STAT 3130 Statistical Methods I. Session 4 Two Way Analysis of Variance (ANOVA). Two Way ANOVA. From previous notes, we understand the following about ANOVA:
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Two Way Analysis of Variance (ANOVA)
From previous notes, we understand the following about 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 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:
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:
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.
In a Two Way ANOVA we are working to ascertain the following:
There are three 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
Lets look at these outcomes using SAS…