Lecture 6 zLast Day: 2.4 and 2.4 zToday: Section 2.6 zNext Day: Section 2.8 and start Chapter 3 zAssignment #2: Chapter 2: 6, 15, (treat Tape Speed and Laser Power as qualitative factors), 27, 32(a), 36 … more to come. Due in 2 weeks.

Example zAn scientist wishes to test the effect of 4 gasoline additives zThe scientist has enough resources to perform 16 trials zThe experiment will be conducted over 4 days which are representative of 4 weather conditions zOnly 4 trials will be performed each day (at 1:30, 2:30, 3:30 and 4:30)

Example zHow can we run the experiment?

Two Blocking Variables ; 1 Factor zCan set up an experiment to remove the effect of 2 blocking variables (e.g., season and time of day) zExperiment is an example of a 4x4 Latin Squares Design

Latin Squares Design zSituation: yHave 2 blocking factors - one for rows and one for columns yHave 1 experimental factor yEach factor has k levels yDesign is arranged so that each level of the experimental factors appears exactly one time in each row and each column yThe levels of the two blocking factors are assigned at random to the columns and rows

zModel:

zConstraints: zMultiple Comparisons:

Hypotheses

ANOVA Table

Two Blocking Variables; Two Factors zCan have 2 blocking factors and 2 experiment factors zExperiment design approach superimposes 2 latin squares

Example zSuppose have 2 blocking factors and 2 experiment factors zEach factor with 3 levels

Graeco-Latin Squares Design zSituation: yHave 2 blocking factors - one for rows and one for columns yHave 2 experimental factors yEach factor has k levels yDesign is arranged so that each pair of level settings of the experiment factors appears exactly one time in each row and each column yThe levels of the two blocking factors are assigned at random to the columns and rows

zModel:

zConstraints: zMultiple Comparisons:

Hypotheses

ANOVA Table

zCan use the Graeco-Latin Squares design for situation with 3 blocking variables and 1 experiment factor

Example: zA Martindale wear tester is a machine used for testing the quality types of cloth, and has the property that it can test 4 pieces of cloth simultaneously zExperiment (Box, Hunter and Hunter, 1978) was run to compare the wear quality of 4 different types of cloth (A-D) zSpecimens of th 4 different types of cloth, whose wearing quality is to be compared, are mounted into 4 position holders (1- 4) on the machine z4 sheets of emery paper is cut into quarters and used to cause the wearing of the cloth zThe response is the material loss (in tenths of a mg)

Data

ANOVA Table