STEPS FOR CONDUCTING AN ANOVA FOR A TWO-FACTOR FACTORIAL EXPERIMENT (PART I)

ACTIVITY

Suppose that USGA tests four different brands (A, B, C, D) of galf balls and two different clubs (driver, five-iron) in a completely randomized design. Each of the eight Brand-Club combinations (treatments) is randomly and independently assigned to four experimental units, each experimental unit consisting of a specific position in the sequence of hits by Iron Byron. The distance response is recorded for each of the 32 hits and the results are shown below.

Use the following steps and Statlets window given above, to carry out ANOVA procedure to appropriate for this two-factor factorial experiment.

First we will carry out one-way ANOVA for each treatment.

STEP 1 of the Conduction ANOVA for the Two-factor Factorial Experiment:

• One-way ANOVA for the "Brand"
  • Step 1. Enter the data:
    • Double click on "Col_1" and relace it with "Brand A".
    • Double click on "Col_2" and relace it with "Brand B".
    • Double click on "Col_3" and relace it with "Brand C".
    • Double click on "Col_4" and relace it with "Brand D".
    • Enter the data for each brand.
  • Step 2. Check the model assumptions:
    • Select the "Scatterplot" menu option and interpret the output.
    • Select the "Stats" menu option and interpret the output.
    • Select the "Boxplot" menu option and interpret the output.
  • Step 3. Create an ANOVA table:
    • Select the "ANOVA" menu option and interpret the output.
    • Report the F-ratio that will be used for testing the equality of the means for the four brands.
    • Report the p-value that will be used for testing the equality of the means for the four brands. What is your conclusion.
  • Step 4 & 5. Compare the means (multiple comparison) or look for the reason of failing to reject:
    • Select the "Means table" menu option.
    • Click on the "Options" button and select the multiple comparison method that you would like to use.
    • Click "OK". Interpret the output and report which barnds are different.
    • Select the "Means plot" menu option.
    • Click on the "Options" button and select the multiple comparison method that you would like to use.
    • Click "OK". Interpret the output and report which barnds are different.

• One-way ANOVA for the "Club"
  • Step 1. Enter the data:
    • Double click on "Col_5" and relace it with "Driver".
    • Double click on "Col_6" and relace it with "Five-iron".
    • Enter the data for each brand.
  • Step 2. Check the model assumptions:
    • Select the "Scatterplot" menu option and interpret the output.
    • Select the "Stats" menu option and interpret the output.
    • Select the "Boxplot" menu option and interpret the output.
  • Step 3. Create an ANOVA table:
    • Select the "ANOVA" menu option and interpret the output.
    • Report the F-ratio that will be used for testing the equality of the means for the four brands.
    • Report the p-value that will be used for testing the equality of the means for the four brands. What is your conclusion.
  • Step 4 & 5. Compare the means (multiple comparison) or look for the reason of failing to reject:
    • Select the "Means table" menu option.
    • Click on the "Options" button and select the multiple comparison method that you would like to use.
    • Click "OK". Interpret the output and report which barnds are different.
    • Select the "Means plot" menu option.
    • Click on the "Options" button and select the multiple comparison method that you would like to use.
    • Click "OK". Interpret the output and report which barnds are different.

CLICK HERE TO CONTINUE TO CARRY OUT ANOVA FOR THE TWO-FACTOR FACTORIAL EXPERIMENT