**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 |

- 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. - 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.

- State Hypotheses:

H_{0}: m _{1}=m
_{2}=m _{3}=m _{4}

H_{a}: At least
two means differ

- 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.

** **