# Chapter 14: Two-Way Analysis of Variance

 Date 16.07.2018 Size 205 Kb.

### Chapter 14: Two-Way Analysis of Variance

Statistics is the art of never having to say you're wrong

and never having to say you're certain. ~~ author unknown

## Learning Objectives

### Upon completion of this chapter, students should know

• When to use a two-way analysis of variance test.

• How variation (variance estimates) is partitioned between and within groups when there is more than one independent variable.

• How to compute and interpret main effects and interactions.

• How to graph interactions.

• How to compute and interpret standard scores.

Key Terms
Factorial experiment is an experiment that has two or more independent variables. This design also examines the effects of the combination of the two independent variables on the dependent variable.
A main effect is the effect of one independent variable on the dependent variable.
An interaction is the effect of the combination of the two independent variables on the dependent variable. The cell means of the interaction are graphed to illustrate the interaction.

#### Lecture and Demonstration Aids

The two-way analysis of variance adds an additional variable to the analyses and the interaction of the two variables. Students tend to do fine with the long computations of the two-way is tedious although computational errors occur. Practice, practice, and more practice helps. Graphing the cell means and interpreting interaction from the graph, seems to be very helpful.

Hair Color & Cosmetic Use. Use the dataset shown on Handout 14-A to introduce students to the two-way analysis of variance. This is a partial dataset from Kyle and Mahler’s (1986) study examining hair color and perception of ability. Participants were randomly assigned to review a job resume with a photograph of a woman depicted with either brown or blond hair and with or without cosmetics. Participants evaluated the capability of the applicant relative to an accounting position on a scale of 1 to 7 (1 = not capable and 7 = very capable). (Note: There were other conditions in the other study, but for simplification purposes, these were not included.) The solution is shown on Transparency 14-3. Note: As in the original study, there were no significant interactions between hair color and cosmetic condition on perception of ability.

#### Active-Learning Activities

Datasets. Have students either individually or in groups, analyze one of the datasets available
in the Instructor’s area of the text website. This give student the extra experience of new data in a
somewhat different format. The Internet and Cyber Sex study has a number of variables and should
be interesting to students.
References:

Kyle, D. J., & Mahler, H. I. M.  (1996).  The effects of hair color and cosmetic use on perception of a female's abilityPsychology of Women Quarterly, 20, 447-458.

Handout 14-A.
Hair Color and Cosmetic Data
IV: Hair Color: Brunette, Blonde

IV: Cosmetics: With, Without

DV: Perceived Capability

 Brunette With Cosmetics 5.4 Brunette With Cosmetics 5.8 Brunette With Cosmetics 3.5 Brunette With Cosmetics 1.7 Brunette With Cosmetics 2.6 Brunette With Cosmetics 4.1 Brunette Without Cosmetics 6 Brunette Without Cosmetics 6.2 Brunette Without Cosmetics 7 Brunette Without Cosmetics 6.5 Brunette Without Cosmetics 5.9 Brunette Without Cosmetics 6.4 Blonde With Cosmetics 3.5 Blonde With Cosmetics 1.8 Blonde With Cosmetics 3.7 Blonde With Cosmetics 3.8 Blonde With Cosmetics 2.1 Blonde With Cosmetics 3 Blonde Without Cosmetics 3 Blonde Without Cosmetics 5.2 Blonde Without Cosmetics 4.3 Blonde Without Cosmetics 3.8 Blonde Without Cosmetics 4.2 Blonde Without Cosmetics 6.1

Transparency 14-1. Interactions

Transparency 14-3.
##### Results of Hair Color & Cosmetic Study

Source Table

Source

Sums of Squares

df

Mean Square

F

p

Rows(Hair Color)

Col (Cosmetics)

###### Interaction

Within

11.482

23.207

1.602

22.890

1

1

1

20

11.482

23.207

1.399

1.144

10.032

20.277

.251

< .05

<.05

>.05

Total

59.180

23

 Condition Means Standard Deviation Brunette With Cosmetics 3.85 1.566 Brunette Without Cosmetics 6.333 .398 Blond With Cosmetics 2.983 .852 Blond Without Cosmetics 4.433 1.086