• to test whether any of the group means are statistically different from the overall (sample) mean
 • to test whether any of the group standard deviations are statistically different from the root mean square error (RMSE)
 • to test whether any of the group ranges are statistically different from the overall mean of the ranges
Note: Within the Contingency platform, you can use the Analysis of Means for Proportions when the response has two categories. For details, see the Contingency Analysis section.
 • ANOM
 • ANOM with Transformed Ranks
This is the nonparametric version of the ANOM analysis. Use this method if your data is clearly non-normal and cannot be transformed to normality. ANOM with Transformed Ranks compares each group’s mean transformed rank to the overall mean transformed rank. The ANOM test involves applying the usual ANOM procedure and critical values to the transformed observations.
Suppose that there are n observations. The transformed observations are computed as follows:
 • Rank all observations from smallest to largest, accounting for ties. For tied observations, assign each one the average of the block of ranks that they share.
 • Denote the ranks by R1, R2, ..., Rn.
 • The transformed rank corresponding to the ith observations is:
The ANOM procedure is applied to the values Transformed Ri. Since the ranks have a uniform distribution, the transformed ranks have a folded normal distribution. For details, see Nelson et al. (2005).
 • ANOM for Variances
 • ANOM for Variances with Levene (ADM)
 • ANOM for Ranges
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 details about the ANOM for Variances with Levene (ADM) test, see Levene (1960) or Brown and Forsythe (1974).
 • 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
 • an upper decision limit (UDL)
 • a lower decision limit (LDL)
 • a horizontal (center) line that falls between the decision limits and is positioned as follows:
 ‒ ANOM: the overall mean
 ‒ ANOM with Transformed Ranks: the overall mean of the transformed ranks
 ‒ ANOM for Variances: the root mean square error (or MSE when in variance scale)
 ‒ ANOM for Variances with Levene (ADM): the overall absolute deviation from the mean
 ‒ ANOM for Ranges: the mean of the group ranges
Select an option from the most common alpha levels or specify any level with the Other selection. Changing the alpha level modifies the upper and lower decision limits.
 • For ANOM, creates a report showing group means and decision limits.
 • For ANOM with Transformed Ranks, creates a report showing group mean transformed ranks and decision limits.
 • For ANOM for Variances, creates a report showing group standard deviations (or variances) and decision limits.
 • For ANOM for Variances with Levene (ADM), creates a report showing group mean ADMs and decision limits.
 • For ANOM for Ranges, creates a report showing group ranges and decision limits.
(Only for ANOM for Variances) Changes the scale of the y-axis from standard deviations to variances.
 • Show Decision Limits shows or hides decision limit lines.
 • Show Decision Limit Shading shows or hides decision limit shading.
 • Show Center Line shows or hides the center line statistic.
 • Point Options
 ‒ Show Needles shows the needles. This is the default option.
 ‒ Show Connected Points shows a line connecting the means for each group.
 ‒ Show Only Points shows only the points representing the means for each group.