ANOVACHI - Chapters 23 and 27 One-Way ANOVA and Chi-Square...

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Chapters 23 and 27: One-Way ANOVA and Chi-Square ANOVA One-way ANOVA vs. multiple t tests and ballooning alpha Conceptual relationship between ANOVA and t test Sums of Squares (definitional formulas) Total sums of squares: SS Total = (X – Xbar Grand ) 2 Between Groups SS: SS BG = n ( Xbar Group – Xbar Grand ) 2 Within Groups SS: SS WG = ( X – Xbar Group ) 2 for each group Total SS = BG SS + WG SS Sums of Squares (computational formulas) SS Total = X 2 - G 2 /N where N = total number of participants and G = Grand total SS BG = T 2 /n - G 2 /N where n = participants/group and T is the group total SS WG = X 2 - T 2 /n for each group 1
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Source Table Source SS df MS F Between k – 1 SS BG /df MS BG /MS WG Within N – k SS WG /df Total N – 1 k = number of groups N = total number of participants When there is a significant F, we need a post hoc test to determine which means differ. The test we will use is the: Tukey HSD Test HSD = q (MS WG /n) where MS WG is the within group mean square and q is a value obtained from Table G in Appendix C.
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