Ch. 9 Flashcards
factorial designs
Experiments that include more than one independent variable in which each level of one independent variable is combined with each level of the others to produce all possible combinations.
Each combination, then, becomes a condition in the experiment.
Just as including multiple levels of a single independent variable allows one to answer more sophisticated research questions, so too does including multiple independent variables in the same experiment.
In a factorial experiment, the decision to take the between-subjects or within-subjects approach must be made separately for each independent variable.
factorial design table
Shows how each level of one independent variable is combined with each level of the others to produce all possible combinations in a factorial design.
2 × 2 (read “two-by-two”) factorial design because it combines two variables, each of which has two levels.
If one of the independent variables had a third level then it would be a 3 × 2 factorial design.
Notice that the number of possible conditions is the product of the numbers of levels.
A 2 × 2 factorial design has four conditions, a 3 × 2 factorial design has six conditions, Etc.
Also notice that each number in the notation represents one factor, one independent variable.
So by looking at how many numbers are in the notation, you can determine how many independent variables there are in the experiment.
2 x 2, 3 x 3, and 2 x 3 designs all have two numbers in the notation and therefore all have two independent variables.
The numerical value of each of the numbers represents the number of levels of each independent variable.
A 2 means that the independent variable has two levels, a 3 means that the independent variable has three levels
In principle, factorial designs can include any number of independent variables with any number of levels.
In practice, it is unusual for there to be more than three independent variables with more than two or three levels each.
This is for at least two reasons:
For one, the number of conditions can quickly become unmanageable.
Second, the number of participants required to populate all of these conditions (while maintaining a reasonable ability to detect a real underlying effect) can render the design unfeasible
between-subjects factorial design
All of the independent variables are manipulated between subjects.
Recall that in a simple between-subjects design, each participant is tested in only one condition.
The between-subjects design is conceptually simpler, avoids order/carryover effects, and minimizes the time and effort of each participant.
within-subjects factorial design
all of the independent variables are manipulated within subjects.
In a simple within-subjects design, each participant is tested in all conditions.
The within-subjects design is more efficient for the researcher and controls extraneous participant variables.
mixed factorial design
A design which manipulates one independent variable between subjects and another within subjects.
Since factorial designs have more than one independent variable, it is also possible to manipulate one independent variable between subjects and another within subjects.
Thus each participant in this mixed design would be tested in two of the four conditions.
Non-Manipulated Independent Variables
An independent variable that is measured but is non-manipulated.
Several points worth making about these.
First, non-manipulated independent variables are usually participant variables (private body consciousness, hypochondriasis, self-esteem, gender, and so on), and as such, they are by definition between-subjects factors.
Second, such studies are generally considered to be experiments as long as at least one independent variable is manipulated, regardless of how many non-manipulated independent variables are included.
Third, it is important to remember that causal conclusions can only be drawn about the manipulated independent variable.
Non-Experimental Studies With Factorial Designs
We have seen that factorial experiments can include manipulated independent variables or a combination of manipulated and non-manipulated independent variables.
But factorial designs can also include only non-manipulated independent variables, in which case they are no longer experiments but are instead non-experimental in nature.
Graphing the Results of Factorial Experiments
The results of factorial experiments with two independent variables can be graphed by representing one independent variable on the x-axis and representing the other by using different colored bars or lines. (The y-axis is always reserved for the dependent variable.)
Main Effect
The effect of one independent variable on the dependent variable—averaging across the levels of any other independent variable(s).
Thus there is one main effect to consider for each independent variable in the study.
Main effects are independent of each other in the sense that whether or not there is a main effect of one independent variable says nothing about whether or not there is a main effect of the other.
interaction effect
When the effect of one independent variable depends on the level of another.
spreading interactions
Means there is an effect of one independent variable at one level of the other independent variable and there is either a weak effect or no effect of that independent variable at the other level of the other independent variable.
Ex: independent variable “B” has an effect at level 1 of independent variable “A” but no effect at level 2 of independent variable “A.”
cross-over interaction
Means the independent variable has an effect at both levels but the effects are in opposite directions.
independent variable “B” again has an effect at both levels of independent variable “A,” but the effects are in opposite directions.
Simple Effects
Are a way of breaking down the interaction to figure out precisely what is going on.
An interaction simply informs us that the effects of at least one independent variable depend on the level of another independent variable.
Whenever an interaction is detected, researchers need to conduct additional analyses to determine where that interaction is coming from.
Specifically, a simple effects analysis allows researchers to determine the effects of each independent variable at each level of the other independent variable.
Once again examining simple effects provides a means of breaking down the interaction and therefore it is only necessary to conduct these analyses when an interaction is present.
When there is no interaction then the main effects will tell the complete and accurate story.
To summarize, rather than averaging across the levels of the other independent variable, as is done in a main effects analysis, simple effects analyses are used to examine the effects of each independent variable at each level of the other independent variable(s).
