Topic: One Way Anova

Data Set: gballs.sav

Example: Golf Ball Distances

Goal: Determine if brand affects the distance a golf ball travels.

Suppose the USGA wants to compare the mean distances associated with four different brands of golf balls when struck with a driver. A completely randomized design is employed, with Iron Byron, the USAGA’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 shown 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
  1. Enter the data correctly. The first column (labeled distance) will have the 40 distances in it. The second column (labeled brand) will be the brand. The first 10 rows will be 1’s, the second 10 rows will have a 2, etc.
  2. Summarize the data and visually inspect the data with side-by-side boxplots. The descriptive statistics and the side-by-side boxplot can both be produced at the same time if one uses the Explore… options. That is, using the following menu selections Analyze\Descriptives\Explore…. In the windows dialog box select the distance variable (Dependent List) as the dependent variable and brand as the factor variable (Factor List) and check the normality tests and plot for normality tests. Click Continue and click OK. The following box plot will appear at the last part of the SPSS output.

  1. State Hypotheses:

H0: m 1=m 2=m 3=m 4

Ha: At least two means differ

  1. To perform the ANOVA click on Analyze\Compare Means\One Way ANOVA. Put distance in the Dependent box and put brand in the factor box. Also, click the Option… button and check the Homogeneity of Variance box to check equal variances assumption and Descriptive Statistics box for descriptive statistics.