Steps of conducting MANOVA in SPSS

Running one-way MANOVA:

RQ: A researcher wants to compare differences in score on the reading subtest of the Wide Range Achievement Test (WRAT-R) and score on the arithmetic subtest (WRAT-A) between students with treatment and those without treatment.

  1. IV: Treatment vs. Not (2 levels)
  2. DVs: WRAT-R and WRAT-A
  • From the menu, click on Analyze -> General Linear Model -> Multivaraite…
  • In the appearance window, move WRAT_R and WRAT_A (Dependent variables) to the Dependent Variables: box & Treat (Independent variable) to the Fixed Factor(s):
  • Then, hit the Options… on bottom right menu.  From a new window, move Treat (IV) to Display Means for: -> check Compare main effects -> check Estimates of effect size and Homogeneity tests, hit Continue and then hit Paste.

Output:

Write up (APA format):

A one-way Multivariate Analysis of Variance (MANOVA) was performed to examine whether differences in score on the reading subtest of the Wide Range Achievement Test (WRAT-R) and score on the arithmetic subtest (WRAT-A) between students with treatment and those without treatment. Results of evaluation assumptions of normality, homogeneity of variance-covariance matrices [The Box’s M of 1.53 indicates that the homogeneity of covariance matrices across groups is assumed (F(3, 46080) = .04, p = .99], linearity, and multicollinearity were satisfactory. With the use of Wilks’ criterion, the combined DVs were significantly different by levels of treatment group (Wilk’s Λ = .34, F(2, 15) = 14.83, p < .01, partial η2 = .66). A follow-up analysis using an alpha level of .025 shows that a significant group difference exists on both WRAT-R (F(1, 16) = 31.36, p < .01, partial η2 = .66) and WRAT-A (F(1, 16) = 13.91, p < .01, partial η2 = .47), demonstrating that treatment group had significantly higher means on WRAT-R and WRAT-A than control group.  A comparison of effect size indicates that WRAT-R is more important to determine treatment effect than WRAT-A in their linear combination. 

Two-way MANOVA:

RQ: A researcher wants to compare differences in score on the reading subtest of the Wide Range Achievement Test (WRAT-R) and score on the arithmetic subtest (WRAT-A) between students with treatment and those without treatment.  Then, a researcher wants to see whether treatment effect differs by degree of disability (i.e., mild, moderate, and severe).

  1. IV1: Treatment vs. Not (2 levels)
  2. IV2: Disability (3 levels – Mild, Moderate, Severe)
  3. DVs: WRAT-R and WRAT-A
  1. From the menu, click on Analyze -> General Linear Model -> Multivaraite…
    1. In the appearance window, move WRAT_R and WRAT_A (Dependent variables) to the Dependent Variables: box & Treat & Disability (Independent variables) to the Fixed Factor(s):
  • Then, hit the Options… on bottom right menu.  From a new window, move Treat, Disability, and Treat*Disability (IV) to Display Means for: -> check Compare main effects -> check Estimates of effect size and Homogeneity tests.
  • Hit Continue and then hit Paste.
  • Edit syntax for post-hoc analysis for interaction effect.

Output:

Write up (APA format):

A two-way Multivariate Analysis of Variance (MANOVA) was performed to examine whether the reading subtest of the Wide Range Achievement Test (WRAT-R) and score on the arithmetic subtest (WRAT-A) differ by treatment status, disability, and their interaction.

Results of evaluation assumptions of normality, homogeneity of variance-covariance matrices [The Box’s M of 1.53 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 .025 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.