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Chapter Fourteen


Title: Chapter Two Author: Instructional Design Last modified by: pe Created Date: 1/10/2003 6:41:18 AM Document presentation format: On-screen Show – PowerPoint PPT presentation

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Title: Chapter Fourteen

Chapter Fourteen
  • Designing and Conducting Experiments with
    Multiple Independent Variables

PowerPoint Presentation created by Dr. Susan R.
BurnsMorningside College
Experimental Design Doubling the Basic Building
  • A factorial design gives us the power we need to
    devise an investigation of several factors (IVs)
    in a single experiment.

Experimental Design Doubling the Basic Building
  • Factors
  • Synonymous with IVs
  • Independent variables (IVs)
  • Stimuli or aspects of the environment that are
    directly manipulated by the experimenter to
    determine their influences on behavior.

Experimental Design Doubling the Basic Building
  • Factorial designs are the lifeblood of
    experimental psychology because they allow us to
    look at combinations of IVs at the same time, a
    situation that is quite similar to the real
  • A factorial design is more like the real world
    because there are probably few, if any,
    situations in which your behavior is affected by
    only a single factor at a time.

Experimental Design Doubling the Basic Building
  • This figure demonstrates a graphical display of
    the simplest possible factorial design (2 x 2).
  • This 2 X 2 shorthand notation tells us that we
    are dealing with a design that has two factors
    (IVs) because there are two digits given and
    that each of the two factors has two levels
    because each digit shown is a two.

How Many IVs?
  • The factorial design gets its name because we
    refer to each IV as a factor.
  • Multiple IVs yield a factorial design.
  • Theoretically, there is no limit to the number of
    IVs that can be used in an experiment.
  • Practically speaking, however, it is unlikely
    that you would want to design an experiment with
    more than two or three IVs.

How many Groups or Levels?
  • Once you have two or more IVs, you will use a
    factorial design.
  • The number of levels of each factor is
    unimportant at this point.

Experimental Design Doubling the Basic Building
How many Groups or Levels?
  • Various factors are often designated by letters,
    so the first factor is labeled Factor A, the
    second as Factor B, and so on.
  • The levels within a factor are often designated
    by the letter that corresponds to the factor and
    a number to differentiate the different levels.
  • Thus, the two levels within the first factor
    would be labeled A1 and A2.

How many Groups or Levels?
  • Main effect
  • A main effect refers to the sole effect of one IV
    in a factorial design.
  • Interaction
  • Another benefit that we get from doing an
    factorial experiment is the ability to examine
    potential interactions between the two IVs.
  • Significant interactions are found when the
    effects of one IV change as the level(s) of the
    other IV changes. In other words, the effects of
    one IV depend on the particular level of another
  • A simple way to discern an interaction is to look
    at your findings graphically. If the lines on the
    graph are not parallel, then there likely is a
    significant interaction.

Psychological Detective
  • Can you interpret the main effects in the figure
    below. Did customer hearing having an effect? Did
    the salesclerk sex have any effect? Study the
    graph to answer these questions.

Assigning Participants to Groups
  • We have two options for this assignment
    independent groups or correlated groups.
  • Factorial designs in which both IVs involve
    random assignment may be called between-subjects
    factorial designs or completely randomized
  • This decision is not as simple as in the
    two-group and multiple-group designs, each of
    which had only one IV.
  • All IVs could have participants assigned
    randomly or in a correlated fashion, or we could
    have one IV with independent groups and one IV
    with correlated groups. This possibility is
    referred to as mixed assignment.

Assigning Participants to Groups
  • Mixed assignment
  • A factorial design that has a mixture of
    independent groups for one IV and correlated
    groups for another IV.
  • In larger factorial designs, at least one IV has
    independent groups and at least one has
    correlated groups (also known as mixed groups).

Nonrandom Assignment to Groups
  • In this section, we deal with factorial designs
    in which participant groups for all IVs have
    been formed through nonrandom assignment.
  • We refer to such designs as completely
    within-groups (or within-subjects) designs.
  • We may want to resort to nonrandom assignment in
    order to assure the equality of participant
    groups before we conduct the experiment.

Nonrandom Assignment to Groups
  • Matched Pairs or Sets
  • Matching can take place in either pairs or sets
    because factorial designs can use IVs with two
    or more levels.
  • The more levels an IV has, the more work matching
    for that variable takes.
  • The more precise the match that is necessary, the
    more difficult matching becomes.

Nonrandom Assignment to Groups
  • Repeated Measures
  • In a completely within-groups experiment using
    repeated measures, participants would take part
    fully and completely.
  • Participants take part in every possible
    treatment combination.
  • This requirement makes it difficult or impossible
    to conduct an experiment with repeated measures
    on multiple IVs.
  • The smaller the design, the more feasible it is
    to include all participants in all conditions of
    the experiment.

Nonrandom Assignment to Groups
  • Natural Pairs or Sets
  • Using natural groups in a totally within-subjects
    design has the same difficulties as the matched
    pairs or sets variation of this design, but it
    would be even harder.
  • The difficulty lies in being able to find an
    adequate number of naturally linked participants.

Nonrandom Assignment to Groups
  • Mixed Assignment to Groups.
  • Mixed assignment designs involve a combination of
    random and nonrandom assignment, with at least
    one IV using each type of assignment to groups.
  • In a two-IV factorial design, mixed assignment
    involves one IV with random assignment and one IV
    with nonrandom assignment.
  • In such designs, the use of repeated measures is
    probably more likely than other types of
    nonrandom assignment.
  • Mixed designs combine the advantages of the two
    types of designs.
  • The conservation of participants through the use
    of repeated measures for a between-subjects
    variable makes for a popular and powerful design.

Comparing the Factorial Design to Two-Group and
Multiple-Group Designs
  • Two-group designs are ideal for a preliminary
    investigation of a particular IV in a
    presence-absence format.
  • The multiple-group design may be used to conduct
    more in-depth investigations of an IV that
    interests us.
  • We took the basic two-group design and extended
    it to include more levels of our IV.
  • We can make the same type of extension with
    factorial designs.
  • Just as with the multiple-group design, there is
    no limit to the number of levels for any IV in a
    factorial design.
  • The number of levels of the IVs can be equal or
  • Interaction effects must be interpreted in
    factorial designs but not in two-group or
    multiple-group designs.
  • A good rule of thumb to follow is to choose the
    simplest research design that will adequately
    test your hypothesis

Experimental Questions
  • Factorial designs provide considerable
    flexibility in devising an experiment to answer
    your questions.
  • The number of questions we can ask in a factorial
    experiment increases dramatically, but.
  • When we ask additional questions, we must make
    certain that the questions coordinate with each
    otherexperimental questions should not clash.
  • (e.g., it would not make sense to propose an
    experiment to examine the effects of self-esteem
    and eye color on test performance)

Control Issues
  • We need to consider independent versus correlated
    groups in factorial designs.
  • A complicating factor for factorial designs is
    that we need to make this decision (independent
    vs. correlated groups) for each IV we include in
    an experiment.

Practical Considerations
  • You are well advised to keep your experiment at
    the bare minimum necessary to answer the
    question(s) that most interest(s) you.
  • Bear in mind that you are complicating matters
    when you add IVs and levels.
  • Remember the principle of parsimony mentioned in
    Chapter 10 and the KISS principle (Keep It Simple

Variations on Factorial Designs
  • Comparing Different Amounts of an IV
  • When you add a level to an IV in a factorial
    design, you add several groups to your
    experiment because each new level must be added
    under each level of your other independent

Comparing Different Amounts of an IV
  • When you add a level to an IV in a factorial
    design, you add several groups to your
    experiment because each new level must be added
    under each level of your other independent
  • For example, expanding a 2 X 2 to a 3 X 2 design
    requires 6 groups rather than 4.
  • Adding levels in a factorial design increases
    groups in a multiplicative fashion.

Using Measured IVs
  • Ex post facto research
  • A research approach in which the experimenter
    cannot directly manipulate the IV but can only
    classify, categorize, or measure the IV because
    it is predetermined in the participants (e.g., IV

Using Measured IVs
  • Using a measured rather than a manipulated IV
    results in ex post facto research.
  • Without the control that comes from directly
    causing an IV to vary, we must exercise extreme
    caution in drawing conclusions from such studies.
  • We can develop an experiment that uses one
    manipulated IV and one measured IV at the same

Dealing with More than Two IVs
  • Designing an experiment with more than two IVs
    is probably the most important variation of the
    factorial design.
  • The simplest possible factorial design with three
    IVs (often referred to as a three-way design)
    has three IVs, each with two levels.
  • This design represents a 2 X 2 X 2 experiment.
  • This design would require eight different groups
    if it is planned as a completely between-groups