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STEPS FOR CONDUCTING AN ANOVA FOR A COMPLETELY RANDOMIZED DESIGN

1. Check for randomization and independent samples

2. Check assumptions of normality and equal variance

3. Create an ANOVA table and carry out F-test

4. If you reject the hypothesis that the means are same:

Conduct a multiple comparison procedure.
Construct confidence intervals for mean(s)

5. If you fail to reject the hypothesis that the means are same then:

The treatment means are equal
The treatment means are not equal. Increase the sample size, consider other factor

ACTIVITY

Suppose that USGA wants to compare the mean distances associated with four different barnds of golf balls when struck with a driver. A completely randomized design is employed, with Iran Byron, the USGA's robotic golfer, using a driver to hit a random sample of 10 balls of each brand in a random sequence. The distance is recorded for each hit, and the results are given below.

Brand A	Brand B	Brand C	Brand D
251.2	263.2	269.7	251.6
245.1	262.9	263.2	248.6
248.0	265.0	277.5	249.4
251.1	254.5	267.4	242.0
260.5	264.3	270.5	246.5
250.0	257.0	265.5	251.3
253.9	262.8	270.7	261.8
244.6	264.4	272.9	249.0
254.6	260.6	275.6	247.1
248.8	255.9	266.5	245.9

Use the following steps and Statlets window given above, to carry out ANOVA procedure to compare the mean distances of the four brands. Use a significance level of 0.10.

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. Compare the means (multiple comparison):
- 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.