1. Factorial Experimental Designs
Chapter 12
Factorial Experimental Designs

2. Testing Multiple Factors in the Same Experiment
Factorial design – Research design in which participants are observed across the combination of levels of two or more factors
In stats class, this was referred to as Two-Way ANOVA (or more)

3. Testing Multiple Factors in the Same Experiment
Factorial experimental design – Research design in which groups are created by manipulating the levels of two or more factors (can be between-, within- and mixed-design)
Completely crossed design: A factorial design in which each level of one factor is combined or crossed with each level of the other factor, with participants observed in each cell or combination of levels

4. Selecting Samples for a Factorial Design in Experimentation
We select ONE sample from a population, then randomly assign the same or different participants to groups created by combining the levels of two or more factors or IVs
Create the groups by combining the levels of each IV
Identify a factorial design by the number of levels for each factor
Then assign participants to groups

5. Selecting Samples for a Factorial Design in Experimentation
Decaf Reg Coffee
Easy Task
Difficult Task
Decaf Reg Coffee Water
Easy Task
Difficult Task

6. Types of Factorial Designs
Between-subjects design – Levels of two or more between-subjects factors are combined to create groups, meaning that different participants are observed in each group
Ex. Researchers recorded how well participants comprehended a passage that varied by type of highlighting and text difficulty (Gier, Kreiner, & Natz-Gonzalez, 2009)

7. Types of Factorial Designs
Within-subjects design – Levels of two or more within-subjects factors are combined to create groups, meaning that the same participants are observed in each group
Ex. Researchers measured activity levels of captive ring-tailed lemurs in each of four environments that varied by visibility of food and arrangement of food (Dishman, Thomson, & Karnovsky, )

8. Types of Factorial Designs
Mixed factorial design – Different participants are observed at each level of a between-subjects factor and also repeatedly observed across the levels of the within- subjects factor

9. Do the morning and evening groups contain the same people?
Time of Day
Morning Evening
Hungry
Not
Hunger
Level
A researcher believes that time of day and hunger level affects how much people will spend on a shopping trip. He gathers together 12 people and brings half of them to a mall in the morning (10am). The other half of the group is taken to the mall in the evening (7pm). Of each group of 6 people, half are fed a heavy meal before their shopping trip while the other half are not fed at all. The scientist measures how much each person spend at the end of the trip. Test this hypothesis using an alpha level of .05.
Variable #1: Time of day.
Do the morning and evening groups contain the same people?
No. = Between Subj
Variable #2: Hunger level.
Do the hungry and not hungry groups contain the same people?
No. = Between Subj

10. Do the morning and evening groups contain the same people?
Time of Day
Morning Evening
Hungry
Not
Hunger
Level
A researcher believes that time of day and hunger level affects how much people will spend on a shopping trip. He gathers together 6 people and brings them to a mall in the morning (10am). Half of the group is fed a heavy meal before their shopping trip while the other half are not fed at all. Then, these same people are brought back at 10pm in the evening, where the same thing happens again. The scientist measures how much each person spend at the end of the trip. Test this hypothesis using an alpha level of .05.
Variable #1: Time of day.
Do the morning and evening groups contain the same people?
Yes. = Within Subj
Variable #2: Hunger level.
Do the hungry and not hungry groups contain the same people?
No. = Between Subj

11. Do the morning and evening groups contain the same people?
A researcher believes that time of day and hunger level affects how much people will spend on a shopping trip. He gathers together 3 people and asks them to participate for 4 days. On the first day, he makes sure everyone hasn’t eaten breakfast and takes them shopping in the morning; the next day he makes sure they havent eaten dinner and takes them shopping in the evening; the next day he feeds them a heavy meal and they are asked to shop in the morning. On the very last day, he feeds them again but before an evening trip. Test this hypothesis using an alpha level of .05.
Time of Day
Morning Evening
Hungry
Not
Hunger
Level
Variable #1: Time of day.
Do the morning and evening groups contain the same people?
Yes.= Within Subj
Variable #2: Hunger level.
Do the hungry and not hungry groups contain the same people?
Yes. Within Subj

12. Types of Factorial Designs
To be a TRUE experiment, the researchers must:
1. Manipulate the levels of each factor
2. Cross the levels of the two factors to create the groups
3. Randomly assign the same or different participants to each level of the between-subjects factor
4. Control for order effects due to observing the same participants at each level of the within-subjects factor (only applies to within-subjects designs)

13. Main Effects and Interactions
Two-way analysis of variance (ANOVA) – Statistical procedure used to analyze the variance in a DV between groups created by combining the levels of two factors
F = Variability between groups
Variability attributed to error
The test statistic can also be used in quasi-experiments however, because the quasi-experiment does not methodologically control for individual differences, the design cannot demonstrate cause and effect

14. Main Effects and Interactions
Two-way factorial design – Research design in which participants are observed in groups created by combining or crossing the levels of two factors
Using this design we can identify three sources of variation:
Main Effect for Factor A
Main Effect for Factor B)
Interaction Effect (the combination of levels of Factors A and B

15. Main Effects and Interactions
Main effects – Source of variation associated with mean differences across the levels of a single factor
A significant main effect indicates that group means significantly vary across the levels of one factor, independent of the second factor
Interactions – Source of variation associated with how the effects of one factor are influenced by, or depend on, the levels of a second factor
A significant interaction indicates that group means significantly vary across the combined levels of two factors
In a table summary, an interaction is a measure of how cell means at each level of one factor change across the levels of a second factor

16. I am interested to see whether performance on an exam is affected by projecting a countdown timer on the board during the test.
Timer
No Timer 5
Overall, is there an effect of presence of timer?

17. I am interested to see whether performance on an exam is affected by projecting a countdown timer on the board during the test.
Timer
No Timer 5 10
Overall, is there an effect of presence of timer?

18. I am interested to see whether performance on an exam is affected by projecting a countdown timer on the board during the test. I also believe that the type of content on the exam affects exam score.
Timer
No Timer
Math 8 5
Verbal 2
6.5
3.5 5 5
Overall, is there an effect of presence of timer?
Overall, is there an effect of content type?

19. I am interested to see whether performance on an exam is affected by projecting a countdown timer on the board during the test. I also believe that the type of content on the exam affects exam score.
Timer
No Timer
Math 6 4
Verbal 8 2 5 5 7 3
Overall, is there an effect of presence of timer?
Overall, is there an effect of content type?

20. I am interested to see whether performance on an exam is affected by projecting a countdown timer on the board during the test. I also believe that the type of content on the exam affects exam score.
Timer
No Timer
Math 5
Verbal 10 5
7.5
7.5 5
Overall, is there an effect of presence of timer?
Overall, is there an effect of content type?

21. Timer
No Timer
Math 8 2
Verbal 5 5 5 5
Overall, is there an effect of presence of timer?
Overall, is there an effect of content type?

22. Timer
No Timer
Math 2 8
Verbal
Main effect of presence of timer.

23. Timer
No Timer
Math 2 4
Verbal 6
Main effect of presence of timer.
Main effect of content type.

24. Timer
No Timer
Math 2
Verbal 4
Main effect of content type.

25. Timer
No Timer
Math 8 2
Verbal 5
Main effect of presence of timer.
Interaction effect.

26. Timer
No Timer
Math 8 2
Verbal
Interaction effect.

27. Timer
No Timer
Math 2 5
Verbal 8
Main effect of content type.
Interaction effect.

28. Identifying Main Effects and Interactions in a Graph
Even if a graph shows a possible main effect or interaction, the use of a test statistic is still needed to determine whether it is significant
Graphing only main effects
We would observe changes at the levels of one factor, independent of the changes in a second factor
When significant, look at the row and column means to describe the effect

29. Including Quasi-Independent Factors in an Experiment
The factorial design can be used when we include preexisting or quasi-independent factors
Participant variable – A quasi-independent or preexisting variable that is related to or characteristic of the personal attributes of a participant
Typically demographic characteristics (ex. age, gender)
An effect of a quasi-independent variable shows that the factor is related to changes in a DV
It does not demonstrate cause and effect because the factor is preexisting

30. Higher-Order Factorial Designs
Higher-order factorial design – Research design in which the levels of more than two groups are combined or crossed to create groups
The “way” of a factorial design indicates the number of factors being combined or crossed to create groups
One consequence of adding factors is that the number of possible effects we could observe also increases
Higher order interaction – An interaction for the combination of levels of three or more factors in a factorial design: can be challenging to interpret