1. Unbalanced 2-Factor Studies
KNNL – Chapter 23

2. Unequal Sample Sizes
When sample sizes are unequal, calculations and parameter interpretations (especially marginal ones) become messier
Observational studies often have unequal sample sizes due to availability of sampling units for certain combinations of factor levels (villagers of certain types in a rural study for instance)
Experimental studies, even when planned with equal sample sizes can end up unbalanced through technical problems or “drop outs”
Some conditions may be cheaper to measure than others, and will have larger sample sizes
Some situations have particular contrasts of higher importance

3. Regression Approach - I

4. Regression Approach - II

5. Regression Approach – Example I

6. Testing Strategies – Models Fit
Model 1: all Factor A, Factor B, and Interaction AB Effects
Model 2:all Factor A, Factor B Effects (Remove Interaction)
Model 3: all Factor B,Interaction AB Effects (Remove A)
Model 4:all Factor A,Interaction AB Effects (Remove B)
To test for Interaction Effects, Model 1 is Full Model, Model 2 is Reduced dfNumerator=(a-1)(b-1) dfden=nT-ab
Testing for Factor A Effects, Full=Model 1, Reduced=Model dfNumerator=(a-1) dfden=nT-ab
Testing for Factor B Effects, Full=Model 1, Reduced=Model 4 dfNumerator=(b-1) dfden=nT-ab

7. Regression Approach – Example - Continued

8. Regression Approach – Example - Continued

9. Regression Approach – Example - Continued

10. Estimating Treatment and Factor Level Means/Contrasts

11. Standard Error Multipliers

12. Creative Life Cycles – Comparing Treatment Means
Conceptualists/Poets Conceptualists/Novelists Experimentalists/Poets Experimentalists/Novelists

13. Creative Life Cycles – Comparing Factor Level Means