Basic Analysis > Oneway Analysis > Analysis of Means Methods > Analysis of Means for Scale
Publication date: 04/12/2021

## Analysis of Means for Scale

You can test for homogeneity of variation within groups using the following options:

ANOM for Variances

ANOM for Variances with Levene (ADM)

ANOM for Ranges

### ANOM for Variances

Use this method to compare group standard deviations (or variances) to the root mean square error (or mean square error). This method assumes that your data is approximately normally distributed. To use this method, each group must have at least four observations. For more information about the ANOM for Variances test, see Wludyka and Nelson (1997) and Nelson et al. (2005). For an example, see Example of an Analysis of Means for Variances Chart.

### ANOM for Variances with Levene (ADM)

This method provides a robust test that compares the group means of the absolute deviations from the median (ADM) to the overall mean ADM. Use ANOM for Variances with Levene (ADM) if you suspect that your data is non-normal and cannot be transformed to normality. ANOM for Variances with Levene (ADM) is a nonparametric analog of the ANOM for Variances analysis. For more information about the ANOM for Variances with Levene (ADM) test, see Levene (1960) or Brown and Forsythe (1974).

### ANOM for Ranges

Use this test to compare group ranges to the mean of the group ranges. This is a test for scale differences based on the range as the measure of spread. See Wheeler (2003).

Note: ANOM for Ranges is available only for balanced designs and specific group sizes. See Restrictions for ANOM for Ranges Test.

#### Restrictions for ANOM for Ranges Test

Unlike the other ANOM decision limits, the decision limits for the ANOM for Ranges chart uses only tabled critical values. For this reason, ANOM for Ranges is available only for the following:

groups of equal sizes

groups specifically of the following sizes: 2–10, 12, 15, and 20

number of groups between 2 and 30

alpha levels of 0.10, 0.05, and 0.01