Two  Factor  Factorial  Experiments  

Chapter  14,  sec8on  14.3  

 Introduc*on  

•  An experiment is a test or series of tests.

•  The design of an experiment plays a major role in the eventual solution of the problem.

•  In a factorial experimental design, experimental trials (or runs) are performed at all combinations of the factor levels.

•  The analysis of variance (ANOVA) will be used as one of the primary tools for statistical data analysis.

3  

The  General  Two-­‐Factor    Factorial  Experiment  

a  levels  of  factor  A;  b  levels  of  factor  B;  n  replicates  

4  

Sta8s8cal  (effects)  model:  

€

yijk = µ +τ i + β j + (τβ)ij +ε ijk

i =1,2,...,aj =1,2,...,bk =1,2,...,n

⎧

⎨ ⎪

⎩ ⎪

5  

Hypotheses  tested  for  Factorial  Designs  

•  For  the  main  effect  of  A:  

•  For  the  main  effect  of  B:  

•  For  the  interac8on  effect  of  A  and  B:  

6  

Two  Factor  ANOVA  

ANOVA  par88oning  of  total  variability:  

Corresponding  dof  par88oning  is:  

7  

ANOVA  Table  –  Two  Factor  Factorial  Experiments  

Example:  BaOery  life  

Example:  BaOery  life  

Example:  BaOery  life  

Example:  BaOery  life  

Example:  BaOery  life  

F0.05,2,27=3.35   F0.05,4,27=2.73  

Material  type,  temperature,  and  the  interac*on  between  them  all  have  significant  effect  on  the  life  of  the  baRery.