1. Nested Designs and Repeated Measures with Treatment and Time Effects
KNNL – Sections , 27.3

2. Nested Factors
Factor is Nested if its levels under different levels of another (Nesting) factor are not the same
Nesting Factor ≡ School, Nested Factor ≡ Teacher
Nesting Factor ≡ Factory, Nested Factor ≡ Machinist
If Factor A (Nesting) has a levels and Each Level of A has b levels of Factor B (Nested), there are a total of ab levels of Factor B, each being observed n times A1 A2 A3
Factor A
Factor B
B1(1)
B2(1)
B1(2)
B2(2)
B1(3)
B2(3)
Replicates
Y111
Y112
Y121
Y122
Y211
Y212
Y221
Y222
Y311
Y312
Y321
Y322
Note: When Programming, give levels of B as: 1,2,...,b,b+1,...,2b,...(a-1)b+1,...,ab

3. 2-Factor Nested Model – Balanced Case

4. Estimators, Analysis of Variance, F-tests

5. Fixed Effects Model (A and B Fixed)

6. Mixed Effects Model (A Fixed and B Random)

7. Random Effects Model (A and B Random)

8. Repeated Measures with Treatment and Time
Goal: Compare a Treatments over b Time Points
Begin with nT = as Subjects, and randomly assign them such that s Subjects receive Treatment 1, s Subjects receive Treatment a
Each Subject receives 1 Treatment (not all Treatments)
Each Subject is observed at b Time points
Treatment is referred to as “Between Subjects” Factor
Time is referred to as “Within Subjects” Factor
Treatment and Time are typically Fixed Factors
Subject (Nested within Treatment) is Random Factor
Generalizes to more than 1 Treatment Factor

9. Statistical Model

10. Analysis of Variance & F-Tests

11. Comparing Treatment and Time Effects – No Interaction

12. Comparing Trt Levels w/in Time Periods