Introduction to Two-Way ANOVA - Applied Statistics - Lecture Slides, Slides of Psychology

Download Introduction to Two-Way ANOVA - Applied Statistics - Lecture Slides and more Slides Psychology in PDF only on Docsity! Introduction to Two-Way ANOVA Docsity.com Qualitative Analysis of Two- Way ANOVA • A more sophisticated technique used to investigate more than one factor (independent variable) • A factorial experiment is one in which the effect of two or more factors are assessed in one experiment Docsity.com Analyzing Data • Test for effects 2 2 2 2 2 2 For A: For B: Interaction between A and B: R obt W C obt W RC obt W sF s sF s sF s = = = Docsity.com Steps in performing the Two-Way ANOVA • The total sum of squares (SST) is partitioned into four components: – Within cells sum of squares (SSW) – Row sum of squares (SSR) – Column sum of squares (SSC) – Row x Column sum of squares (SSRC) • Four variance estimates are formed by dividing each of the above four sum of squares by their degrees of freedom • F ratios compared to F critical Docsity.com Within-cells Variance Estimate sW2 • Equivalent to sW2 in one way ANOVA • Provides estimate of σ2 • Measure of inherent variability of the scores from subject to subject • Variability of scores within each cell • Does not reflect any treatment effect Docsity.com Row Variance Estimate sR2 • Measures main effect of variable A • Based on differences between row means • If variable A has no effect then the population row means are equal • Each sample row mean is from the same population Docsity.com Row Variance Estimate sR2 • Equations: 2 2 2 2 21 2 .... 1 R R R row row rowr allscores R row R SSs df X X X X SS n N df r =         + + +                 = −       = − ∑ ∑ ∑ ∑ Docsity.com Column Variance Estimate sC2 • Measures main effect of variable B • Based on differences between column means • If variable B has no effect, then the population column means are equal • Differences among sample column means are due to random sampling from identical populations Docsity.com