Psychology 203 Examining Main Effects and Interactions

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Psychology 203Examining Main Effects and
Interactions
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Announcements

• Quiz 1 Results available on WebCT
• Quiz 2 format
• 70 questions
• Multiple choice (1 from 4)
• NO true/false
• Duration 1 hr
• Value 10
• Week 13 (High Speed Memory Processing Lab Report
  also due 9am Monday 28th May Value 20)

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Format for the Exam

• 2 hrs duration
• 2 Sections
• Section 1 80 multiple choice questions
• Simple formulas (not provided)
• Tables (F, t, chi square provided)
• Section 2 10 short answer questions
• Each question in each section weighted equally
• Each section weighted equally

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Things you will need to know

• How to look up statistics tables
• Formulae s2, z, sd, ss, F, d, t, chi square, df
  (also handy for quiz 2)
• Laboratory work
• Content of text Gravetter Wallnau. Excluding
  chapters 19-20

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Two-Way DesignANOVA Summary Table
Sums of Squared Deviations about a mean
Sums of squared deviations of factor level means
from grand mean
Source SS df MS F
Between Factor A SSA a - 1 MSA
MSA/MSW Factor B SSB b - 1 MSB
MSB/MSW A x B SSAxB (a - 1)(b -
1) MSAxB MSAxB/MSW Within SSW
ab(ncell - 1) MSW Total SST N - 1
Average of the sum of the squared deviations for
each group
Where a number of levels of Factor A b
number of levels of Factor B N total number of
observations (subjects) across all cells ncell
number of observations in each cell
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Two-Way DesignANOVA Summary Table
Degrees of freedom
Lose 1 Degree of freedom for each variance
estimate to be made from SS for factor levels
and interaction
Lose 1 degree of freedom per group based on
numbers (n) in the groups
Source SS df MS F
Between Factor A SSA a - 1 MSA
MSA/MSW Factor B SSB b - 1 MSB
MSB/MSW A x B SSAxB (a - 1)(b -
1) MSAxB MSAxB/MSW Within SSW
ab(ncell - 1) MSW Total SST N - 1
Sum of all deviations must add to zero Provides
unbiased estimate of population variance
Where a number of levels of Factor A b
number of levels of Factor B N total number of
observations (subjects) across all cells ncell
number of observations in each cell
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Two-Way DesignANOVA Summary Table
Mean of the Summed Squared Deviations about the
Mean
Source SS df MS F
Between Factor A SSA a - 1 MSA
MSA/MSW Factor B SSB b - 1 MSB
MSB/MSW A x B SSAxB (a - 1)(b -
1) MSAxB MSAxB/MSW Within SSW
ab(ncell - 1) MSW Total SST N - 1
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Interpreting Two-Way DesignsInteractions vs
Main Effects

• The effect of one factor differs across levels of
  the other factor(s)
• Interactions take interpretative precedence over
  main effects

No main effects but interaction present
2 main effects no interaction
Case II
o
x
b2
o
o
b2
x
o
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Main Effects
b2
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Plotting the Results for each condition
The effect of exercise depends on the time it is
taken
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Other forms of interaction
1 main effect of a interaction averaging within
b will give roughly the same means for b1 b2.
Averaging within a will show the main effect of a
1 main effect of b interaction averaging
within a would give roughly same means for a1
a2 . Averaging within b will show the main effect
of b
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An Example
Dep Var
Alcohol Dose
Sex
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The pull down menus
Univariate
General Linear Model
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Assign Variables
In most experiments we use a fixed effects model
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Different post hoc tests
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Plot the means
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Mean Plots
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Summary Tables
You dont need this
Or this
Or this
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Are all the groups different?

• The F test is an omnibus test that does not tell
  us where the differences lie
• We could compare each group with a standard
  t-test but this is inefficient and does not use
  all the data
• Usually we formally compare between individual
  groups using special types of t-tests
• Planned (a priori) and unplanned (post hoc)
  comparisons

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Tukeys HSD
Group 4 is different from all others
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Still Sig
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The Same Data Using a Mixed ANOVA Design

• What do we mean by mixed design?
• Sometimes referred to as split plot factorial
• At least one repeated measures factor
• At least one between groups factor
• In our experiment drug could be repeated and of
  course sex is a between groups variable

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These are the exact same data as the previous
example except driving behaviour is a repeated
measure
This is a 2 x 4 design Not a 4x2 design
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Same plots as previously
Dose
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Dose
Dose
Error Dose
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Note this is not significant!
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Effect Size Comparison (Partial eta squared)
Notice how the effects are all bigger in the
split plot design
However, in the split plot the effect of sex is
not significant. How might this be explained?
In the independent groups design n 48 In the
split plot design n 6
As the n is smaller the power of the between grps
analysis is weaker
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Thats it for ANOVA

• The completely repeated measures design with
  multiple factors is what you will cover in the
  memory search laboratory this week