Use Test for Equal Variances to assess the equality (also called the homogeneity) of the variances or the standard deviations of multiple populations. For example, a lumber distributor wants to compare the variation of beams that are cut by three different sawmills. The distributor measures the length of the beams to determine whether the consistency of the beam lengths differs among the sawmills.

Both the variance and the standard deviation measure the variability in a sample or a population. (The standard deviation is the square root of the variance.) If the variances are significantly different, then the standard deviations are also significantly different, and vice versa.

Many statistical procedures, including analysis of variance (ANOVA), assume that the different populations have the same variance. Unequal variances may affect inferences depending on:

·    whether your model includes fixed or random factors

·    how different the sample sizes are

·    which multiple comparison procedure you use

Inequality of variances may only slightly affect an ANOVA if the model contains only fixed factors and has equal or nearly equal sample sizes. However, ANOVA involving random effects may be substantially affected by unequal variances.

A study was done to compare experienced and inexperienced drivers on three types of roads. The two factors are:

·    Driving experience. Eight inexperienced drivers and eight experienced drivers took part in the study. The two levels were coded as experience =1 and inexperience = 0.

·    Road type. Each driver drove on one of three road types. The three levels were coded as first class road = 1, second class road = 2, and dirt road = 3.

The number of steering corrections each driver made on each type of road was recorded. The response variable is Corrects. The data set is given below:

                     Road Type

Experience      1       2       3

0               4      23      16

               18      15      27

                8      21      23

               10      13      14

1               6       2      20

                4       6      15

               13       8       8

                7      12      17

Data: Driving.MTW (available in the Sample Data folder).