﻿ Analysis of Variance (ANOVA) with Post-Hoc Tests : WinSTAT Statistics Software Add-In for Excel the Statistics Add-In for Microsoft® Excel

## 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.