##
Example 13-3
Section* *

A researcher was interested in investigating whether Holocaust survivors have more sleep problems than others. She evaluated \(n = 120\) subjects in total, a subset of them were Holocaust survivors, a subset of them were documented as being depressed, and another subset of them were deemed healthy. (Of course, it's not at all obvious that these are mutually exclusive groups.) At any rate, all *n* = 120 subjects completed a questionnaire about the quality and duration of their regular sleep patterns. As a result of the questionnaire, each subject was assigned a Pittsburgh Sleep Quality Index (PSQI). Here's a dot plot of the resulting data:

Is there sufficient evidence at the \(\alpha = 0.05\) level to conclude that the mean PSQI for the three groups differ?

### Answer

We can use Minitab to obtain the analysis of variance table. Doing so, we get:

Source | DF | SS | MS | F | P |
---|---|---|---|---|---|

Factor | 2 | 1723.8 | 861.9 | 61.69 | 0.000 |

Error | 117 | 1634.8 | 14.0 | ||

Total | 119 | 3358.6 |

Since *P* < 0.001 ≤ 0.05, we reject the null hypothesis of equal means in favor of the alternative hypothesis of unequal means. There is sufficient evidence at the 0.05 level to conclude that the mean Pittsburgh Sleep Quality Index differs among the three groups.

##
Minitab^{®}

##
Using Minitab
Section* *

There is no doubt that you'll want to use Minitab when performing an analysis of variance. The commands necessary to perform a one-factor analysis of variance in Minitab depends on whether the data in your worksheet are "stacked" or "unstacked." Let's illustrate using the learning method study data. Here's what the data would look like unstacked:

std1 | osm1 | shk1 |
---|---|---|

51 | 58 | 77 |

45 | 68 | 72 |

40 | 64 | 78 |

41 | 63 | 73 |

41 | 62 | 75 |

That is, the data from each group resides in a different column in the worksheet. If your data are entered in this way, then follow these instructions for performing the one-factor analysis of variance:

- Under the
`Stat`menu, select`ANOVA`. - Select
`One-Way (Unstacked)`. - In the box labeled
**Responses**, specify the columns containing the data. - If you want dot plots and/or boxplots of the data, select
`Graphs...` - Select
`OK`. - The output should appear in the Session Window.

Here's what the data would look like stacked:

Method | Score |
---|---|

1 | 51 |

1 | 45 |

1 | 40 |

1 | 41 |

1 | 41 |

2 | 58 |

2 | 68 |

2 | 64 |

2 | 63 |

2 | 62 |

3 | 77 |

3 | 72 |

3 | 78 |

3 | 73 |

3 | 75 |

That is, one column contains a grouping variable, and another column contains the responses. If your data are entered in this way, then follow these instructions for performing the one-factor analysis of variance:

- Under the
`Stat`menu, select`ANOVA`. - Select
`One-Way`. - In the box labeled
**Response**, specify the column containing the responses. - In the box labeled
**Factor**, specify the column containing the grouping variable. - If you want dot plots and/or boxplots of the data, select
`Graphs...` - Select
`OK`. - The output should appear in the Session Window.