Example 10.9 Employee Empowerment at ArmCo Company

1. Example 10.9Employee Empowerment at ArmCo Company One-Way ANOVA

3. Background Information We discussed the ArmCo Company in Example 10.6. It initiated an employee empowerment program at its Midwest plant, and the reaction from employees was basically positive. Let�s assume now that ArmCo has initiated this policy in all five of its plants - in the South, Midwest, Northeast, Southwest, West - and several months later it wants to see whether the policy is being perceived equally by employees across the plants.

4. Empower2.xls Random samples of employees at the five plants have been asked to rate the success of the empowerment policy on a scale of 1 to 10 scale, 10 being the most favorable rating. The data appears in this file and here. Is there any indication of mean differences across the plants? If so, which plants appear to differ from which others?

5. Solution First, note that the sample sizes are not equal. This could be because some employees opted not to cooperate or it could be due to other reasons. Fortunately, equal sample sizes are not necessary for the ANOVA test. The output consists of three basic parts: summary statistics the ANOVA table confidence intervals The next slide contains this output.

7. Summary Statistics The summary statistics show that the Southwest has the largest mean rating (6.745), and the Northeast has the smallest (4.140), with the others in between. The sample standard deviations (or variances) vary somewhat across the plants, but not enough to invalidate the procedure. The side-by-side boxplots in the figure on the next slide illustrate these summary measures graphically. However, there is too much overlap to tell whether the differences are statistically significant.

8. Boxplots

9. ANOVA Tables A one-way analysis variance or one-way ANOVA is the procedure for for analyzing the differences between more than two population means. A one-way ANOVA is also used in randomized experiments where a single population is treated in one of several ways. The data analysis in these two situations is identical; only the interpretation of the results differ.

10. ANOVA Tables -- continued The one-way ANOVA procedure is usually run in two stages. The first stage tests the null hypothesis. If the p-value is not sufficiently small, then there is not enough evidence to reject the equal-means hypothesis, and the analysis stops. If the p-value is sufficiently small, we can conclude with some assurance that the means are not all equal. In this example, the ANOVA table in rows 26-28 show the elements for the F test of equal means.

11. Results The Total variation in row 28 is based on the total variation of all observations around the grand mean in cell I15, and is used mainly to aid in calculations. The grand mean is the sample mean of all observations. The F-ratio for the test is 10.480 with a corresponding p-value of 0.000. This leaves practically no doubt that the five population means are not all equal.

12. Results -- continued The 95% confidence intervals in rows 32-41 indicate which plants differ significantly from which others. For example, the mean of the Southwest plant is somewhere between 1.455 and 3.756 rating points above the mean for the Northeast plant. The Southwest plant is rated significantly higher than the Northeast, West and Midwest plants; and the South and Midwest plants are also rated significantly higher than the Northeast plant. Now it is up to ArmCo management to decide whether the magnitude of these differences are practically significant, and, if so, what they can do to increase employee perception at the low-rated plants.