Transcript Lecture 13 -- two way ANOVA [PPT]

Two-Way Between
Groups ANOVA
Chapter 14
Two-Way ANOVAs
• Are used to evaluate effects of more than one
IV on a DV
• Can determine individual and combined
effects of the IVs
The basic 2 WayANOVA
situation
2 or more Nominal Independent Variable with two or
more levels
1 Scale Dependent Variable
Effects of Drug and Age on recovery time
Effects of Exercise and Diet on number of friends
Effects of Toy Color and Gender on toy popularity
One Way ANOVA is Limited
Hours of Working Out as an Effect of
Relationship Status
Sex Differences in Workout
Hours/Week
Avg Weekly Hours Workout
7
9
8
6
7
5
6
5
4
4
3
Total
Total
3
2
2
1
1
0
Committed Relationship
0
Female
Exclusive Dating
Single
Male
Sex
• Previous data, hour of exercise by relationship status. If I want to
look at sex differences for hours of exercise, I have to do a second
one-way ANOVA, and it will not tell me if there is a connection
between sex and relationship status on hours of exercise.
Testing for Interactions
• An interaction occurs when two IVs have
an effect in combination that we do not see
when looking at each IV individually
• Two-Way ANOVAs include to nominal IVs
and a scale DV
• Factorial ANOVA uses one scale DV and at
least two nominal IVs (factors)
– Factor: IV in a study with more than one IV
Why Use Two-Way ANOVAs
• To evaluate effects of two IVs, it is more
efficient to do a single study than two studies
with one IV each.
• Can explore interactions between variables
More ANOVA Vocabulary
• Cell: box depicting a unique combination of
levels of IVs in a factorial design
• Main effect: When one IV influences the DV
Two Types of Interactions in
ANOVA
• Quantitative: interaction in which one IV
exhibits strengthening or weakening of its
effects at one or more levels of the other IV,
but the direction of the effect does not
change
• Qualitative: interaction of two or more IVs
in which one IV reverses its effect
depending on the level of the other IV
What if both IVs influence the
DV?
• This is an interaction
Understanding Graphs
• Main Effects:
distance between
lines
• Quantitative
Understanding Graphs
• Interactions:
slopes of lines
• Qualitative
Six Steps for Two-Way BetweenGroups ANOVA
• Step 1. Identify the populations, distribution, and
assumptions.
• Step 2. State the null and research hypotheses.
• Step 3. Determine the characteristics of the
comparison distribution.
• Step 4. Determine critical values, or cutoffs.
• Step 5. Calculate the test statistic.
• Step 6. Make a decision.
df Formulae for ANOVAs
df rows  N rows  1
df columns  N columns  1
df interaction  (df rows )( df columns )
df within  dfY ,1  dfY ,3  df O ,1  df O ,3
df total  Ntotal  1
Determining the Cutoff Point
Effect Size for Two-Way
ANOVA
2
Rrows

SS rows
( SStotal  SS columns  SSinteraction )
2
columns
R
SS columns

( SStotal  SS rows  SSinteraction )
2
interaction
R
SSinteraction

( SStotal  SS rows  SS columns )
Variations on ANOVA