1. Answer the questions using the ANOVA tables given as follows:

Design 1 Source of variation SS  MS p value Between groups 640.85 2 320.43 0.0135 Within groups 827.41 15 55.16 Total 1468.27 17 Source of variation SS  MS p value Treatment 16.116 3 5.372 <0.0001 Block 1.100 6 0.183 0.0104 Error 0.828 18 0.046 Total 18.044 27 Design 2 Design 3 Source of variation SS  MS p value Factor A 15.68 1 15.68 <0.0001 Factor B 0.11 1 0.11 0.0007 Interaction A×B 0.05 1 0.05 0.0133 Error 0.10 16 0.01 Total 15.94 19 0.80 Design 4 Source of variation SS  MS p value Between-time 96221.000 3 32073.667 <0.0001 Between-subject 171171.400 9 19019.044 Error 83836.000 27 4517.972 Total 351228.400 39 Design 5 Source of variation SS  MS p value Drug 8.61 1 8.61 <0.0001 Period 0.08 1 0.08 0.4901 Between-subject 6.33 11 0.58 0.0238 Error 1.55 10 Total 16.57 23

(a) What design does each table correspond to, and what is the primary purpose of each design?

(b) Although these designs serve different research purposes, what are the similarities between these designs and what is the common fundamental principle underlining them?

(c) Give the assumptions for each model.

(d) For design 2, which is the factor of interest to study? What role does the block factor play in this design? How can we benefit from incorporating block factor in the design?

(e) For design 3, what does interaction effect imply? What is main effect? What is simple effect? Why do we need to test simple effect following a significant interaction?

(f) For design 4, what is the advantageous characteristic of repeatedly measuring subjects?