behaviour
individually
jointly
Ex.: two factor design
three seperate sets of mean differences
Mean differences from main effect of Factor A
Mean differences from main effect of factor B
Mean differences from interaction between factors
seperate sets of differences => independent
Main Effect
= mean differences among levels of one factor
Interaction Between Variables
= occurs when two factors, acting together, produce mean differences, not explainable by the main effects
main effect applies equally across all levels of a factor
=> no interaction
effects of one factor depend on different levels of a second factor
=> interaction exists
identify
in Graph
=> statistical test is needed
nonparallel lines (crossing/converging) undicate an interaction
in Data Matrix
Compare mean differences of every row
size + direction of differences changes from one row to another
evidence => statistical test needed
Interpretation
interaction can obscure / distort the main effects
main effect = average
may not represent any individual
effect to compute the average
Types of Factorial Design
Mixed Design
Exp. / Non-Exp. Research Strategies
Factorial design == purely experimental research
all IV's are manipulated
Factorial study of quasi independent V's
nonexperimental
quasi experimental
non-manipulated variables == calles factors
Pretest-Posttest Control Group Design
one factor = between-subjects (treatment/control)
other factor = within-subject (pretest-posttest) factor
combining different research strategies
Within- / Between-Subject Design
Between-Subject
One group of 30 participants in a 2x4 design == measuring each participant 8 times
participant attrition
order effects
Within-Subject
groups of 30 participants in a 2x4 design == 240 participants
many individual differences
possible confounders
many participants
Combined Strategy
uses two different research strategies in same factorial design
Factors
One factor = true IV (experimental strategy)
Second factor = quasi indepentent variable
nonexperimental / quasi-experimental strategy
categories
Person-By-Experiment
add participant characteristic as a second factor
Time as second factor =
how different treatments effects persist over time
Higher Order Factorial Designs
3 factors => complex results
Statistical Analysis of Factorial Designs
Compute the mean for each treatment condition (matrix-cell)
Using ANOVA to evaluate statistical significance of mean differences
Application of Factorial Design
Replication of studies
Expansion of studies
Participant Variable:
Reduce Variance Within Groups
No lost external validity
Order of Treatments
Within Subjects Design
evaluate order effects
outcomes
no order effects
treatment 1 has a mean
treatment 2 has a mean
Symmetrical Order effect
an order effect only occurs in the treatment given second
of same size over all treatments
Nonsymmetrical Order Effect
different order of treatments
causes different levelts of fatigue
hard to identify in the data
