Transcript Welcome to PSY 202 with Dr. Chris Cunningham

Slides to accompany Weathington,
Cunningham & Pittenger (2010),
Chapter 12: Single Variable BetweenSubjects Research
1
Objectives
• Independent Variable
• Cause and Effect
• Gaining Control Over the Variables
• The General Linear Model
• Components of Variance
• The F-ratio
• ANOVA Summary Table
• Interpreting the F-ratio
• Effect Size and Power
• Multiple Comparisons of the Means
2
Multi-level Independent Variable
• More than 2 levels of the IV
• Permits more detailed analysis
– Can’t identify certain types of relationships
with only two data points (Figure 12.1)
• Can increase a study’s power by reducing
variability within the multiple treatment
condition groups
3
Figure 12.1
4
Searching for Cause and Effect
• Identifying differences among multiple
groups is a starting point for causal study
• Control is the key:
– Through research design
– Through research procedure
5
Control through Design
• Most easily secured in a true experiment
• You manipulate and control the IV
– Control groups are possible  isolating effects
of IV
• You control random assignment of
participants
– Helps to reduce confounding effects
6
Control through Procedure
• Each participant needs to experience the
same process (except the manipulation)
– Systematic
• Identifying and trying to limit as many
confounding factors as possible
• Pilot studies are a great way to test your
process and your control strategies
7
General Linear Model
• Xij = µ + αj + εij
• A person’s performance (score = Xij) will
reflect:
– Typical score in that group (µ)
– Effect of the treatment/manipulation (αj)
– Random error (εij)
• Ho: all µi equal
8
Figure 12.2
Sampling frame
µ, σ
Sample
M= µ
SD = σ
Xi = µ + ε
Random Assignment
No feedback
Intelligence feedback
Effort feedback
Control
M = µ + α1
SD = σ
Xi1 = µ + α1 + εi1
Intelligence
M = µ + α2
SD = σ
Xi2 = µ + α2 + εi2
Effort
M = µ + α3
SD = σ
Xi3 = µ + α3 + εi3
9
GLM and Between-Subj. Research
• Goal is to determine proportion of total
variance due to IV and proportion due to
random error
• Size of between-groups variance is due to
error (εij) and IV (αj)
• If b-g variance > w-g variance  IV has
some effect
10
ANOVA
• Compares different types of variance
– Total variance = variability among all
participants’ scores (groups do not matter)
– Within-groups variance = average variability
among scores within a group or condition
(random)
– Between-groups variance = variability among
means of the different treatment groups
• Reflects joint effects of IV and error
11
F-ratio
• Allows us to determine if b-g variance >
w-g variance
• F = Treatment Variance + Error Variance
Error Variance
• F = MSbetween/MSwithin
12
F-ratio: No Effect
• Treatment group M may not all be exactly
equal, but if they do not differ
substantially relative to the variability
within each group  nonsignificant result
• When b-g variance = w-g variance, F =
1.00, n.s.
13
Figure 12.4
Condition
|-----M1-----|
Control
|-----M2-----|
Intelligence
|-----M3-----|
Effort
|---Moverall---|
0
1
2
3
4
5
6
7
Score range
Between-groups
8
9
10
14
F-ratio: Significant Effect
• If IV influences DV, then b-g variance >
w-g variance and F > 1.00
• Examining the M can highlight the
difference(s)
15
Figure 12.5
Condition
|-----M1-----|
Control
|-----M2-----|
Intelligence
|-----M3-----|
Effort
|------------------------Moverall------------------------|
0
1
2
3
4
5
6
7
Score range
8
Between-groups
9
10
16
F-ratio Distribution
• Represents probability of various F-ratios
when Ho is true
• Shape is determined by two df
– 1st = b-g = (# of groups) - 1
– 2nd = w-g = (# of participants in a group) – 1
• Positive skew, α on right extreme region
17
Figure 12.6
18
Summarizing ANOVA Results
• Figure 12.7
• Using the critical value from appropriate
table in Appendix B, if Fobs > Fcrit 
significant difference among the M
• Rejecting Ho requires further
interpretation
– Follow-up contrasts
19
Figure 12.7
20
Interpreting F-ratio
• Omega squared indicates degree of
association between IV and DV
• f is similar to d for the t-test
• Typically requires further M comparisons
– t-test time, but with reduced α to limit
chances of committing a Type I error
21
Multiple Means Comparisons
• You could consider lowering α to .01, but this
would increase your Type II probability
• Instead use a post-hoc correction for α:
– αe= 1 – (1 – αp)c
– Tukey’s HSD = difference required to
consider M statistically different from each
other
22
What is Next?
• **instructor to provide details
23