MANOVA and MANCOVA (Dr See Kin Hai)1. To determine the effects (main and interacting) of one or more

independent variables on several dependent variables concurrently.2. 1-way ANOVA is used for 1 independent variable with more than 2–level

(e.g. achievement scores depend on race (3 levels): Malay, Chinese, Dusun)

3. 2 or 3-way ANOVA is used for multiple independent variables (e.g. Attitude and Perception affecting Achievement Scores)

4. ANCOVA is used to covariate out the effect of pretest on posttest scores5. MONOVA / MANCOVA is used to determine the effects of 1 or more indep

vars on several dep vars simultaneously.

Example: You are to determine the effects of students’ [section= 1,2,3], upper or lower division [lowup: 1=lower, 2=upper] on student’s scores (Dep Vars 0-10) on the 5 quizzes [quiz1 to quiz5] {removing or covariate out [gpa: 1-4] . (Use grades.sav) not in this example}

How to run MANOVA and MANCOVA1. [Analyze] then [General Linear Model], then [Multivariate]2. This study has 2 independent variables ( Section (1,2,3), Lowup(1,2)) enter

into [Fixed Factors Box] and 5 dependent variables (Quiz1–Quiz5) enter into [Dependent variables Box].

3. To factor out the effect of [GPA] enter into [Covariates Box]4. Select [Plots] to see plots of means of dep vars as determined by different

levels of the factors. (normally without covariate to see the actual means instead of adjusted means)

1

5. Select [Model] which calls up the screen below.

5. To see the main effects and the interactions select [Custom] and move (section, lowup,gpa) to Model Box.

6. For [Sum of Squares], you can select [Type I,II, III or IV], the default is [Type III], [Type IV] for missing cells with no participants.

7. As for the [Plots] is to plot the means of dep vars by different factors.

8. Move [Factors] to [Horizontal Axis] and [Separate Lines] first then for different levels of factor then [Separate Plots] for many different plots then [Add] and [Continue].

9. Click on [Post Hoc] to go to [Post Hoc Multiple Comparison] dialog box to determine which levels of a variable are sig different from other levels of that variable. The tests are repeated for other factors. (Post hoc tests not for covariate)

2

Fig 2

Fig 3

Fig 1

10. Move the [Factors] by 1 or more into [Post Hoc Tests for] and you can run any of the 18 tests selected.

Examples of some of the 18 tests

11. The post hoc tests assumed that the variances of all the cells are equal

12. To check, click on [Options] then [Homogeneity tests].

3

Fig 4

13. Move the factors to [Display Means for] then means for each dep var at each level will be shown. If covariate is included, then the means will be adjusted.

14. [Factors and Factor Interactions] (Overall) means grand mean across all cells

15. [Compare main effects] produces a series of post hoc tests examining differences between cells in each factor

How to run MANOVA:Dependent variables: quiz1 to quiz5Independent variables: section (1,2 and 3), status= lowup (lower =1, upper-division =2)[Fig 1]

1. Move [quiz1 to quiz5] into [Dependent variables] box

4

Fig 5

2. Move [section], [lowup] into [Fixed Factors] box, then [Plots][Fig 3]

1. Move [Section] into [Horizontal Axis]2. Move [lowup] into [Separate Lines] then select [Add] then [Continue]

[Fig 1]1. Select [Post Hoc]

[Fig 4]1. [section] into [Post Hoc Tests for] select [Bonferroni], [Tukey] then

[Continue][Fig 1]

1. Select [Options][Fig 5]

1. [section] and [lowup] into [DisplayMeans for] then select [Descriptive stat], [Estimates of effect size], [Parameter estimates], [Observed power], [Homogeneity tests] then [Continue]

[Fig 1]1. [OK]

Interpretation of output

(a) Bewteen-Subjects Factors

(b) Descriptive Staatistics

(c) Box’s Test of Equality of Covariance Maatrices

5

(d) Multivariate Tests

(e) Lavine;s Test of Equality of Error Variances

(f) Tests of Between-Subjects Effects

6

7

(g) Parameter Estimates

(h) Estimated Marginal Means

8

(i) Post Hoc Tests

Coursework (Use Work18.sav)

You are interested to find out the influence of history on variables related to community attachment. 388 community residents located across 2 areas of

9

differing settlement period were asked to complete a social support scale, a sense of community scale and were required to state the size of their community networks. It was hypothesized that people living in the community settled prior to 1850 would have significantly larger networks, and higher levels of social support and sense of community than those people residing in the community settled after 1850. The independent variable was period of settlement with 2 levels (1800-1850 and 1851-1900) and the dependent variables were sense of community, quality of social support and network size. (Conceptually and theoretically these dependent variables were related).

Hint:1. [Analyze] [General Linear Model] [Multivariate] to open the dialogue

box (Fig 1)2. Move (network, soc, ss) into [Dependent Variables] box3. Move Independent variables (history) into [Factors] box4. Click [Model] under [Specify Model] [Full factorial] [Type III]

[Continue] [Post Hoc] (Fig 1) 5. Fig 4, move (history) into [Post Hoc Test for] [REG-WF]6. Fig 5, move (history) [Display Means for ] refer to steps above….

10