MANOVA/MANCOVA using SPSS · 2020. 7. 23. · MANOVA/MANCOVA using SPSS Overview MANOVA/MANCOVA - The unique aspect of MANOVA/ MANCOVA is that the variate (supervariable, or a linear

MANOVA/MANCOVA using SPSS

Presented by Nasser Hasan - Statistical Supporting Unit7/23/2020

[email protected]

Overview

• Brief introduction of MANOVA/MANCOVA.

• Performing the Analysis Using SPSS.


OverviewMANOVA/MANCOVA

- MANOVA tests whether there are statistically significant mean differences among groups on multiple DVs, [after controlling for covariate(s) – MANCOVA].

- MANOVA/ MANCOVA is a straightforward extension of ANOVA/ ANCOVA, in which main effects and interaction effects of categorical IV(s) are assessed on multiple DVs.


OverviewMANOVA/MANCOVA

- The unique aspect of MANOVA/ MANCOVA is that the variate (supervariable, or a linear combination of dependent variables, Y*) optimally combines multiple DVs into a single value that maximizes difference across groups.

- In other words, a new DV (variate, supervariable, linear combination of DVs) is created and then ANOVA is performed on the newly created DV (Y*).


OverviewMANOVA Test Statistics

• Most MANOVA packages output many of the approximate multivariate tests. The four most widely used measures for assessing statistical significance between groups on the independent variables are:o Roy’s Largest Rooto Wilk’s Lambdao Pillai’s Criterion o Hotelling’s Trace


OverviewMANOVA Test Statistics – What to Use?

- When there is only one factor with two levels, Wilks’ Lambda, Pillai’s trace, Hotelling’s trace, and Roy’s largest root are the same. The associated F might be slightly different, but the decision regarding whether effect is significant or not will be the same.

- As sample size decreases, unequal n’s appear, and the assumption of homogeneity of variance-covariance matrices is violated, Pillai’s criterion is more robust.

- In general, all four tests are relatively robust to violations of multivariate normality.- Here are two suggestions: - Roy’s root is not robust when the homogeneity of covariance matrix assumption is

untenable (Stevens, 1979)- When sample sizes are equal, the Pillai’s trace is the most robust to violations of

assumptions (Bray & Maxwell, 1985).

Stevens, J. P. (1979). Comment on Olson: choosing a test statistic in multivariate analysis of variance. Psychological Bulletin, 86, 355-360.Bray, J. H. & Maxwell, S. E. (1985). Multivariate analysis of variance. Sage university paper series on quantitative applications in the social sciences, 07-054. Newbury Park, CA: Sage.


OverviewMANOVA Assumptions

- Independence of observations- Reliability of continuous variables- Multivariate Normality (MVN) – MVN is assumed, but many times hard to

assess. Univariate normality does not guarantee multivariate normality, but if all variables meet the univariate normality requirement then departures from multivariate normality are inconsequential. As usual, with larger samples the central limit theorem suggests normality.

- Linearity among all pairs of DVs – Departure from linearity reduces power as the linear combinations of DVs do not maximize the difference between groups.

- Absence of multicollinearity and singularity among the dependent variables. - Equality of variance-covariance matrices – variance-covariance matrices for all

groups (non-significant result from Box’s M test)


Performing the Analysis Using SPSS - MANOVADataset

Please download the dataset using this link:

https://miami.box.com/s/tbt9oqs31certhwxr5l0z05a5h1q6uta

And open it in SPSS

https://miami.box.com/s/tbt9oqs31certhwxr5l0z05a5h1q6uta


Variables in the Dataset

- Disability: Degree of disability à categorical- Treat: Treatment (2 groups) à categorical- WRAT_R: Scores on reading subtest of Wide Range Achievement Test

à continuous- WRAT_A: Scores on arthimetic subtest of Wide Range Achievement

Test à continuous- IQ à continuous

Performing the Analysis Using SPSS - MANOVA


Research Question

- Main effect of the degree of disability:1. Disregarding the treatment, does degree of disability affect children’s reading and arithmetic scores? - Main effect of treatment:2. Disregarding degree of disability, does treatment affect children’s reading and arithmetic scores?- Interaction between treatment and disability: 3. Does the effect of treatment on children’s reading and arithmetic achievement differ as a function of degree of disability?



Analyze à General Linear Model à Multivariate



Move IVs to Fixed Factors and DVs to Dependent Variables



Click on Plots à Move each IV to Horizontal Axis à Click on Add



Click on Post Hoc à Move both IVs to Post Hoc Tests for



Click on EM Means à Move everything from the left to the rightClick on Compare main effects and choose the appropriate method



Click on Options and Choose needed descriptive



SPSS output


The Box’s M of 6.86 indicates that the homogeneity of covariance matrices across groups is assumed (F(15, 787.64) = .26, p = .99).


SPSS output


• The Main effect of disability is statistically significant (Wilks’ Λ = .26, F(4, 22) = 5.39, p = .004, partial η2 = .50)

• The Main effect of treatment is statistically significant (Wilks’ Λ = .14, F(2, 11) = 24.44, p < .01, partial η2 = .86)

• The interaction effect is not statistically significant (Wilks’ Λ = .91, F(4, 22) = .27, p = .89, partial η2 = .05).


SPSS output



APA-write up:


A 3 (Disability) × 2 (Treatment) between-subjects multivariate analysis of variance was performed on two dependent variables: WRAT-R and WRAT-A. Independent variables are levels of disability (Mild, Moderate, Severe) and treatment group (Treatment, Control groups). Results of evaluation assumptions of normality, homogeneity of variance-covariance matrices [The Box’s M of 6.86 indicates that the homogeneity of covariance matrices across groups is assumed (F(15, 787.64) = .26, p = .99], linearity, and multicollinearity were satisfactory. With the use of Wilks’ criterion, the combined DVs were significantly different by levels of disability (Wilk’s Λ = .26, F(4, 22) = 5.39, p = .004, partial η2 = .50) and treatment group (Wilk’s Λ = .14, F(2, 11) = 24.44, p < .01, partial η2 = .86). No significant interaction was found (Wilk’s Λ = .91, F(4, 22) = .27, p = .89, partial η2 = .05). To investigate the impact of each effect on the individual DVs, a univariate F-test using an alpha level of .05 was performed. Pair-wise comparison followed by a univariate F-test indicates that the significant difference was found between children with mild disability and those with severe disabilities, only in WRAT-A. The main effects of treatment were significant on both WRAT-R and WRAT-A, with approximately equal effect. In particular, treatment group showed significantly higher means on both WRAT-R and WRAT-A, when compared to control group.


Analyze à General Linear Model à Multivariate

Performing the Analysis Using SPSS - MANCOVA


Move IVs to Fixed Factors, DVs to Dependent Variables, and Covariates to Covariates



SPSS output


The Box’s M of 6.86 indicates that the homogeneity of covariance matrices across groups is assumed (F(15, 787.64) = .26, p = .99).


SPSS output



APA-write up:


A 3 (Disability) × 2 (Treatment) between-subjects multivariate analysis of covariance was performed on two dependent variables: WRAT-R and WRAT-A, after controlling for IQ scores. Independent variables are levels of disability (Mild, Moderate, Severe) and treatment group (Treatment, Control groups). Results of evaluation assumptions of normality, homogeneity of variance-covariance matrices [The Box’s M of 6.86 indicates that the homogeneity of covariance matrices across groups is assumed (F(15, 787.64) = .26, p = .99], linearity, and multicollinearity were satisfactory. With the use of Wilks’ criterion, the combined DVs were significantly different by levels of disability (Wilk’s Λ = .24, F(4, 20) = 5.15, p = .005, partial η2 = .51) and treatment group (Wilk’s Λ = .10, F(2, 10) = 45.13, p < .01, partial η2 = .90), after controlling for IQ. No significant interaction was found (Wilk’s Λ = .95, F(4, 20) = .27, p = .96, partial η2 = .03). To investigate the impact of each effect on the individual DVs, a univariate F-test using an alpha level of .05 was performed. The main effects of disability was significant on only WRAT-A. The main effects of treatment were significant on both WRAT-R and WRAT-A, showing a slightly higher effect on WRAT-A. Pair-wise comparison followed by a univariate F-test indicates that the significant difference was found between children with mild disability and those with severe disabilities, only in WRAT-A. The main effects of treatment were significant on both WRAT-R and WRAT-A, with approximately equal effect. In particular, treatment group showed significantly higher means on both WRAT-R and WRAT-A, when compared to control group.

Multiple Regression Using SPSS

Presented by Nasser Hasan - Statistical Supporting Unit6/3/2020

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MANOVA/MANCOVA using SPSS · 2020. 7. 23. · MANOVA/MANCOVA using SPSS Overview MANOVA/MANCOVA - The unique aspect of MANOVA/ MANCOVA is that the variate (supervariable, or a linear