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Stat 470-8

Stat 470-8. Today: Greco-Latin Squares, some examples Assignment 2: 2.8, 2.15 (2-way ANOVA only) 2.16 2.20 (use only transformations discussed in class) 2.27 AND 2.25 & 2.26. Example:.

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Stat 470-8

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  1. Stat 470-8 • Today: Greco-Latin Squares, some examples • Assignment 2: • 2.8, • 2.15 (2-way ANOVA only) • 2.16 • 2.20 (use only transformations discussed in class) • 2.27 • AND 2.25 & 2.26

  2. Example: • A 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 • Experiment (Box, Hunter and Hunter, 1978) was run to compare the wear quality of 4 different types of cloth (A-D) • Specimens 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 • 4 sheets of emery paper is cut into quarters and used to cause the wearing of the cloth • The response is the material loss (in tenths of a mg)

  3. Data

  4. Two Blocking Variables; Two Factors • Can have 2 blocking factors and 2 experiment factors • Experiment design approach superimposes 2 latin squares

  5. Graeco-Latin Squares Design • Situation: • Have 2 blocking factors - one for rows and one for columns • Have 2 experimental factors • Each factor has k levels • Design is arranged so that each pair of level settings of the experiment factors appears exactly one time in each row and each column • The levels of the two blocking factors are assigned at random to the columns and rows

  6. Model: • i, j=1,2,…,k • l indicates the index for the Latin letter in the (i,j)th cell • m indicates the index for the Latin letter in the (i,j)th cell

  7. Notes • No interaction, since interactions cannot be estimated in an un-replicated experiment • Usual assumptions apply • Can do multiple comparisons in usual way, but must adjust the degrees of freedom

  8. Hypotheses • For the factor corresponding to the Latin letter • For the factor corresponding to the Greek letter

  9. ANOVA Table

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

  11. Example: • A 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 • Experiment (Box, Hunter and Hunter, 1978) was run to compare the wear quality of 4 different types of cloth (A-D) • Specimens 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 • 4 sheets of emery paper is cut into quarters and used to cause the wearing of the cloth • The response is the material loss (in tenths of a mg)

  12. Data

  13. ANOVA Table

  14. Multiple Comparisons

  15. Multiple Comparisons

  16. Example 1 • An engineer is conducting an experiment on eye focus time. He is interested in the effect of the distance of an object from the eye on the focus time • Four different distances are of interest (4, 6, 8 and 10 feet) • There are five individuals available to participate in the experiment • Design an experiment to investigate the impact of distance on focus time (includes treatments, experimental units, randomization and the model to be fit) • What is the name of your experiment design?

  17. Example 2 • A chemist wishes to run an experiment to see how the standing time of the chemicals (2, 4, 6, 8 and 10 minutes), acid concentrations (50, 100, 150, 200 and 250 ionic parts per million) and also the catalyst concentration (5, 20, 15, 20 and 25 % of volume) impact the yield of a chemical process • There are 5 batches of raw material available, each which can be split into 5 sub-batches • Design an experiment to investigate the impact of distance on focus time (includes treatments, experimental units, randomization and the model to be fit) • What is the name of your experiment design?

  18. Example 3 • Parking is a problem at the University of Michigan, particularly in the Church Street lot • There are two types of parking permit for the Church Street lot: Blue and Gold parking • There are always lots of empty gold parking spots in the lot…too many if you ask me • The would be more parking for your instructor if there were fewer gold spots • Design an experiment to estimate the number of empty gold spots as a function of the time of day

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