Transcript mixed assignment.

Chapter Eleven.
Designing, Conducting,
Analyzing, and Interpreting
Experiments with Multiple
Independent Variables
Experimental Design: Doubling
the Basic Building Block

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 Block

Factors
Experimental Design: Doubling
the Basic Building Block

Factors

Synonymous with IVs
Experimental Design: Doubling
the Basic Building Block

Factors


Synonymous with IVs
Independent variables (IVs)
Experimental Design: Doubling
the Basic Building Block

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 Block

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 world.
Experimental Design: Doubling
the Basic Building Block

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 world.

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.
How Many IV’s?

The factorial design gets its name because we refer to each IV
as a factor.
How Many IV’s?

The factorial design gets its name because we refer to each IV
as a factor.

Multiple IV’s yield a factorial design.
How Many IV’s?

The factorial design gets its name because we refer to each IV
as a factor.


Multiple IV’s yield a factorial design.
Theoretically, there is no limit to the number of IV’s that can be
used in an experiment.
How Many IV’s?

The factorial design gets its name because we refer to each IV
as a factor.


Multiple IV’s yield a factorial design.
Theoretically, there is no limit to the number of IV’s 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 IV’s.
How many Groups or Levels?

Once you have two or more IV’s, you will use a factorial design.
How many Groups or Levels?


Once you have two or more IV’s, you will use a factorial design.
The number of levels of each factor is unimportant at this point.
How many Groups or Levels?

the simplest possible factorial design is known as a 2 X 2
design.

This 2 X 2 shorthand notation tells us that we are dealing with a
design that has two factors (IV’s) 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 Groups or Levels?

The number of numbers tells us how many IV’s
there are.
How many Groups or Levels?


The number of numbers tells us how many IV’s there are.
The value of each number tells us how many levels each IV
has.
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.
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.
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
(A sub 1) and A2 (A sub 2).
How many Groups or Levels?

Main effect
How many Groups or Levels?

Main effect

A main effect refers to the sole effect of one IV in a factorial
design.
Assigning Participants to Groups

We have two options for this assignment – independent
groups or correlated groups.
Assigning Participants to Groups


We have two options for this assignment – independent
groups or correlated groups.
However, this question is not answered in such a simple manner
as in the two-group and multiple-group designs, each of which
had only one IV.
Assigning Participants to Groups

However, this question is not answered in such a simple manner
as in the two-group and multiple-group designs, each of which
had only one IV.

All IV’s 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
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.
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).
Random Assignment to Groups

Factorial designs in which both IV’s involve random assignment
may be called between-subjects factorial designs or completely
randomized designs Random Assignment to Groups
Nonrandom Assignment to
Groups

In this section, we deal with factorial designs in which
participant groups for all IV’s have been formed through
nonrandom assignment.
Nonrandom Assignment to
Groups


In this section, we deal with factorial designs in which
participant groups for all IV’s have been formed through
nonrandom assignment.
We refer to such designs as completely within-groups (or within-
subjects) designs.
Nonrandom Assignment to
Groups


In this section, we deal with factorial designs in which
participant groups for all IV’s 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.
Nonrandom Assignment to
Groups

Matched Pairs or Sets.

Matching can take place in either pairs or sets because factorial
designs can use IV’s with two or more levels.
Nonrandom Assignment to
Groups

Matched Pairs or Sets.


Matching can take place in either pairs or sets because factorial
designs can use IV’s with two or more levels.
The more levels an IV has, the more work matching for that
variable takes.
Nonrandom Assignment to
Groups

Matched Pairs or Sets.



Matching can take place in either pairs or sets because factorial
designs can use IV’s 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.
Nonrandom Assignment to
Groups

Repeated Measures.

In a completely within-groups experiment using repeated
measures, participants would take part fully and completely.
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.
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 IV’s.
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 IV’s.
 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.
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.
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.
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.
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.
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.
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.
Mixed designs combine the advantages of the two types of designs.
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.
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.
Comparing the Factorial Design to
Two-Group and Multiple-Group
Designs

In a similar fashion, 2 X 2 factorial designs may be used for
preliminary investigations of two IV’s.
Comparing the Factorial Design to
Two-Group and Multiple-Group
Designs

The multiple-group design may be used to conduct more indepth investigations of an IV that interests us (chapter 10).
Comparing the Factorial Design to
Two-Group and Multiple-Group
Designs


The multiple-group design may be used to conduct more indepth investigations of an IV that interests us.
We took the basic two-group design (chapter 9) and extended it
to include more levels of our IV (chapter 10).
Comparing the Factorial Design to
Two-Group and Multiple-Group
Designs



The multiple-group design may be used to conduct more indepth 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.
Comparing the Factorial Design to
Two-Group and Multiple-Group
Designs




The multiple-group design may be used to conduct more indepth 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.
Comparing the Factorial Design to
Two-Group and Multiple-Group
Designs




The multiple-group design may be used to conduct more indepth 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 IV’s can be equal or unequal.
Comparing the Factorial Design to
Two-Group and Multiple-Group
Designs






The multiple-group design may be used to conduct more indepth 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.
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.
Choosing a Factorial Design

Experimental Questions
Experimental Questions

Factorial designs provide considerable flexibility in devising an
experiment to answer your questions.
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….
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 other…experimental questions
should not clash.
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 other…experimental 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.
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.
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 IV’s
and levels.
Variations on Factorial Designs

Comparing Different Amounts of an IV.
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 variable(s).
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
variable(s).

For example, expanding a 2 X 2 to a 3 X 2 design requires 6 groups
rather than 4.
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
variable(s).


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 IV’s

Using a measured rather than a manipulated IV results in ex
post facto research.
Using Measured IV’s
 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 = sex).
Using Measured IV’s


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.
Using Measured IV’s



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 time.
Dealing with More than Two
IV’s

Designing an experiment with more than two IV’s is probably
the most important variation of the factorial design.
Dealing with More than Two
IV’s

The simplest possible factorial design with three IV’s (often
referred to as a three-way design) has three IV’s, each with
two levels.
Dealing with More than Two IV’s

The simplest possible factorial design with three IV’s (often
referred to as a three-way design) has three IV’s, each with
two levels.

This design represents a 2 X 2 X 2 experiment.
Dealing with More than Two IV’s

The simplest possible factorial design with three IV’s (often
referred to as a three-way design) has three IV’s, 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 design.
Statistical Analysis: What Do
Your Data Show?

Naming Factorial Designs

Labels you may hear that reflect the size of the design include:
Statistical Analysis: What Do
Your Data Show?

Naming Factorial Designs

Labels you may hear that reflect the size of the design include:
 Factorial ANOVA
Statistical Analysis: What Do
Your Data Show?

Naming Factorial Designs

Labels you may hear that reflect the size of the design include:
 Factorial ANOVA
 Two-way ANOVA
Statistical Analysis: What Do
Your Data Show?

Naming Factorial Designs

Labels you may hear that reflect the size of the design include:
 Factorial ANOVA
 Two-way ANOVA
 Three-way ANOVA
Statistical Analysis: What Do
Your Data Show?

Naming Factorial Designs

Labels you may hear that reflect the size of the design include:
 Factorial ANOVA
 Two-way ANOVA
 Three-way ANOVA
 X by Y
Naming Factorial Designs

For designs that use random assignment for all IV’s, labels that
describe how participants are assigned to groups might include:
Naming Factorial Designs
 For designs that use random assignment for all IV’s, labels that
describe how participants are assigned to groups might include:
 Independent groups
Naming Factorial Designs
 For designs that use random assignment for all IV’s, labels that
describe how participants are assigned to groups might include:


Independent groups
Completely randomized
Naming Factorial Designs
 For designs that use random assignment for all IV’s, labels that
describe how participants are assigned to groups might include:
 Independent groups
 Completely randomized
 Completely between-subjects
Naming Factorial Designs
 For designs that use random assignment for all IV’s, labels that
describe how participants are assigned to groups might include:




Independent groups
Completely randomized
Completely between-subjects
Completely between-groups
Naming Factorial Designs
 For designs that use random assignment for all IV’s, labels that
describe how participants are assigned to groups might include:





Independent groups
Completely randomized
Completely between-subjects
Completely between-groups
Totally between-subjects
Naming Factorial Designs
 For designs that use random assignment for all IV’s, labels that
describe how participants are assigned to groups might include:






Independent groups
Completely randomized
Completely between-subjects
Completely between-groups
Totally between-subjects
Totally between-groups
Naming Factorial Designs
 Designs that use matching or repeated measures may be called:
Naming Factorial Designs
 Designs that use matching or repeated measures may be called:
 Randomized block
Naming Factorial Designs
 Designs that use matching or repeated measures may be called:
 Randomized block
 Completely within-subjects
Naming Factorial Designs
 Designs that use matching or repeated measures may be called:
 Randomized block
 Completely within-subjects
 Completely within-groups
Naming Factorial Designs
 Designs that use matching or repeated measures may be called:




Randomized block
Completely within-subjects
Completely within-groups
Totally within-subjects
Naming Factorial Designs
 Designs that use matching or repeated measures may be called:





Randomized block
Completely within-subjects
Completely within-groups
Totally within-subjects
Totally within-groups
Naming Factorial Designs
 Designs that use a mixture of “between” and “within”
assignment procedures may be referred to as:
Naming Factorial Designs
 Designs that use a mixture of “between” and “within”
assignment procedures may be referred to as:
 Mixed factorial
Naming Factorial Designs
 Designs that use a mixture of “between” and “within”
assignment procedures may be referred to as:
 Mixed factorial
 Split-plot factorial
Planning the Statistical Analysis

Suppose you are examining the data from the previous (chapter
10) experiment and you think you detected an oddity in the
data:
Planning the Statistical Analysis

Suppose you are examining the data from the previous (chapter
10) experiment and you think you detected an oddity in the
data:

It appears that salesclerks may have responded differently to
female and male customers in addition to the different styles of
dress.
Planning the Statistical Analysis

You decide to investigate this question in order to find out
whether both customer sex and dress affect salesclerks’
response times to customers.
Planning the Statistical Analysis

You decide to investigate this question in order to find out
whether both customer sex and dress affect salesclerks’
response times to customers.

Because there was no difference between responses to customers
in dressy and casual clothing (see chapter 10), you decide to use
only casual and sloppy clothes.
Planning the Statistical Analysis

Thus, you have designed a 2 X 2 experiment in which the two
IV’s are clothing style (casual and sloppy) and customer sex
(male and female).
Rationale for ANOVA

The rationale behind ANOVA for factorial designs is basically the
same as we saw in Chapter 10, with one major modification.
Rationale for ANOVA

The rationale behind ANOVA for factorial designs is basically the
same as we saw in Chapter 10, with one major modification.

We still use ANOVA to partition (divide) the variability into two
sources – treatment variability and error variability.
Rationale for ANOVA

With factorial designs, the sources of treatment variability
increase.
Rationale for ANOVA


With factorial designs, the sources of treatment variability
increase.
Instead of having one IV as the sole source of treatment
variability, factorial designs have multiple IV’s and their
interactions as sources of treatment variability.
Rationale for ANOVA


With factorial designs, the sources of treatment variability
increase.
Instead of having one IV as the sole source of treatment
variability, factorial designs have multiple IV’s and their
interactions as sources of treatment variability.
Rationale for ANOVA

The actual distribution of the variance among the factors would
depend, of course, on which effects were significant.
Rationale for ANOVA

For a two-IV factorial design we use the following equations:
Rationale for ANOVA

For a two-IV factorial design we use the following equations:

Factor A = IV A variability
error variability
Rationale for ANOVA

For a two-IV factorial design we use the following equations:

Factor B = IV B variability
error variability
Rationale for ANOVA

For a two-IV factorial design we use the following equations:

Factor A by B = interaction variability
error variability
Understanding Interactions

When two variables interact, their joint effect may not be
obvious or predictable from examining their separate effects.
Understanding Interactions

When two variables interact, their joint effect may not be
obvious or predictable from examining their separate effects.

For example, drinking a glass or two of wine may be a pleasurable
and relaxing experience and driving may be a pleasurable and
relaxing experience but is drinking wine and driving an extremely
pleasurable and relaxing experience?
Understanding Interactions

When two variables interact, their joint effect may not be
obvious or predictable from examining their separate effects.

For example, drinking a glass or two of wine may be a pleasurable
and relaxing experience and driving may be a pleasurable and
relaxing experience but is drinking wine and driving an extremely
pleasurable and relaxing experience?
 Of course not.
Understanding Interactions


When two variables interact, their joint effect may not be
obvious or predictable from examining their separate effects.
Combinations of drugs, in particular, are likely to have
synergistic effects so that a joint effect occurs that is not
predictable from either drug alone.
Understanding Interactions

Synergistic effects
Understanding Interactions

Synergistic effects

Dramatic consequences that occur when you combine two or more
substances, conditions, or organisms.
Understanding Interactions

Synergistic effects


Dramatic consequences that occur when you combine two or more
substances, conditions, or organisms.
The effects are greater than what is individually possible.
Understanding Interactions

A significant interaction means that the effects of the various
IV’s are not straightforward and simple.
Understanding Interactions


A significant interaction means that the effects of the various
IV’s are not straightforward and simple.
For this reason, we virtually ignore our IV main effects when we
find a significant interaction.
Understanding Interactions



A significant interaction means that the effects of the various
IV’s are not straightforward and simple.
For this reason, we virtually ignore our IV main effects when we
find a significant interaction.
Sometimes interactions are difficult to interpret, particularly
when we have more than two IV’s or many levels of an IV.
Understanding Interactions

A strategy that often helps us to make sense of an interaction is
to graph it.
Understanding Interactions


A strategy that often helps us to make sense of an interaction is
to graph it.
By graphing your DV on the y axis and one IV on the x axis,
you can depict your other IV with lines on the graph (see
Chapter 8).
Understanding Interactions



A strategy that often helps us to make sense of an interaction is
to graph it.
By graphing your DV on the y axis and one IV on the x axis,
you can depict your other IV with lines on the graph (see
Chapter 8).
By studying such as graph, you can usually deduce what
happened to cause a significant interaction.
Understanding Interactions

When you graph a significant interaction, you will often notice
that the lines of the graph cross or converge.
Understanding Interactions


When you graph a significant interaction, you will often notice
that the lines of the graph cross or converge.
This pattern is a visual indication that the effects of one IV
change as the second IV is varied.
Understanding Interactions



When you graph a significant interaction, you will often notice
that the lines of the graph cross or converge.
This pattern is a visual indication that the effects of one IV
change as the second IV is varied.
Nonsignificant interactions typically show lines that are close to
parallel.
Interpretation: Making Sense
of Your Statistics

Our statistical analyses of factorial designs will provide us more
information than we got from two-group or multiple-group
designs.
Interpretation: Making Sense
of Your Statistics


Our statistical analyses of factorial designs will provide us more
information than we got from two-group or multiple-group
designs.
The analyses are not necessarily more complicated than those
we saw in Chapters 9 and 10, but they do provide more
information because we have multiple IV’s and interaction
effects to analyze.
Interpreting Computer
Statistical Output

We will deal with 2 X 2 analyses in these three different
categories to fit our clothing-by-customer-sex experiment:
Interpreting Computer
Statistical Output

We will deal with 2 X 2 analyses in these three different
categories to fit our clothing-by-customer-sex experiment:

Two-way ANOVA for independent samples
Interpreting Computer
Statistical Output

We will deal with 2 X 2 analyses in these three different
categories to fit our clothing-by-customer-sex experiment:


Two-way ANOVA for independent samples
Two-way ANOVA for correlated samples
Interpreting Computer
Statistical Output

We will deal with 2 X 2 analyses in these three different
categories to fit our clothing-by-customer-sex experiment:



Two-way ANOVA for independent samples
Two-way ANOVA for correlated samples
Two-way ANOVA for mixed samples
Two-Way ANOVA for
Independent Samples

The two-way ANOVA for independent samples requires that we
have two IV’s (clothing style and customer sex) with
independent groups.
Two-Way ANOVA for
Independent Samples


The two-way ANOVA for independent samples requires that we
have two IV’s (clothing style and customer sex) with
independent groups.
To create this design we would use four different randomly
assigned groups of salesclerks.
Two-Way ANOVA for
Independent Samples



The two-way ANOVA for independent samples requires that we
have two IV’s (clothing style and customer sex) with
independent groups.
To create this design we would use four different randomly
assigned groups of salesclerks.
The DV scores represent clerks’ response times in waiting on
customers.
Two-Way ANOVA for
Independent Samples

Source Table
Two-Way ANOVA for
Independent Samples

Source Table

In the body of the source table, we want to examine only the
effects of the two IV’s (clothing and customer sex) and their
interaction.
Two-Way ANOVA for
Independent Samples

Source Table


In the body of the source table, we want to examine only the
effects of the two IV’s (clothing and customer sex) and their
interaction.
The remaining source (w. cell or Within) is the error term and is
used to test the IV effects.
Two-Way ANOVA for
Independent Samples

Source Table


In the body of the source table, we want to examine only the
effects of the two IV’s (clothing and customer sex) and their
interaction.
The remaining source (w. cell or Within) is the error term and is
used to test the IV effects.
 Different statistical programs will use a variety of different
names for the error term.
Two-Way ANOVA for
Independent Samples

Source Table

The effect of sex shows an F ratio of 3.70, with a probability of .07.
 This IV shows marginal significance.
Two-Way ANOVA for
Independent Samples

Marginal significance

Marginal significance refers to statistical results with a probability of
chance between 5% and 10% (almost significant but not quite).
Two-Way ANOVA for
Independent Samples

Marginal significance


Marginal significance refers to statistical results with a probability of
chance between 5% and 10% (almost significant but not quite).
Researchers often talk about such results as if they reached the p
= .05 level.
Two-Way ANOVA for
Independent Samples

Marginal significance



Marginal significance refers to statistical results with a probability of
chance between 5% and 10% (almost significant but not quite).
Researchers often talk about such results as if they reached the p
= .05 level.
Dealing with marginally significant results means you run an
increased risk of making a Type I error (accepting the experimental
hypothesis when the null hypothesis is true).
Two-Way ANOVA for
Independent Samples

Source Table

The effect of sex shows an F ratio of 3.70, with a probability of .07.


This IV shows marginal significance.
The probability of “clothes” falls below .01 in the table.
Two-Way ANOVA for
Independent Samples

Source Table



The effect of sex shows an F ratio of 3.70, with a probability of .07.
 This IV shows marginal significance.
The probability of “clothes” falls below .01 in the table.
The interaction between clothing and customer sex produced an F
ratio of 6.65 and has p = .02, therefore denoting significance.
Two-Way ANOVA for
Independent Samples

Source Table

A significant interaction renders the main effects moot because
those main effects are qualified by the interaction and are not
straightforward.
Two-Way ANOVA for
Independent Samples

Source Table


A significant interaction renders the main effects moot because
those main effects are qualified by the interaction and are not
straightforward.
The first step in interpreting an interaction is to draw a graph of
the results from the descriptive statistics (from source table).
Two-Way ANOVA for
Independent Samples

Source Table


A significant interaction renders the main effects moot because
those main effects are qualified by the interaction and are not
straightforward.
The first step in interpreting an interaction is to draw a graph of
the results from the descriptive statistics (from source table).
Two-Way ANOVA for
Independent Samples

Crossing lines, in conjunction with the low probability of chance
for the interaction term, denote a significant interaction.
Two-Way ANOVA for
Independent Samples

Crossing lines, in conjunction with the low probability of chance
for the interaction term, denote a significant interaction.

When we examine the figure, the point that seems to differ most
represents the clerks’ response times to male customers in sloppy
clothes.
Two-Way ANOVA for
Independent Samples

Crossing lines, in conjunction with the low probability of chance
for the interaction term, denote a significant interaction.

When we examine the figure, the point that seems to differ most
represents the clerks’ response times to male customers in sloppy
clothes.
 This mean is considerably higher than the others.
Two-Way ANOVA for
Independent Samples

Thus, we would conclude that clerks take longer to wait on men
who are sloppily dressed than other customers.
Two-Way ANOVA for
Independent Samples


Thus, we would conclude that clerks take longer to wait on men
who are sloppily dressed than other customers.
Notice that our explanation of an interaction effect must
include a reference to both IV’s in order to make sense.
Two-Way ANOVA for
Independent Samples

If you attempt to interpret the main effects in a straightforward
fashion when you have a significant interaction, you end up
trying to make a gray situation into a black-and-white picture.
Two-Way ANOVA for
Independent Samples


If
you attempt to interpret the main effects in a straightforward
fashion when you have a significant interaction, you end up
trying to make a gray situation into a black-and-white picture.
In other words, you will be guilty of oversimplifying the results.
Two-Way ANOVA for
Independent Samples

Here is one way you could present the results from this
experiment:
Two-Way ANOVA for
Independent Samples

Here is one way you could present the results from this
experiment:

The effect of the clothing on the clerks’ response times was
significant, F(1, 20) = 11.92, p = .003. The customer sex effect
was marginally significant, F(1, 20) = 3.70, p = .069. However,
the main effects were qualified by a significant interaction between
clothing and customer sex, F(1, 20) = 6.65, p = .018. The
proportion of the variance accounted for by the interaction was
0.25. The results of the interaction are graphed in Figure 1. Visual
inspection of the graph shows that clerks’ response times for the
sloppy clothes-male customer condition were higher than the other
conditions.
Two-Way ANOVA for
Correlated Samples

The two-way ANOVA for correlated samples requires that we
have two IV’s with correlated groups for both IV’s.
Two-Way ANOVA for
Correlated Samples


The two-way ANOVA for correlated samples requires that we
have two IV’s with correlated groups for both IV’s.
Most often these correlated groups would be formed by
matching or by using repeated measures.
Two-Way ANOVA for
Correlated Samples

In our example of the clothing-customer sex experiment,
repeated measures on both IV’s would be appropriate -
Two-Way ANOVA for
Correlated Samples

In our example of the clothing-customer sex experiment,
repeated measures on both IV’s would be appropriate –

We would merely get one sample of salesclerks and have them
wait on customers of both sexes wearing each style of clothing.
Two-Way ANOVA for
Correlated Samples

Computer results
Two-Way ANOVA for
Correlated Samples

Computer results

The clothing effect is significant at the .001 level and the sex effect
is significant at the .014 level.
Two-Way ANOVA for
Correlated Samples

Computer results


The clothing effect is significant at the .001 level and the sex effect
is significant at the .014 level.
However, both main effects are qualified by the significant clothingby-sex interaction (p = 0.0001).
Two-Way ANOVA for
Correlated Samples

Computer results


The clothing effect is significant at the .001 level and the sex effect
is significant at the .014 level.
However, both main effects are qualified by the significant clothingby-sex interaction (p = 0.0001).
 To make sense of the interaction, we must plot the means for
the combinations of clothing and customer sex.
Two-Way ANOVA for
Correlated Samples

Computer results

However, both main effects are qualified by the significant clothingby-sex interaction (p = 0.0001).

To make sense of the interaction, we must plot the means for the
combinations of clothing and customer sex.
Two-Way ANOVA for
Correlated Samples

One possible way of summarizing these results follows:
Two-Way ANOVA for
Correlated Samples

One possible way of summarizing these results follows:

Both the main effects of clothing and customer sex were
significant, F(1, 5) = 24.69, p = .001 and F(1, 5) = 7.66, p = .014,
respectively. However, the interaction of clothing and customer sex
was also significant, F(1, 5) = 13.77, p = .001. The proportion of
variance accounted for by the interaction was .78. This interaction
appears in Figure 1. Salesclerks waiting on sloppily attired male
customers were considerably slower than clerks with any other
combination of customer sex and clothing.
Two-Way ANOVA for
Correlated Samples

One possible way of summarizing these results follows:
Both the main effects of clothing and customer sex were
significant, F(1, 5) = 24.69, p = .001 and F(1, 5) = 7.66, p = .014,
respectively. However, the interaction of clothing and customer sex
was also significant, F(1, 5) = 13.77, p = .001. The proportion of
variance accounted for by the interaction was .78. This interaction
appears in Figure 1. Salesclerks waiting on sloppily attired male
customers were considerably slower than clerks with any other
combination of customer sex and clothing.
You would provide a fuller explanation and interpretation of this
interaction in the discussion section of your experimental report.


Two-Way ANOVA for Mixed
Samples

The two-way ANOVA for mixed samples requires that we have
two IV’s with independent groups for one IV and correlated
groups for the second IV.
Two-Way ANOVA for Mixed
Samples


The two-way ANOVA for mixed samples requires that we have
two IV’s with independent groups for one IV and correlated
groups for the second IV.
One possible way to create this design in our clothing-customer
sex experiment would be to use a different randomly assigned
group of salesclerks for each customer sex.
Two-Way ANOVA for Mixed
Samples


The two-way ANOVA for mixed samples requires that we have
two IV’s with independent groups for one IV and correlated
groups for the second IV.
One possible way to create this design in our clothing-customer
sex experiment would be to use a different randomly assigned
group of salesclerks for each customer sex.

Clerks waiting on each sex, however, would assist customers attired
in both types of clothing.
Two-Way ANOVA for Mixed
Samples

Computer Results

Once again, the descriptive statistics did not change from our first
and second analysis -
Two-Way ANOVA for Mixed
Samples

Computer Results

Once again, the descriptive statistics did not change from our first
and second analysis –
 We are still analyzing the same data.
Two-Way ANOVA for Mixed
Samples

Source Table


The source table appears at the bottom of Table 11-4 in your text.
As you can see from the headings, the between-subjects effects
(independent groups) and the within-subjects effects (repeated
measures) are divided in the source table.
Two-Way ANOVA for Mixed
Samples

Source Table



The source table appears at the bottom of Table 11-4 in your text.
As you can see from the headings, the between-subjects effects
(independent groups) and the within-subjects effects (repeated
measures) are divided in the source table.
This division is necessary because the between-subjects effects and
the within-subjects effects use different error terms.
Two-Way ANOVA for Mixed
Samples

Source Table


This division is necessary because the between-subjects effects and
the within-subjects effects use different error terms.
The interaction appears in the within-subjects portion of the table
because it involves repeated measures across one of the variables
involved.
Two-Way ANOVA for Mixed
Samples

Here’s one possibility for communicating the results of this study
in APA format:
Two-Way ANOVA for Mixed Samples

Here’s one possibility for communicating the results of this study
in APA format:

Results from the mixed factorial ANOVA showed no effect on the
customer sex, F(1, 10) = 2.42, p = .15. The clothing effect was
significant, F(1, 10) = 25.21, p = .001. This main effect, however,
was qualified by a significant customer-sex-by-clothing interaction,
F(1, 10) = 14.06, p = .004. The proportion of variance accounted
for by the significant interaction was .58. This interaction is shown
in Figure 1, indicating that salesclerks who waited on sloppily
dressed male customers were slower in responding than clerks who
waited on casually dressed men or women dressed in either
manner.
A Final Note

Assuming that a significant main effect is not qualified by an
interaction, you need to calculate a set of post hoc tests to
determine exactly where the significance of that IV occurred.
The Continuing Research
Problem

Pursuing a line of programmatic research is challenging,
invigorating, and interesting.
The Continuing Research
Problem


Pursuing a line of programmatic research is challenging,
invigorating, and interesting.
Programmatic research refers to a series of experiments that
deal with a related topic or question.
The Continuing Research
Problem



Pursuing a line of programmatic research is challenging,
invigorating, and interesting.
Programmatic research refers to a series of experiments that
deal with a related topic or question.
Remember that pursuing such a line of research is how most
famous psychologists have made names for themselves.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:

After our preliminary research in chapters 9 and 10, we decided to
use two IV’s (clothing and customer sex) in these experiments.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:


After our preliminary research in chapters 9 and 10, we decided to
use two IV’s (clothing and customer sex) in these experiments.
Each IV had two levels (clothing  casual, sloppy; customer sex 
men, women).
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:



After our preliminary research in chapters 9 and 10, we decided to
use two IV’s (clothing and customer sex) in these experiments.
Each IV had two levels (clothing  casual, sloppy; customer sex 
men, women).
This design allows us to determine the effects of the clothing, the
effects of the customer sex, and the interaction between clothing
and customer sex.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:

The DV was the time it took salesclerks to respond to customers.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:

With large numbers of clerks, we randomly formed four groups of
clerks, with each waiting on one sex of customer in one type of
clothing, resulting in a factorial between-groups design.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:


With large numbers of clerks, we randomly formed four groups of
clerks, with each waiting on one sex of customer in one type of
clothing, resulting in a factorial between-groups design.
We analyzed the response times using a factorial ANOVA for
independent groups and found that clerks were slower to wait on
male customers in sloppy clothing than all other customers.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:

In a hypothetical situation with fewer clerks for the experiment, we
used repeated measures on both IV’s; that is, each salesclerk
waited on both sexes of customers attired in both types of clothing,
so that each clerk waited on four different customers.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:


In a hypothetical situation with fewer clerks for the experiment, we
used repeated measures on both IV’s; that is, each salesclerk
waited on both sexes of customers attired in both types of clothing,
so that each clerk waited on four different customers.
Thus, this experiment used a factorial within-groups design.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:



In a hypothetical situation with fewer clerks for the experiment, we
used repeated measures on both IV’s; that is, each salesclerk
waited on both sexes of customers attired in both types of clothing,
so that each clerk waited on four different customers.
Thus, this experiment used a factorial within-groups design.
We analyzed the data with a factorial ANOVA for correlated groups
and found that clerks were slowest in waiting on sloppily dressed
men.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:

In a third hypothetical situation, we randomly assigned salesclerks
to the two customer sex groups but used repeated measures on
the clothing IV so that clerks waited either on men in both types of
clothing or women in both types of clothing.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:


In a third hypothetical situation, we randomly assigned salesclerks
to the two customer sex groups but used repeated measures on
the clothing IV so that clerks waited either on men in both types of
clothing or women in both types of clothing.
This arrangement resulted in a factorial mixed-groups design (one
IV using independent groups, one using correlated groups).
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:



In a third hypothetical situation, we randomly assigned salesclerks
to the two customer sex groups but used repeated measures on
the clothing IV so that clerks waited either on men in both types of
clothing or women in both types of clothing.
This arrangement resulted in a factorial mixed-groups design (one
IV using independent groups, one using correlated groups).
We analyzed the response times with a factorial ANOVA for mixed
groups and found the slowest response times to male customers in
sloppy clothes (see Table 11-4 and Figure 11-13).
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:

We concluded that clothing and customer sex interacted to affect
salesclerks’ response times.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:


We concluded that clothing and customer sex interacted to affect
salesclerks’ response times.
Women received help quickly regardless of their attire, but men
received help quickly only if they were not sloppily dressed.
The Continuing Research
Problem

Let’s review the steps we took in designing the experiments in
this chapter:



We concluded that clothing and customer sex interacted to affect
salesclerks’ response times.
Women received help quickly regardless of their attire, but men
received help quickly only if they were not sloppily dressed.
Men attired in sloppy clothes had to wait longer for help than the
other three groups.