# An Adventure in Statistics: The Reality Enigma

## Student Resources

# Chapter 17: Factorial designs

Quizzes are available to test your understanding of the key concepts covered in each chapter. Click on the quiz below to get started.

1. Which of the following is an example of perfect mediation?

- The strength of the relationship between the predictor and the outcome is reduced by exactly half when the mediator is included in the model.
- The relationship between the predictor and the outcome remains the same when the mediator is included in the model.
- The relationship between the predictor and the outcome is completely wiped out when the mediator is included in the model.
- The interaction of the predictor and the mediator significantly predict the outcome, but the variables themselves do not.

The correct answer is C. The relationship between the predictor and the outcome is completely wiped out when the mediator is included in the model.

2. Mediation has occurred when:

- The strength of the relationship between a predictor variable and an outcome variable is reduced by including another variable in the model.
- The strength of the relationship between a predictor variable and an outcome variable is increased by including another variable as a predictor.
- The relationship between two variables changes as a function of a third variable.
- The relationship between two variables decreases as a function of a third variable.

The correct answer is A. The strength of the relationship between a predictor variable and an outcome variable is reduced by including another variable in the model.

3. Imagine we wanted to investigate whether a person’s profession can predict scores on a self-report psychopathy scale. We collected data from people in eight professions and a group of unemployed people. The eight professions were: bank traders, insurance brokers, health care professionals, business executives, volunteer workers, full-time mums, teachers, construction workers. The outcome was a psychopathy score. How could we analyse these data?

- ANOVA only
- ANOVA or chi-square
- Regression only
- ANOVA or regression

The correct answer is D. ANOVA or regression. This is because you could use either an independent factorial ANOVA or multiple regression on these data because ANOVA and regression are basically the same.

4. An experiment was done to look at the positive arousing effects of imagery on different people. A sample of statistics lecturers was compared against a group of students. Both groups received presentations of positive images (e.g., cats and bunnies), neutral images (e.g., duvets and light bulbs), and negative images (e.g., corpses and vivisection photographs). Positive arousal was measured physiologically (high values indicate positive arousal) both before and after each batch of images. The order in which participants saw the batches of positive, neutral and negative images was randomized to avoid order effects. It was hypothesized that positive images would increase positive arousal, negative images would reduce positive arousal and that neutral images would have no effect. Differences between the subject groups (lecturers and students) were not expected. What technique should be used to analyse these data?

- Two-way mixed ANOVA
- Three-way mixed ANOVA
- Three-way repeated measures ANOVA
- Two-way mixed analysis of covariance

The correct answer is B. Three-way mixed ANOVA. This is because we could run a 2 (Time: before and after) × 2 (Group: students and lecturers) × 3 (Image: positive, negative and neutral) mixed ANOVA with between subjects on the Group variable.

5. Simple effects analysis looks at:

(*Hint*: Simple effects analysis can be used to break down interaction effects.)

- The effect of one independent variable at individual levels of the other independent variable
- The difference between the main effects of two independent variables controlling for error
- The effect of one independent variable at individual levels of the dependent variable
- The main effects of the independent variables, controlling for interaction effects

The correct answer is A. The effect of one independent variable at individual levels of the other independent variable.