How Do I Create a One-Way ANOVA & Means Matrix in Excel Using SigmaXL?

One-Way ANOVA & Means Matrix

1. One-Way ANOVA and Means Matrix allows you to quickly do multiple pairwise comparisons. The One-Way ANOVA tests H0: μ1 = μ2 = μ3; Ha: at least one pairwise set of means are not equal.
2. Open Customer Data.xls, click on Sheet 1 tab (or press F4 to activate last worksheet).
3. Click SigmaXL > Statistical Tools > One-Way ANOVA & Means Matrix. Ensure that the entire data table is selected. If not, check Use Entire Data Table.
4. Click Next. Ensure that Stacked Column Format is checked. Select Overall Satisfaction, click Numeric Data Variable (Y) >>; select Customer Type, click Group Category (X) >>.



5. Click OK. The results are shown below:




6. The ANOVA p-value of 0.0000 tells us that at least one pairwise set of means are not equal. From the means matrix, we conclude that Mean Overall Satisfaction is significantly different between Customer Type 2 and 3, as well as 1 and 2.
7. A graphical view of the Overall Satisfaction Mean and 95% Confidence Intervals are given to complement the Means Matrix. The fact that the CI’s for Customer Type 2 do not overlap those of Type 1 or 3, clearly shows that Customer Type 2 has a significantly higher mean satisfaction score. The overlap of CI’s for Type 1 and 3 shows that the mean satisfaction scores for 1 and 3 are not significantly different.
8. The R-Square (R-Sq) value of 20.95% indicates that Customer type “explains” approximately 21% of the variation in Overall Satisfaction. We need to “drill down” to understand the root causes and best practices associated with Customer Type 2.
9. Note that the p-value for 2-3 is slightly different than the previous two sample test result because the variances from all 3 customer types are “pooled” here. This also results in slightly different confidence intervals. One-Way ANOVA & Means Matrix assume equal variance, but analysis above in Part H indicates that this assumption is not true, so this analysis should be treated with caution. An alternative nonparametric test is the Kruskal-Wallis test for Medians (SigmaXL > Statistical Tools > Nonparametric Tests > Kruskal-Wallis Median Test) or Mood’s Median (SigmaXL > Statistical Tools > Nonparametric Tests > Mood’s Median Test). These are discussed in Part M.
   
   Note also that the means matrix p-values could easily trigger type I errors when the number of X levels gets large. You should only consider the results of the Means Matrix if the ANOVA p-value is < .05.