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How Do I Perform ANOM Nonparametric Transformed Rank Test in Excel Using SigmaXL?

ANOM Nonparametric Transformed Ranks is complementary to a Kruskal-Wallis test. Note that it is not included as an option in the Kruskal-Wallis dialog because there is a difference in the statistic used (Kruskal-Wallis uses ANOVA on ranks, whereas the ANOM utilizes a normal transformed rank).

1. Open Customer Data.xlsx, click on Sheet 1 tab.

2. Click SigmaXL > Graphical Tools > Analysis of Means (ANOM) > ANOM Nonparametric
Transformed Ranks. Ensure that the entire data table is selected. If not, check Use Entire Data
Table.

3. Click Next. Ensure that Stacked Column Format is checked. Select Overall Satisfaction, click
Numeric Data Variable (Y) >>; select Customer Type, click Group Category (X) >>. Set Alpha
Level = 0.05.

4. Click OK. The ANOM Nonparametric Transformed Ranks chart is shown below:

5. Here we see that Customer Type 1 mean transformed rank satisfaction score is significantly
below the grand mean and Customer Type 2 is significantly higher. This is consistent with the
results that were observed in the Kruskal-Wallis analysis

6. The varying decision limits are due to the varying sample sizes for each Customer Type, with
smaller sample size giving wider limits in a manner similar to a control chart. If the data are
balanced, the decision limit lines will be constant.

7. Open ANOM Examples.xlsx, click on the Exponential Data – TR tab. This is exponential data,
Example 9.16 from the ANOM book with alpha level = 0.01 (used with author permission).

8. Click SigmaXL > Graphical Tools > Analysis of Means (ANOM) > ANOM Nonparametric
Transformed Ranks. Ensure that the entire data table is selected. If not, check Use Entire Data
Table.

9. Click Next. Ensure that Stacked Column Format is checked. Select Y, click Numeric Data
Variable (Y) >>; select X, click Group Category (X) >>. Set Alpha Level = 0.01.

10. Click OK. The ANOM Nonparametric Transformed Ranks chart is shown below:

11. X = 1 shows as significantly higher than the grand mean transformed rank and X = 3 is
significantly lower (at alpha = 0.01). These results match those given in the ANOM book.

12. By way of comparison, rerun the analysis using ANOM One-Way Normal (with alpha = 0.01).
The results are:

13. ANOM Normal fails to detect the significant differences in mean noted above.

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