STAT 3450 Lecture Notes - Lecture 22: Factorial Experiment, Analysis Of Variance, Ssab

• School: Ohio State University
• Department: Statistics
• Course: STAT 3450
• Professor: Bach Judit

Document Summary

Rather than one treatment affecting the response, there are 2. Can analyze, not only how they affect the response individually but also how they jointly affect the response. If responses are observed on every treatment combination then the design is called complete or a full factorial design. Model: (cid:3036)(cid:3037)(cid:3038)=+(cid:2009)(cid:3036)+(cid:2010)(cid:3037)+(cid:2011)(cid:3036)(cid:3037)+(cid:3036)(cid:3037)(cid:3038) (cid:2009)(cid:3036) = row effect (cid:2010)(cid:3037) = column effect (cid:2011)(cid:3036)(cid:3037) = interaction (cid:3036)(cid:3037)(cid:3038) = error. If the interaction is non-significant (i. e. , the independent variables affect the response individually but not together), we can drop it. Hypothesis test: (cid:3036)(cid:3037)(cid:3038)=+(cid:2009)(cid:3036)+(cid:2010)(cid:3037)+(cid:3036)(cid:3037)(cid:3038: test if the interaction is significant (cid:2868): (cid:2011)(cid:2869)(cid:2869)=(cid:2011)(cid:2869)(cid:2870)= =(cid:2011)(cid:3010)(cid:3011)=0 vs. (cid:2869):(cid:1872) (cid:1871)(cid:1872) (cid:1867)(cid:1866) (cid:2011)(cid:3036)(cid:3037) (cid:1871) 0. If so, both factors are required because the individual level work together in predicting the response. If not, the factors can be examined individually: test if each factor is significant (is the mean response the same for each factor level?) The test uses the sum of squares the same way as in one-way anova: