Lecture 19: Factorial Designs l

Question 1

factor

Answer 1

an independent variable (IV) in an experiment with more than 1 IV

Question 2

factorial design

Answer 2

a research design that includes two or more factors

Question 3

two-factor design

Answer 3

a factorial design with 2 independent vairables

Question 4

how many conditions are there in a 2 x 3 x 2 design?

Answer 4

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)

Question 5

why do we use factorial designs?

Answer 5

to examine complex relationships among variables in a single study

Question 6

factorial designs examine:

Answer 6

• The effects of more than one IV on a DV
• The interactions between the IVs (combined effects)

Question 7

Experimental factor design

Answer 7

when all of the factors are manipulated

Question 8

Quasi-experimental factorial design

Answer 8

when one factor is not manipulated

Question 9

factorial designs and interactions

Answer 9

• 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

Question 10

two-factor designs

Answer 10

• 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

Question 11

formula for an interaction

Answer 11

Interaction = difference (A) - difference (B)

Question 12

interaction

Answer 12

when the effects of one factor depend on the levels of a second factor

Question 13

interpreting interactions graphically

Answer 13

Non-parallel lines between two factors in a 2x2 plot generally indicate an interaction

Question 14

factorial designs can have:

Answer 14

• All between-subject factors
• All within-subject factors
• A mix of between-subject and within-subject factors

Question 15

mixed design

Answer 15

some IVs are between-subject, others are within-subject

Question 16

example of a mixed-design

Answer 16

treatment (between-subjects) x test time (within-subject)

Question 17

can you always choose whether a factor is within- or between-subjects

Answer 17

no (ex. age)

Question 18

how should you graphically depict categorical x-variables?

Answer 18

with a bar chart

Question 19

mean differences evaluated in factorial designs

Answer 19

• 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

Question 20

computing a two-way interaction

Answer 20

• 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

Question 21

why do we use factorial designs in psychology?

Answer 21

because human behaviour is complex and influenced by a variety of interacting factors

Question 22

validity of factorial designs

Answer 22

Factorial designs tend to have higher ecological validity than one-IV designs

Question 23

notation of factorial designs

Answer 23

• Each factor is donated by a letter and each level of the IV is represented by a number
• Factor A = rows; Factor B = columns

Question 24

what does the number of IVs and the number of levels for each IV indicate?

Answer 24

the total number of conditions

Question 25

blending research designs in a factorial design

Answer 25

• 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

Question 26

example of blending research designs in a factorial design

Answer 26

• 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

Question 27

example of 3 null hypotheses of a 2 x 2 factorial design

Answer 27

• 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

Question 28

example of 3 alternative hypotheses of a 2 x 3 factorial design

Answer 28

• 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

Question 29

the null hypotheses correspond to statistical tests of:

Answer 29

• Main effects of Factor A
• Main effects of Factor B
• Interaction of Factors A & B

Question 30

people run studies to test ___

Answer 30

the alternative hypothesis

Question 31

warning about means-based examples

Answer 31

• 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

Question 32

interpreting results of factorial designs

Answer 32

• 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)

Question 33

how to discuss results of a factorial design

Answer 33

• 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