# Example of General MANOVA

An automotive parts supplier assesses the usability and quality of the door locks that they provide. The locks are manufactured using two different methods at three plants. The production manager wants to determine whether the production method and the plant affect the final product. The production manager collects data on locks from each plant, produced by each method.

The manager collects data on the quality and usability of samples of locks. To assess how method and plant affect both response variables at the same time, the manager does a general MANOVA. The manager decides to use a significance level of 0.10 to decide which effects to examine in more detail.

1. Open the sample data, CarLockRatings.MTW.
2. Choose Stat > ANOVA > General MANOVA.
3. In Responses, enter 'Usability Rating' 'Quality Rating'.
4. In Model, enter Method Plant Method*Plant.
5. Click OK.

## Interpret the results

The p-values for the production method are statistically significant at the 0.10 significance level. The p-values for the manufacturing plant are not significant at the 0.10 significance level for any of the tests. The p-values for the interaction between plant and method are statistically significant at the 0.10 significance level. Because the interaction is statistically significant, the effect of the method depends on the plant.

### General Linear Model: Usability Ra, Quality Rati versus Method, Plant

MANOVA Tests for Method Test DF Criterion Statistic F Num Denom P Wilks’ 0.63099 16.082 2 55 0.000 Lawley-Hotelling 0.58482 16.082 2 55 0.000 Pillai’s 0.36901 16.082 2 55 0.000 Roy’s 0.58482 s = 1 m = 0.0 n = 26.5
MANOVA Tests for Plant Test DF Criterion Statistic F Num Denom P Wilks’ 0.89178 1.621 4 110 0.174 Lawley-Hotelling 0.11972 1.616 4 108 0.175 Pillai’s 0.10967 1.625 4 112 0.173 Roy’s 0.10400 s = 2 m = -0.5 n = 26.5
MANOVA Tests for Method*Plant Test DF Criterion Statistic F Num Denom P Wilks’ 0.85826 2.184 4 110 0.075 Lawley-Hotelling 0.16439 2.219 4 108 0.072 Pillai’s 0.14239 2.146 4 112 0.080 Roy’s 0.15966 s = 2 m = -0.5 n = 26.5
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