Lecture 19: Factorial Designs l Flashcards
factor
an independent variable (IV) in an experiment with more than 1 IV
factorial design
a research design that includes two or more factors
two-factor design
a factorial design with 2 independent vairables
how many conditions are there in a 2 x 3 x 2 design?
a 2 X 3 X 2 design is a three-factor design with a total of 12 conditions formed from the first IV (2 conditions), second IV (3 conditions), and third IV (2 conditions) = 12 conditions total because all factors are CROSSED (all possible combinations of the 3 factors are included)
why do we use factorial designs?
to examine complex relationships among variables in a single study
factorial designs examine:
- The effects of more than one IV on a DV
- The interactions between the IVs (combined effects)
Experimental factor design
when all of the factors are manipulated
Quasi-experimental factorial design
when one factor is not manipulated
factorial designs and interactions
- An interaction among 2 factors = a difference between differences = the effect of one IV at each level of another IV
- The levels of one factor determine the columns; the levels of the second factor determine the rows
two-factor designs
- A two-factor design can be represented by a matrix
Each cell corresponds to a separate treatment condition (a specific combination of the factors). - Data provide three separate and distinct sets of information.
Describes how the two factors independently and jointly affect behaviour
formula for an interaction
Interaction = difference (A) - difference (B)
interaction
when the effects of one factor depend on the levels of a second factor
interpreting interactions graphically
Non-parallel lines between two factors in a 2x2 plot generally indicate an interaction
factorial designs can have:
- All between-subject factors
- All within-subject factors
- A mix of between-subject and within-subject factors
mixed design
some IVs are between-subject, others are within-subject
example of a mixed-design
treatment (between-subjects) x test time (within-subject)
can you always choose whether a factor is within- or between-subjects
no (ex. age)
how should you graphically depict categorical x-variables?
with a bar chart
mean differences evaluated in factorial designs
- The mean differences from the main effect of factor A
- The mean differences from the main effect of factor B
- The mean differences from the interaction of factors A and B
computing a two-way interaction
- if the size and the direction of the row differences are the same as the corresponding column differences = no interaction
- If the size and direction of the differences change from rows to columns = evidence of an interaction
why do we use factorial designs in psychology?
because human behaviour is complex and influenced by a variety of interacting factors
validity of factorial designs
Factorial designs tend to have higher ecological validity than one-IV designs
notation of factorial designs
- Each factor is donated by a letter and each level of the IV is represented by a number
- Factor A = rows; Factor B = columns
what does the number of IVs and the number of levels for each IV indicate?
the total number of conditions
blending research designs in a factorial design
- The ability to mix factors within a single study allows researchers to blend several different research strategies within one study
- Researchers can develop studies that address scientific questions that could not be answered by a single strategy
example of blending research designs in a factorial design
- Independent factors of Test Anxiety (2 levels) and Trait Anxiety (3 levels) = 2 X 3 design
- 3 tests:
Effects of Test Anxiety
Effects of Trait Anxiety
Interaction of Test Anxiety and Trait Anxiety - Now let’s say you wanted to add a third IV, such as gender
- You would end up with a 2 x 3 x 2 factorial design
2 levels for test anxiety
3 levels for trait anxiety
2 levels of gender - Each factor: test anxiety, trait anxiety, and gender is a between-subjects factor
- Cannot be manipulated within the subject
- This yields a 2 x 3 x 2 factorial design with the need for many subjects
example of 3 null hypotheses of a 2 x 2 factorial design
- There is no significant difference between the levels of Factor A
- There is no significant difference between the levels of Factor B
- There is no significant interaction of Factors A & B
example of 3 alternative hypotheses of a 2 x 3 factorial design
- Factor A: Level 1 > Level 2
- Factor B: Level 1 < Level 2
- Interaction: Level 1 of Factor A > Level 2 of Factor A when Factor B = Level 1 than when Factor B = Level 2
the null hypotheses correspond to statistical tests of:
- Main effects of Factor A
- Main effects of Factor B
- Interaction of Factors A & B
people run studies to test ___
the alternative hypothesis
warning about means-based examples
- Means x, y of 2 factors significantly = small amount of overlap in variance
- Means x, y, of 2 factors do not differ significantly = large amount of overlap in variances
- Statistical tests (ANOVA) are needed to determine whether the difference in mean values exceeds the variance in the factors sufficiently to be statistically significant
interpreting results of factorial designs
- Look for the main effects first
- Compare the column means for Factor A to determine the main effect of Factor A
- Compare the row means to determine the main effect of Factor B
- To look for interactions check if the difference in row means is consistent across columns
- If the differences are identical, there is no interaction (parallel lines)
how to discuss results of a factorial design
- When discussing results, consider the interaction before or at the same time as considering the main effects
- The presence of an interaction can obscure or distort the main effects of each factor
- When reporting an interaction, your statement should include the phrase “depends on”
- If there is no interaction, discuss the main effects by themselves
