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Introduction to 2-way ANOVA

Introduction to 2-way ANOVA. Statistics Spring 2005. 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. HYPOTHESES TESTED in 2-WAY ANOVA.

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Introduction to 2-way ANOVA

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  1. Introduction to 2-way ANOVA Statistics Spring 2005

  2. 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

  3. 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”

  4. 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

  5. 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

  6. To run the test of these hypotheses in SPSS….. Analyze  General Linear Model  Univariate NOTE: Use this method of analysis when both IV’s are not repeated measures.

  7. 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)

  8. Types of 2-Way ANOVA designs • Both IV’s are between subjects(i.e. not-repeated measures) • Both IV’s are within subjects(i.e. repeated measures) • One IV is between subjects, the other IV is within subjects

  9. Both IV’s are between subjects(i.e. not-repeated measures) Analyze  General Linear Model  Univariate

  10. Both IV’s are within subjects(i.e. repeated measures) Analyze  General Linear Model  Repeated Measures

  11. Analyze  General Linear Model  Repeated Measures

  12. One IV is between subjects, other IV is within subjects Analyze  General Linear Model  Repeated Measures

  13. 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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