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Understanding 2-Way ANOVA: Concepts, Hypotheses, and Statistical Analysis

This introduction to 2-way ANOVA covers essential terminology and concepts, focusing on scenarios involving two independent variables and one dependent variable. It explains the hypotheses tested, including main effects and interactions, using examples such as the impact of education and gender on income. The guide highlights the statistical analyses conducted using SPSS, demonstrating various 2-way ANOVA designs suitable for different measurement types. A practical understanding of these concepts is vital for performing accurate statistical analyses in research.

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Understanding 2-Way ANOVA: Concepts, Hypotheses, and Statistical Analysis

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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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