Introduction to 2-way ANOVA

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Introduction to 2-way ANOVA

• Statistics
• Spring 2005

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Terminology

• 2-Way ANOVA means
• 2 independent variables
• 1 dependent variable
• 3X4 ANOVA means
• 2 independent variables
• 1 dependent variable
• one IV has 3 levels
• one IV has 4 levels

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HYPOTHESES TESTEDin 2-WAY ANOVA

• No differences for IV 1 (A - 3 levels)
• H0 MA1 MA2 MA3
• No differences for IV 2 (B - 4 levels)
• H0 MB1 MB2 MB3 MB4
• No interaction
• At least one MAiBj ? MAmBn

These are called Main Effects
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EXAMPLE

• One might suspect that level of education and
  gender both have significant impacts on salary.
  Using the data found inCensus90
  condensed.savdetermine if this statement is true.

Dependent Variable INCOME (ratio level data)
Independent Variables GENDER (2 levels) EDUCAT (6
levels)
? .05
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HYPOTHESES TESTEDfor a 2X6 ANOVA
No differences for GENDER (2 levels) H0 MMale
MFemale No differences for EDUCATION (6
levels) H0 MB1 MB2 MB3 MB4 MB5 MB6 No
interaction At least one MAiBj ? MAmBn
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To run the test of these hypotheses in SPSS..
Analyze ? General Linear Model ? Univariate
NOTE Use this method of analysis when both IVs
are not repeated measures.
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HYPOTHESES TESTEDfor a 2X6 ANOVA
No differences for GENDER(2 levels) H0 MMale
MFemale No differences for EDUCATION (6
levels) H0 MB1 MB2 MB3 MB4 MB5 MB6 No
interaction At least one MAiBj ? MAmBn
Reject H0 (F(1,471)29.95 p.000)
Reject H0 (F(5,471)13.75 p.000)
Reject H0 (F(5,471)2.96 p.012)
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Types of 2-Way ANOVA designs

• Both IVs are between subjects(i.e. not-repeated
  measures)
• Both IVs are within subjects(i.e. repeated
  measures)
• One IV is between subjects, the other IV is
  within subjects

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• Both IVs are between subjects(i.e. not-repeated
  measures)

Analyze ? General Linear Model ? Univariate
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• Both IVs are within subjects(i.e. repeated
  measures)

Analyze ? General Linear Model ? Repeated Measures
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Analyze ? General Linear Model ? Repeated Measures
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• One IV is between subjects, other IV is within
  subjects

Analyze ? General Linear Model ? Repeated Measures
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HYPOTHESES TESTEDin 2-WAY ANOVA

• No differences for IV 1 (A - 3 levels)
• H0 MA1 MA2 MA3
• No differences for IV 2 (B - 4 levels)
• H0 MB1 MB2 MB3 MB4
• No interaction
• At least one MAiBj ? MAmBn

These are called Main Effects