Introduction to 2-way ANOVA Statistics Spring 2005

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

HYPOTHESES TESTED in 2-WAY ANOVA u No differences for IV #1 (A - 3 levels) u H 0 : M A1 = M A2 = M A3 u No differences for IV #2 (B - 4 levels) u H 0 : M B1 = M B2 = M B3 = M B4 u No interaction u At least one M AiBj  M AmBn These are called “Main Effects”

EXAMPLE u One might suspect that level of education and gender both have significant impacts on salary. Using the data found in Census90 condensed.sav determine if this statement is true. Dependent Variable INCOME (ratio level data) Independent Variables GENDER (2 levels) EDUCAT (6 levels)  =.05

No differences for GENDER (2 levels) H 0 : M Male = M Female No differences for EDUCATION (6 levels) H 0 : M B1 = M B2 = M B3 = M B4 = M B5 = M B6 No interaction At least one M AiBj  M AmBn HYPOTHESES TESTED for a 2X6 ANOVA

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.

No differences for GENDER (2 levels) H 0 : M Male = M Female No differences for EDUCATION (6 levels) H 0 : M B1 = M B2 = M B3 = M B4 = M B5 = M B6 No interaction At least one M AiBj  M AmBn HYPOTHESES TESTED for a 2X6 ANOVA Reject H 0 (F(1,471)=29.95: p=.000) Reject H 0 (F(5,471)=13.75: p=.000) Reject H 0 (F(5,471)=2.96: p=.012)

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

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

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

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

HYPOTHESES TESTED in 2-WAY ANOVA u No differences for IV #1 (A - 3 levels) u H 0 : M A1 = M A2 = M A3 u No differences for IV #2 (B - 4 levels) u H 0 : M B1 = M B2 = M B3 = M B4 u No interaction u At least one M AiBj  M AmBn These are called “Main Effects”