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S13.4 - Two-Way Analysis of Variance
Two-Way Analysis of Variance
12
Mathematics
Graduate
11/21/2013

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Term
2 x 2 factorial design
Definition
Manipulating two factors and fixing them at two or more levels and then randomly assigning experimental units to a treatment
Term
Cell
Definition
Each of the n observations of the response variable for the different levels of the factors
Term
Crossed
Definition
In a factorial design, when all levels of factor A are combined with all levels of factor B
Term
Main effects
Definition
The two effects of A and B together
Term
Interaction effect
Definition
If changes in the level of factor A result in different changes in the value of the response variable for the different levels of factor B
Term
3 requirements for the two-way analysis of variance
Definition
1. The populations from which the samples are drawn must be normal
2. The samples are independent
3. The populations all have the same variance
Term
In a two-way ANOVA, there are 3 hypotheses
Definition
1 regarding the interaction effect
2. 2 regarding main effects
Term
1. In a two-way ANOVA, there are 3 hypotheses
Definition
H0: There is no interaction between the factors
H1: There is interaction between the factors
Term
2. In a two-way ANOVA, there are 3 hypotheses
Definition
H0: There is no effect of factor A on the response variable
H1: There is an effect of factor A on the response variable
Term
3. In a two-way ANOVA, there are 3 hypotheses
Definition
H0: There is no effect of factor B on the response variable
H1: There is an effect of factor B on the response variable
Term
If the null of no interaction is rejected, then
Definition
We do not interpret the results of the hypotheses involving the main effects
Term
Interaction plots
Definition
Graphically representing the role interaction plans in any factorial design
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