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
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
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