Factorial Designs Flashcards
(36 cards)
Much experimental psychology asks the question:
What effect does a single independent variable have on a single dependent variable?
It is quite reasonable to ask the following question as well:
What effects do multiple independent variables have on a single dependent variable?
Factorial designs are:
Designs which include multiple independent variables
An example of a factorial design
If we were looking at GENDER and TIME OF EXAM
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
The name of an experimental design depends on three pieces of information:
- 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)
If there is only one independent variable then:
The design is a one-way design (e.g. does coffee drinking influence exam scores)
If there are two independent variables:
The design is a two-way design (e.g. does time of day or coffee drinking influence exam scores).
If there are three independent variables:
The design is a three-way design (e.g. does time of day, coffee drinking or age influence exam scores).
Analytical comparisons in general
- 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).
Using ExperStat it possible to conduct a
simple main effects analysis relatively easily
Simple main effects analysis
- 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
Experimental design names
- 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
If all the IVs are between groups then
It is a Between Groups design
If all the IVs are repeated measures
It is a Repeated Measures design
If at least one IV is between groups and at least one IV is repeated measures
is a Mixed or Split-Plot design
Experimental design names
Three IVS
- 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.
What is a main effect?
The effect of a single variable
What is an interaction?
The effect of two variables considered together
For the two-way between groups design, an F-ratio is calculated for each of the following:
- The main effect of the first variable
- The main effect of the second variable
- The interaction between the first and second variables
To analyse the two-way between groups design we have to follow the same steps as the one-way between groups design:
- State the Null Hypotheses
- Partition the Variability
- Calculate the Mean Squares
- Calculate the F-Ratios
A significant interaction effect
- “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.
A significant main effect of Factor A
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).
No significant effect of Factor B
•“The main effect of worksheets was not significant (F1,16=0.039, MSe=11.500, p=0.846)”
An example 2x2 between groups ANOVA
- Factor A - Lectures (2 levels: yes, no)
- Factor B - Worksheets (2 levels: yes, no)
- Dependent Variable - Exam performance (0…30)
