Factorial Designs

Question 1

Much experimental psychology asks the question:

Answer 1

What effect does a single independent variable have on a single dependent variable?

Question 2

It is quite reasonable to ask the following question as well:

Answer 2

What effects do multiple independent variables have on a single dependent variable?

Question 3

Factorial designs are:

Answer 3

Designs which include multiple independent variables

Question 4

An example of a factorial design

If we were looking at GENDER and TIME OF EXAM

Answer 4

these would be two independent factors
•GENDER would only have two levels: male or female
•TIME OF EXAM might have multiple levels, e.g. morning, noon or night
•This is a factorial design

Question 5

The name of an experimental design depends on three pieces of information:

Answer 5

• The number of independent variables
• The number of levels of each independent variable
• The kind of independent variable
• Between Groups
• Within Subjects (or Repeated Measures)

Question 6

If there is only one independent variable then:

Answer 6

The design is a one-way design (e.g. does coffee drinking influence exam scores)

Question 7

If there are two independent variables:

Answer 7

The design is a two-way design (e.g. does time of day or coffee drinking influence exam scores).

Question 8

If there are three independent variables:

Answer 8

The design is a three-way design (e.g. does time of day, coffee drinking or age influence exam scores).

Question 9

Analytical comparisons in general

Answer 9

• If there are more than two levels of a Factor
• And, if there is a significant effect (either main effect or simple main effect)
• Analytical comparisons are required.
• Post hoc comparisons include tukey tests, Scheffé test or t-tests (bonferroni corrected).

Question 10

Using ExperStat it possible to conduct a

Answer 10

simple main effects analysis relatively easily

Question 11

Simple main effects analysis

Answer 11

• We can think of a two-way between groups analysis of variance as a combination of smaller one-way anovas.
• The analysis of simple main effects partitions the overall experiment in this way

Question 12

Experimental design names

Answer 12

• If there are 2 levels of the first IV and 3 levels of the second IV
• It is a 2x3 design
• E.G.: coffee drinking x time of day
• Factor coffee has two levels: cup of coffee or cup of water
• Factor time of day has three levels: morning, noon and night
• If there are 3 levels of the first IV, 2 levels of the second IV and 4 levels of the third IV
• It is a 3x2x4 design
• E.G.: coffee drinking x time of day x exam duration
• Factor coffee has three levels: 1 cup, 2 cup 3 cups
• Factor time of day has two levels: morning or night
• Factor exam duration has 4 levels: 30min, 60min, 90min, 120min

Question 13

If all the IVs are between groups then

Answer 13

It is a Between Groups design

Question 14

If all the IVs are repeated measures

Answer 14

It is a Repeated Measures design

Question 15

If at least one IV is between groups and at least one IV is repeated measures

Answer 15

is a Mixed or Split-Plot design

Question 16

Experimental design names

Three IVS

Answer 16

• IV 1 is between groups and has two levels (e.g. a.m., p.m.)
• IV 2 is between groups and has two levels (e.g. coffee, water).
• IV 3 is repeated measures and has 3 levels (e.g. 1st year, 2nd year and 3rd year).
• The design is:
• A three-way (2x2x3) mixed design.

Question 17

What is a main effect?

Answer 17

The effect of a single variable

Question 18

What is an interaction?

Answer 18

The effect of two variables considered together

Question 19

For the two-way between groups design, an F-ratio is calculated for each of the following:

Answer 19

• The main effect of the first variable
• The main effect of the second variable
• The interaction between the first and second variables

Question 20

To analyse the two-way between groups design we have to follow the same steps as the one-way between groups design:

Answer 20

• State the Null Hypotheses
• Partition the Variability
• Calculate the Mean Squares
• Calculate the F-Ratios

Question 21

A significant interaction effect

Answer 21

• “There was a significant interaction between the lecture and worksheet factors (F1,16=16.178, MSe=11.500, p=0.001)”
• However, we cannot at this point say anything specific about the differences between the means unless we look at the null hypothesis

•Many researches prefer to continue to make more specific observations.

Question 22

A significant main effect of Factor A

Answer 22

There was a significant main effect of lectures (F1,16=37.604, MSe=11.500, p<0.001). The students who attended lectures on average scored higher (mean=22.100) than those who did not (mean=12.800).

Question 23

No significant effect of Factor B

Answer 23

•“The main effect of worksheets was not significant (F1,16=0.039, MSe=11.500, p=0.846)”

Question 24

An example 2x2 between groups ANOVA

Answer 24

• Factor A - Lectures (2 levels: yes, no)
• Factor B - Worksheets (2 levels: yes, no)
• Dependent Variable - Exam performance (0…30)

Question 25

There are 3 null hypotheses for the two-way (between groups design:

Answer 25

The means of the different levels of the first IV will be the same, The means of the different levels of the second IV will be the same, The differences between the means of the different levels of the interaction are the same,

Question 26

An example null hypothesis for an interaction

Answer 26

The differences betweens the levels of factor A are not the same.

Question 27

Partitioning the variability If we consider the different levels of a one-way ANOVA then we can look at the deviations due to the between groups variability and the within groups variability.

Answer 27

If we substitute AB into the above equation we get This provides the deviations associated with between and within groups variability for the two-way between groups design.

Question 28

Partitioning the variability The between groups deviation can be thought of as a deviation that is comprised of three effects:

Answer 28

In other words the between groups variability is due to the effect of the first independent variable A, the effect of the second variable B, and the interaction between the two variables AxB.

Question 29

Partitioning the variability The effect of A is given by

Answer 29

A-T

Question 30

Partitioning the variability The effect of B is given by

Answer 30

B-T

Question 31

Partitioning the variability | The effect of the interaction AxB equals

Answer 31

(AB-T)-(Ā-T)-(B-T)

Question 32

The effect of the interaction AXB is known as the

Answer 32

Residual

Question 33

The F ratio for the first main effect is

Answer 33

MSA / MSSAB

Question 34

The F ratio for the second main effect is

Answer 34

MSB/ MSSAB

Question 35

The F ratio for the interaction is

Answer 35

MSAB/MSSAB

Question 36

In order to calculate F-Ratios we must calculate an Mean Square associated with ...

Answer 36

The Main Effect of the first IV The Main Effect of the second IV The Interaction. The Error Term