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Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 12: Single Variable...
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Transcript of Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 12: Single Variable...
Slides to accompany Weathington, Cunningham & Pittenger (2010),
Chapter 12: Single Variable Between-Subjects Research
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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
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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
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Figure 12.1
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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
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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
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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
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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 equal8
Figure 12.2
ControlM = µ + α1
SD = σXi1 = µ + α1 + εi1
Sampling frameµ, σ
SampleM = µSD = σ
Xi = µ + ε
Random Assignment
Intelligence feedback Effort feedbackNo feedback
EffortM = µ + α3
SD = σXi3 = µ + α3 + εi3
IntelligenceM = µ + α2
SD = σXi2 = µ + α2 + εi2
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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
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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
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F-ratio• Allows us to determine if b-g
variance > w-g variance• F = Treatment Variance + Error
Variance
Error Variance
• F = MSbetween/MSwithin
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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.
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Figure 12.4
|-----M1-----|
|-----M2-----|
|-----M3-----|
|---Moverall---|
Condition
Control
Intelligence
Effort
Between-groups
0 1 2 3 4 5 6 7 8 9 10Score range
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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)
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Figure 12.5
|-----M1-----|
|-----M2-----|
|-----M3-----|
|------------------------Moverall------------------------|
Condition
Control
Intelligence
Effort
Between-groups
0 1 2 3 4 5 6 7 8 9 10Score range
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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
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Figure 12.6
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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
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Figure 12.7
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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
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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
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What is Next?• **instructor to provide details
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