# 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 Rating, Quality Rating versus Method, Plant

## MANOVA Tests for Method

Test
Statistic

DF
CriterionFNumDenomP
Wilks'0.6309916.0822550.000
Lawley-Hotelling0.5848216.0822550.000
Pillai's0.3690116.0822550.000
Roy's0.58482
s = 1    m = 0    n = 26.5

## MANOVA Tests for Plant

Test
Statistic

DF
CriterionFNumDenomP
Wilks'0.891781.62141100.174
Lawley-Hotelling0.119721.61641080.175
Pillai's0.109671.62541120.173
Roy's0.10400
s = 2    m = -0.5    n = 26.5

## MANOVA Tests for Method*Plant

Test
Statistic

DF
CriterionFNumDenomP
Wilks'0.858262.18441100.075
Lawley-Hotelling0.164392.21941080.072
Pillai's0.142392.14641120.080
Roy's0.15966
s = 2    m = -0.5    n = 26.5