Analysis of Variance is used as a test of means for two or more populations
H0 is that all means are equal:
Мю1 = Мю2 = ... = Мюk
DV is metric (interval or ratio scaled)
IVs are called factors. Each combination of factors is called a treatment
One-Way or Simple ANOVA
has only one categorical IV. Hence, a treatment is the same as a factor level.
Examples in Marketing
Are customers equally satisfied with brand A, B, and C?
Do store 1, 2, and 3 differ in their performances?
Do segments differ in terms of the amount of their coffee consumption?
Do the evaluations of different ads vary?
2) Decompose the total variation
3) Measure the effects
1) Identify DV and IVs
4) Test the significance
5) Interpret the results
Example from lecture:
Do the store sales depend on the level of promotion in each store?
A department store chain wants to determine the effect of in- store promotion (IV) on sales (DV).
Results: (for high, medium and low in-store promotion)
Column mean: 8.3, 6.2, 3.7.
Grand mean: 6.067
Suppose you had to guess the sales level of an arbitrary store. What would be your best guess?
What if you would know that the store has a high level of in-store promotion?
A certain store is likely to differ from the group mean. In other words, there is a
for each specific store.
concerned with the effect of more than one factor simultaneously
How does satisfaction with brand A, B, and C vary with sex?
Do ad evaluations depend on brand familiarity (high, medium, and low)?
How does the effect of in-store promotion on sales depend on the size of the store (small, medium, large)?
Relationships among techniques
Categorical & Interval
One way ANOVA
More than one factor
Analysis of Covariance