Factorial Designs

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Factorial Designs

• Week 5 lecture 1

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Whats factorial designs

• Two or more independent variables are manipulated
  in a single experiment
• They are referred to as factors
• The major purpose of the research is to explore
  their effects jointly
• Factorial design produce efficient experiments,
  each observation supplies information about all
  of the factors

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A simple example

• Research problem
• The effect of start and external reference prices
  on value judgments in Internet auction
• Four group of bidders

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2 x 2 factorial design

• Independent variables (factors)
• start price
• Two different levels low (20 below cv), high
  (10 below cv)
• Reference price
• Two different levels not available, catalog
  value(cv)
• 2 x 2 factorial design
• Number of numbers tells how many factors
• Number values tell how many levels
• The result of multiplying tells how many
  treatment groups that we have in a factorial
  design

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Design notation

• Whats the number of factors, levels and groups
  in a 3 x 4 factorial design?
• Design notation
• Dependent variable final selling prices

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Main effect

• The main effect of a factor are contrasts between
  levels of one factor averaged over all levels of
  another factor
• One possible results
• Main effect of Reference price is 1.08 13.39
  12.31

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Main effect illustrations
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Interaction effect

• An interaction effect exists when differences on
  one factor depend on the level of another factor
• How do we know if there is an interaction in a
  factorial design?
• Statistical analysis will report all main effects
  and interactions.
• If you can not talk about effect on one factor
  without mentioning the other factor
• Spot an interaction in the graphs of group means
  whenever there are lines that are not parallel
  there is an interaction present!

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Results with interaction effect
Interaction as a difference in magnitude of
response
Interaction contrast (13.71-12.40) (12.51
12.10) 1.3
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Results with interaction effect (II)
Interaction as a difference in direction of
response
Interaction contrast (13.71-13.07) (12.51
13.40) 1.63
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Factorial design analysis

• Analysis of variance (ANOVA)
• used to uncover the main and interaction effects
  of categorical independent variables on an
  interval dependent variable
• focuses on F-tests of significance of differences
  in group means
• Factorial ANOVA
• analyzes one interval dependent in terms of the
  categories (groups) formed by two or more
  independents
• Two-way ANOVA

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Interpretation of two-way ANOVA table
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Factorial design variations

• A three-factor example

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What are the major statistics?

• Main effects of each of the three factors
• Three two way interactions
• Number of bidders vs. reference price
• Reference price vs. start price
• Number of bidders vs. start price
• One three way interactions

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Incomplete factorial design

• Leave some treatment groups empty

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Advantages of factorial design

• Factorial designs are cost efficient
• Factorial design may enhance external validity
• External validity to what extent research
  findings can be generalize to other conditions.
• Whenever we are interested in examining treatment
  variations, factorial designs should be strong
  candidates as the designs of choice
• Factorial designs are the only effective way to
  examine interaction effects

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2x3 factorial design example

• Research problem
• Whether the structure of a decision task
  moderates the effects of GDSS on the patterns of
  group communication and decision quality in a
  decision making group
• Unit of study
• Group decision making (process and outcome)
• Dependent variables
• Communication pattern (qualitative measure)
• Decision quality (quantitative measure)

-- Adapted from the effect of group decision
support systems and task structures on group
communication and decision quality by Simon S K
Lam, JMIS, Spring 1997
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Independent variables

• Level of support
• GDSS support
• No support
• Task structure
• Additive task
• Each group member contributes a part to the group
  decision
• Disjunctive task
• A group select one optimal solution from an array
  of solutions proposed by individual group members
• Conjunctive task
• Each group member has different information, the
  successful decision can only be achieved when the
  unique information is accurately communicated to
  other group members

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Research methods

• Experiment with 2x3 full factorial design
• Subjects 216 midlevel managers from 35 diverse
  organization
• Subject assignment each treatment group
  contains 12 three-person decision groups

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Research method (II)

• Experimental Task
• Selecting a product manager for a new division of
  a company.
• GDSS provides
• Chatting facility
• Multi-criterion decision model support
• Voting feature

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Experimental Manipulation

• Manipulation of level of support
• Manipulation of task structure
• Three piece of informationa resume, a detailed
  work history and a confidential character
  evaluation report
• Additive task
• Each group member received all three piece of
  information and worked together to reach an
  decision
• Disjunctive task
• Each group member received all three piece of
  information, ranked the candidates individually,
  then decide whose ranking was optimal
• Conjunctive task
• Each group member received only one type of
  information about all candidates

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Experimental procedures

• Introduction
• Fill out a questionnaire about background,
  experience
• Distributing information packet
• Randomly assign subjects to different decision
  groups, and decision groups to treatment groups
• Decision groups start to work on the recruiting
  task
• Hand in decision and fill out a questionnaire
  about decision making procedure and decision
  making environment
• Measuring dependent variables

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Results

• Manipulation checks
• Which of the following best describes how you
  made a decision on the task you have just
  finished
• Which of the following best describes your
  groups decision-making environment?
• Control checks
• Run statistical test to compare subjects
  background across all six experimental treatments
• Two-way ANOVA on decision quality was conducted
  to test hypotheses on decision quality