Recall: OneWay ANOVA

1
Recall One-Way ANOVA

• Calculate and check residuals, eij Oi - Ei
• plot residuals vs treatments
• normal probability plot
• Perform ANOVA and determine if there is a
  difference in the means
• Identify which means are different using Tukeys
  procedure
• Model yij µ ai eij

2
Blocking

• Creating a group of one or more people, machines,
  processes, etc. in such a manner that the
  entities within the block are more similar to
  each other than to entities outside the block.
• Balanced design each treatment appears in each
  block.
• Model yij µ a i ßj eij

3
Example

• Robins Air Force Base uses CO2 to strip paint
  from F-15s. You have been asked to design a
  test to determine the optimal pressure for
  spraying the CO2. You realize that there are
  five machines that are being used in the paint
  stripping operation. Therefore, you have
  designed an experiment that uses the machines as
  blocking variables. You emphasized the
  importance of balanced design and a random order
  of testing. The test has been run with these
  results (values are minutes to strip one fighter)

4
ANOVA One-Way with Blocking

• Construct the ANOVA table
• Where,

5
Blocking Example

• Your turn fill in the blanks in the following
  ANOVA table (from Excel)
• Make decision and draw conclusions

6
Two-Way ANOVA

• Blocking is used to keep extraneous factors from
  masking the effects of the treatments you are
  interested in studying.
• A two-way ANOVA is used when you are interested
  in determining the effect of two treatments.
• Model yijk µ a i ßj (a ß)ijk eij

7
Two-Way ANOVA w/ Replication

• Your fame as an experimental design expert grows.
  You have been called in as a consultant to help
  the Pratt and Whitney plant in Columbus determine
  the best method of applying the reflective stripe
  that is used to guide the Automated Guided
  Vehicles (AGVs) along their path. There are two
  ways of applying the stripe (paint and coated
  adhesive tape) and three types of flooring
  (linoleum and two types of concrete) in the
  facilities using the AGVs. You have set up two
  identical test tracks on each type of flooring
  and applied the stripe using the two methods
  under study. You run 3 replications in random
  order and count the number of tracking errors per
  1000 ft of track. The results are as follows

8
Two-Way ANOVA Example

• Analysis is the same as with blocking, except we
  are now concerned with interaction effects

9
Two-Way ANOVA
10
Your Turn

• Fill in the blanks
• What does this mean?

11
What if Interaction Effects are Significant?

• For example, suppose a new test was run using
  different types of paint and adhesive, with the
  following results

12
Understanding Interaction Effects

• Graphical methods
• graph means vs factors
• identify where the effect will change the result
  for one factor based on the value of the other.