ANOVA Designs

Questions

• What are factors and levels of each factor?
• What is a between-subjects or a within-subjects factor
• What is factorial design
• What kind of types of experimental designs can be analyzed by ANOVA?

Factors and Levels

• In the case study Smiles and Leniency, the effect of different types of smiles on the leniency showed to a person was investigated
• Type of smile (neutral, false, felt, miserable) is independent variable or factor
• "Type of Smile" has four levels

Single or Multi factor ANOVA

• An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA
• If an experiment has two factors, then the ANOVA is called a two-way ANOVA

Suppose an experiment on the effects of age and gender on reading speed were conducted using three age groups (10 yr, 15 yr, and 20 yr) and the two genders (males and females)

What are the factors and levels in this experiment?

Answer >>

The factors would be age and gender. Age would have three levels and gender would have two levels

Between- and Within-Subject Factors

Between-subjects

• In the Smiles and Leniency study, the four levels of the factor "Type of Smile" were represented by four separate groups of subjects
• When different subjects are used for the levels of the factor, the factor is called a between-subjects factor or a between-subjects variable
• The term "between subjects" reflects the fact that comparisons are between different groups of subjects.

Within-subjects

• In the ADHD Treatment Study, every subject was tested with each of four dosage levels (0, 0.15, 0.30, 0.60 mg/kg) of a drug
• Therefore there was only one group of subjects and comparisons were not between different groups of subjects but between conditions within the same subjects
• When the same subjects are used for the levels of the factor, the factor is called a within-subjects factor or within-subjects variable
• Within-subjects variables are sometimes referred to as repeated-measures variables since there are repeated measurements of the same subjects.

Multi-Factor Designs

• Consider a hypothetical study of the effects of age and gender on reading speed in which males and females from the age levels of 8 years, 10 years, and 12 years were tested.
• There would be a total of six different groups:

Group	Gender	Age
1	Female	8
2	Female	10
3	Female	12
4	Male	8
5	Male	10
6	Male	12

• This design has two factors: age and gender
  • age has three levels
  • gender has two levels

• When all combinations of the levels are included (as they are here) the design is called a factorial design
• A concise way of describing this design is as a Gender (2) x Age (3) factorial design where the numbers in parentheses indicate the number of levels
• Complex designs frequently have more than two factors and may have combinations of between- and within-subject factors.

Questions

1 A multifactor ANOVA is used to analyze designs only with 3 or more independent variables (factors).

	True
	False

Answer >>

False, a multifactor ANOVA is used for designs with 2 or more independent variables.

2 There is an A x B interaction if the effect of A is different at level 1 of B than it is at level 2 of B.

	True
	False

Answer >>

True, by definition, an interaction occurs when the effect of one independent variable differs as a function of the level of another independent variable.

3 There is an interaction if one variable affects the level of another variable.

	True
	False

Answer >>

Variables affect the dependent variable, not the levels of another independent variable.

4 A sports performance researcher was interested in determining the effect height (short, average, and tall) has on basketball performance during childhood and adolescence. Which is an example of a factor, level?

	a. short, average
	b. basketball performance, average
	c. height, short
	d. childhood, adolescence
	e. age, child

Answer >>

c and e. A factor is an independent variable such as height or age. Each independent variable (such as height) has a number of levels (such as short or tall). It is important to distinguish between an independent variable, which is the variable that is being deliberately manipulated by a researcher and a dependent variable (such as basketball performance) which is dependent upon an independent variable manipulation.