Unbalanced 2-Factor Studies KNNL – Chapter 23

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

Regression Approach - I

Regression Approach - II

Regression Approach – Example I

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 3 dfNumerator=(a-1) dfden=nT-ab Testing for Factor B Effects, Full=Model 1, Reduced=Model 4 dfNumerator=(b-1) dfden=nT-ab

Regression Approach – Example - Continued

Regression Approach – Example - Continued

Regression Approach – Example - Continued

Estimating Treatment and Factor Level Means/Contrasts

Standard Error Multipliers

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

Creative Life Cycles – Comparing Factor Level Means