Complex ANOVA Designs

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Part III Additional Hypothesis Tests
Chapter 11 Complex ANOVA Designs
Renee R. Ha, Ph.D. James C. Ha, Ph.D
Integrative Statistics for the Social
Behavioral Sciences
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What is a Factorial Design?

• The simplest factorial design is a 2 2 design
  which involves two independent variables, each
  with two levels. E.g. gender (male vs. female)
  on two levels of a treatment drug (low vs. high).

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What is a Factorial Design?

• Factorial designs can involve more levels of each
  independent variable and thus become a 2 3
  design, a 3 3 design, and so on.

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Definitions

• Main effect Influence of your independent
  variable on your dependent variable.

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Definitions

• Interaction The combined effect of both (or all)
  independent variables over and above the separate
  effects of each variable alone.

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Figure 11.1

• Examples of Main Effects and Interactions in
  Graphical Form

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Linear or Additive Equation
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Table 11.3
Two-Way ANOVA Summary Table (Hesitation Time
Example)
Source SS df S2 (MS) F obt.
Row (sex)        
Column (group)        
Row Column (sex group)        
Within (within a cell)        
Total    
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Types of Variance
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F-obtained Formulas
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Figure 11.2

• Craik and Lockhart (1972) Memorization Experiment

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Results if you use Microsoft Excel to calculate
the Two-way ANOVA
Anova Two-Factor Anova Two-Factor Anova Two-Factor
ANOVA
Source of Variation SS Df MS F P-value F crit
Sample 249.64 1 249.64 35.73091603 4.4838E-08 3.946865945
Columns 1476.66 4 369.165 52.83850191 7.85493E-23 2.472930305
Interaction 195.26 4 48.815 6.986879771 6.04944E-05 2.472930305
Within 628.8 90 6.9866667

Total 2550.36 99        
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Results if you use SPSS to calculate the ANOVA
(or F test) Tests of Between-Subjects
Effects Dependent Variable SCORE
Source Type III Sum of Squares df Mean Square F Sig.
Model 15331.200 10 1533.120 219.435 .000
AGE 249.640 1 249.640 35.731 .000
TECH 1476.660 4 369.165 52.839 .000
AGE TECH 195.260 4 48.815 6.987 .000
Error 628.800 90 6.987 628.800
Total 15960.000 100
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Figure 11.3
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Results if you use Microsoft Excel to calculate
the Two-way ANOVA
ANOVA ANOVA ANOVA
Source of Variation SS df MS F P-value F crit
Sample 30.33333 2 15.16667 1.95279 0.153715 3.20432
Columns 254.3333 2 127.1667 16.37339 4.54E-06 3.20432
Interaction 13.33333 4 3.333333 0.429185 0.786769 2.578737
Within 349.5 45 7.766667

Total 647.5 53        
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Results if you use SPSS to calculate the ANOVA
(or F test) Tests of Between-Subjects
Effects Dependent Variable EYEGLAN
Source Type III Sum of Squares df Mean Square F Sig.

Model 298.000 8 37.250 4.796 .000
DISCTYP 30.333 2 15.167 1.953 .154
PAIRGEN 254.333 2 127.167 16.373 .000
DISCTYP PAIRGEN 13.333 4 3.333 .429 .787
Error 349.500 45 7.767
Total 701.000 54
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When to Use Two-Way ANOVA?

• 1. You have two independent variables and a
  between-groups (independent groups) design, and
• The sampling distribution is normally
  distributed, and
• The dependent variable is on an interval or ratio
  scale (typically), and
• 4. When the variances of the groups are the same,
  or are homogeneous.

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Multifactorial ANOVA

• Also called MANOVA

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Repeated-Measures ANOVA
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When to Use a RM ANOVA?

1. You have one independent variable with more than
   two levels and a within-groups design.
2. The sampling distribution is normally
   distributed.
3. The dependent variable is on an interval or ratio
   scale (typically).

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Overview of Single-Sample, Two-Sample, and Three
or More Sample Tests