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Chapter 6 Randomized Block Design Two Factor ANOVA ...

Chapter 6 Randomized Block DesignTwo Factor ANOVAI nteraction in ANOVATwo Factor (two way) ANOVATwo Factor ANOVA is used when: Y is a quantitative response variable There are two categorical explanatory variables, called Factors: Factor A has K levels, k =1, .., K Factor B has J levels, j = 1, .., J The combination of level k for A and level j for B has sample size nkjbut if all equal, just use n. Use N for overall sample case: Using BLOCKS Definition: A Block is a group of similar units, or the same unit measured multiple are used to reduce known sources of variability, by comparing levels of a Factor within (explained in detail in class): Factor = 3 methods of reducing blood pressure; Blocks defined using initial blood pressure. Factor = 4 methods for enhancing memory; Blocks defined by age. Factor = Impairment while driving (alcohol, marijuana, no sleep, control); Blocks = individuals.

Randomized Block—Calculations 1. Find the mean for each treatment (row means), each block (column means), and grand mean. 2. Partition the SSTotal into three pieces: ( )2 ( 1) 2 SSTotal y y n s Y (As usual) SSA J(y y)2 k Compare row means (exams) SSB K(y y)2 j Compare column means (students) SSE SSTotal SSA SSB

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