FACTORIAL DESIGNS What is a Factorial Design?Why are Factorials Useful?What is a Main Effect?What is an Interaction?Examples of Factorial Designs.

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Presentation transcript:

FACTORIAL DESIGNS What is a Factorial Design?Why are Factorials Useful?What is a Main Effect?What is an Interaction?Examples of Factorial Designs

What is a Factorial Design? A design containing two or more independent variables (factors), with all combinations of levels of factors measured.

Levels and Conditions A level is a value of a factor. Each factor has two or more levels. A condition is a combination of levels of different factors.

Factor A Factor B Level 1Level 2 Level 1 Level 2 Level 3 condition

Types of Factorial Designs between subjects within subjects mixed

Between Subjects B 1 2 A 12 Subjects 1-10 Subjects Subjects Subjects 21-30

Within Subjects B 1 2 A 12 Subjects 1-40 Subjects 1-40 Subjects 1-40 Subjects 1-40

Mixed (A Between, B Within) B 1 2 A 12 Subjects 1-20 Subjects 1-20 Subjects Subjects 21-40

Notation for Factorials The number of numbers tells you how many IV’s. The numbers tell you how many levels. A factorial with two IV’s that each have two levels is a 2 x 2 factorial.

Notation for Factorials 2x22x33x4 How many i.v.’s? How many d.v.’s? How many conditions?

Why Are Factorials Useful? Reduce amount of non-systematic variance Ability to measure interaction – Many behaviors are affected by interactions – Main effects can be misleading without considering the interaction

Drug Therapy

What is a Main Effect? The overall effect of one IV, averaging over the levels of the other IV. If the means of the levels (marginal means) are different, there is a main effect. On a graph of means, marginal means can be estimated visually.

A B

A B

What is an Interaction? The effect of one IV changes depending on the level of the other IV. If the simple effects are different, there is an interaction.

What is an Interaction? A simple effect is the difference in means between levels of an IV for just one level of another IV. On a graph, non-parallel lines indicate an interaction.

A B

A B

A B

Drug Therapy