## Analysis of Variance (ANOVA)

This command is used to perform a univariate one-factor or two-factor analysis of variance. This means that a single variable (measured at the interval level and assumed to have a normal distribution) is grouped according to the values of one or two independent variables. The arithmetic mean of the dependent variable will generally be different for the different groups. The analysis of variance determines to what extent the difference is significant. The analysis of variance is valid only if the groups can be assumed to have equal variances. A Bartlett test is automatically performed to test this assumption.

#### Sample Results as an Excel Table:

Analysis of Variance | |||||

Variable: | Price | ||||

grouped by: | Size | ||||

Sum of Squares | Degrees of Freedom | Mean Square | F | P | |

Between Groups | 641822014.5 | 2 | 320911007.3 | 13.96376784 | 8.08847E-06 |

Within Groups | 1585736726 | 69 | 22981691.68 | ||

Total | 2227558740 | 71 | 31374066.77 | ||

Bartlett-Test for homogeneity of variances | |||||

Chi-square | Degrees of Freedom | P | |||

20.754688 | 2 | 3.11298E-05 | |||

Multiple comparisons | |||||

Method: | LSD | Significance (p): | 0.05 | ||

Critical differences in mean between group pairs (upper right) | |||||

and calculation of significances (lower left): | |||||

(Mean) | compact | medium | large | ||

compact | 3832.5 | ---- | 3095.449373 | 3130.427312 | |

medium | 6129.1 | no | ---- | 2513.022437 | |

large | 11277.71429 | yes | yes | ---- | |

Homogeneous Subsets | |||||

1 | 2 | ||||

compact | * | ||||

medium | * | ||||

large | * |

A two-way analysis of variance is also possible, with or without interaction.