# 10.4 - Minitab Express: One-Way ANOVA

10.4 - Minitab Express: One-Way ANOVAIn one research study, 20 young pigs are assigned at random among 4 experimental groups. Each group is fed a different diet. (This design is a completely randomized design.) The data are the pigs' weights in kg after being raised on these diets for 10 months. We wish to ask whether mean pig weights are the same for all 4 diets.

- \(H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4\)
- \(H_a:\) Not all \(\mu\) are equal

Feed_1 | Feed_2 | Feed_3 | Feed_4 |
---|---|---|---|

60.8 | 68.3 | 102.6 | 87.9 |

57.1 | 67.7 | 102.2 | 84.7 |

65.0 | 74.0 | 100.5 | 83.2 |

58.7 | 66.3 | 97.5 | 85.8 |

61.8 | 69.9 | 98.9 | 90.3 |

Contained in the Minitab Express file:

Note that in this file the data were entered so that each group is in its own column. In other words the responses are in a separate column for each factor level. In later examples you will see that Minitab Express will also conduct a one-way ANOVA if the responses are all in one column with the factor codes in another column.

## MinitabExpress – One-Way ANOVA

To perform an Analysis of Variance (ANOVA) test in Minitab Express:

- Open the ANOVA_ex.MTW data set.
- From the menu bar, select
**Statistics**>**ANOVA**>**One-Way ANOVA**. - Click the drop-down menu and select "
**Responses are in a separate column for each factor level**". - Double-click on the variables
*Feed_1*,*Feed_2*,*Feed_3*, and*Feed_4*to insert them into the "**Responses**" box. - Click the comparisons tab and check the box next to "
**Tukey (family error rate)**". - Click
**OK**.

The result should be the following output:

Null hypothesis | All means are equal |
---|---|

Alternative hypothesis | At least one mean is different |

Significance level | \(\alpha=0.05\) |

*Equal variances were assumed for the analysis*

Factor | Levels | Values |
---|---|---|

Factor | 4 | Feed_1, Feed_2, Feed_3, Feed_4 |

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

Factor | 3 | 4703.188 | 1567.72933 | 206.72 | <0.0001 |

Error | 16 | 121.340 | 7.58375 | ||

Total | 19 | 4824.528 |

S | R-sq | R-sq(adj) | R-sq(pred) |
---|---|---|---|

2.75386093 | 97.48% | 97.01% | 96.07% |

Factor | N | Mean | StDev | 95% CI |
---|---|---|---|---|

Feed_1 | 5 | 60.680 | 3.028 | (58.069, 63.291) |

Feed_2 | 5 | 69.240 | 2.958 | (66.629, 71.851) |

Feed_3 | 5 | 100.3400 | 2.1640 | (97.7292, 102.9508) |

Feed_4 | 5 | 86.380 | 2.782 | (83.769, 88.991) |

*Pooled StDev = 2.75386093*

Factor | N | Mean | Grouping | |||
---|---|---|---|---|---|---|

Feed_3 | 5 | 100.34 | A | |||

Feed_4 | 5 | 86.38 | B | |||

Feed_2 | 5 | 69.24 | C | |||

Feed_1 | 5 | 60.68 | D |

*Means that do not share a letter are significantly different.*

Difference of Levels | Difference of Means | SE of Difference | 95% CI | T-Value | Adjusted P-Value |
---|---|---|---|---|---|

Feed_2-Feed_1 | 8.560 | 1.742 | (3.572, 13.548) | 4.91 | 0.0008 |

Feed_3-Feed_1 | 39.660 | 1.742 | (34.672, 44.648) | 22.77 | <0.0001 |

Feed_4-Feed_1 | 25.700 | 1.742 | (20.712, 30.688) | 14.76 | <0.0001 |

Feed_3-Feed_2 | 31.100 | 1.742 | (26.112, 36.088) | 17.86 | <0.0001 |

Feed_4-Feed_2 | 17.140 | 1.742 | (12.152, 22.128) | 9.84 | <0.0001 |

Feed_4-Feed_3 | -13.960 | 1.742 | (-18.948,-8.972) | -9.02 | <0.0001 |

*Individual confidence level = 98.87%*

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