Transcript Two Way ANOVA

INCM 9102
Quantitative Methods
TWO WAY ANOVA
Two Way ANOVA
From previous notes, we understand the following about ANOVA:
 It allows us to determine if significant differences of a quantitative
variable exist across 3 or more levels of a qualitative variable.
 What the hypothesis statements look like.
 The assumptions which need to be met.
 How to read the ANOVA table.
 The test statistic and the F-distribution.
 How to make a decision with the results.
 If the results allow us to reject the null, we know to run a post hoc test
and how to find the differences.
Two Way ANOVA
But the notes on ANOVA so far, only allow us to evaluate a single
qualitative variable (with 3+ levels) with a quantitative variable.
What if we have a two qualitative variables and a single quantitative
variable?
For example, what if we wanted to examine how music affects the
productivity of our employees? Specifically, we want to examine the
type of music (rock, country, jazz) as well as the loudness of the music
(soft or loud).
To do this, we would need to run a two way ANOVA.
Two Way ANOVA
Two Way ANOVA will provide us with not only the main effects (the
results of each qualitative variable individually) but it will also provide
us with the interaction effects BETWEEN the qualitative variables.
Interaction effects are commonly present, so you need to look for them.
Here are some examples:
 Diet Plan A resulted in a greater weight loss for women than for men,
but Diet Plan B resulted in a greater weight loss for men than for women.
 Fertilizer A was best in high sunlight areas but Fertilizer B was best in
low light areas.
Two Way ANOVA
As we saw with the One Way ANOVA, we have some important
assumptions which need to be checked prior to executing a Two Way
ANOVA:
1. The samples must have been randomly drawn and must be
independent of each other.
2. The variances of the samples must be approximately equal.
3. The groups should all have approximately the same sample size.
Two Way ANOVA
In a Two Way ANOVA, we actually test three sets of hypothesis
statements simultaneously:
H1a: The population means of the first factor are not equal.
H1b: The population means of the second factor are not equal.
H1c: There is an interaction effect between the first and second factors.
Two Way ANOVA
In a Two Way ANOVA we are working to ascertain the following:
1. What is the variability in the data attributable to Factor A?
2. What is the variability in the data attributable to Factor B?
3. What is the variability in the data attributable to the interaction
between Factors A and B?
4. What is the variability in the data which is random and cannot be
attributed to A, B or A and B?
Two Way ANOVA
There are four possible outcomes from your analysis…
1. Significant main effects but no significant interaction
2. One significant main effect, one nonsignificant main effect, and
significant interaction
3. Significant main effects and significant interaction
4. No effects present.
Lets look at these outcomes using SPSS…