Transcript Factorial Designs - Villanova University

Factorial Designs
and
ANOVA
Factorial Designs
 Very efficient design
– Multiple comparison groups
– Multiple independent variables
 Avoids some of the artificiality of
traditional experiment where x varies and
all other things held constant.
Researcher can:
 Analyze effects of two or more variables
simultaneously
 Determine if variables interact to produce
differences in outcome that would not occur
if effects of each variable were considered
separately
 Test several hypotheses
Research Example: Damrosh
Nursing students’ perceptions of an act
of rape
48 nursing students were given four different vignettes about a rape to read.
32 yo female raped in her car outside all night drug store
Group A--rape occurred at 10PM, car door left unlocked
Group B--rape occurred at 12 Mid., car door left unlocked
Group C--rape occurred at 10PM, car door locked
Group D--rape occurred at 12 Mid., car door locked
Subjects questioned as to how responsible the victim was
How much they liked and identified with the victim
How severly the rapist should be punished
What are the independent
variables
1 Time
2 treatment conditions
10 Pm
12 Mid
2 Condition of Lock 2 treatment conditions
locked
unlocked
Graphic Representation
Condition of Lock
unocked
T
I
M
E
locked
Group A
Group C
Group B
Group D
10
12
Number of cells
 Equal to the number of independent
variables X tx conditions
 2 indep var x 2 tx cond = 4
Compare
Mean scores for each group
Mean scores for each time period
10 A+C
12 B+D
Mean scores for each locked condition
unlocked A+B
locked C+D
Answers research questions
 What is the main effect of time variable?
 What is the main effect of locked condition
variable?
 Is there an interactive effect of time with
locked condition?
Hypotheses
 One for each independent variable (main
effects)
 One for the interactive effect
never more than one interaction
ANOVA
Analysis of Variance
Decomposes the variability into variability
caused by independent variable from that
caused by all other sources
F ratio=
variance between groups
variance within groups
F=MSb
MSw
between group variance
within group variance
F ratio
The higher the value of f, the greater the
probability that the measures being
compared are significantly different from
each other, and variance is caused by
independent variable
f<1=never statistically significant
Factorial designs
 Sound basis for external validity
 Mortality a real threat to validity
(should have the same number in each cell)
Now try your hand at quiz three for class discussion
for # 7
a. What are the independent variables and their treatment conditions? (diagram the
study)
B. Is there a main effect to each?
C. Is there an interactive effect?