Mastering One-Way MANCOVA Using SPSS Statistics

The Multivariate Analysis of Covariance (MANCOVA) is an extension of the ANCOVA (Analysis of Covariance)
that allows for the comparison of multiple dependent variables while controlling for one or more covariates.
This tutorial will guide you through performing a one-way MANCOVA in SPSS Statistics, including assumptions,
real-world examples, SPSS output tables, and APA-style results interpretation.

Understanding MANCOVA

MANCOVA is used to test whether the means of the dependent variables differ across the levels of a categorical
independent variable, while statistically controlling for the effects of covariates. This technique is particularly
useful when you have multiple dependent variables that may be correlated.

Assumptions for One-Way MANCOVA

• Independence of observations.
• Normality of the dependent variables for each level of the independent variable.
• Homogeneity of variances and covariances.
• Linear relationship between dependent variables and covariates.
• Homogeneity of regression slopes.
• No multicollinearity.

Performing One-Way MANCOVA in SPSS

To illustrate how to perform a one-way MANCOVA, we will use a hypothetical dataset where we examine the effect
of different teaching methods on students’ performance in mathematics and science, while controlling for their
previous academic performance.

Step-by-Step Guide:

1. Load your data into SPSS.
2. Go to Analyze > General Linear Model > Multivariate…
3. Move your dependent variables (e.g., Mathematics and Science scores) to the Dependent Variables box.
4. Move your independent variable (e.g., Teaching Method) to the Fixed Factor(s) box.
5. Move your covariate (e.g., Previous Academic Performance) to the Covariate(s) box.
6. Click on Model and ensure the full factorial model is specified.
7. Click on Options… and select Descriptive statistics, Estimates of effect size,
   and Homogeneity tests.
8. Click on Plots… if you need profile plots.
9. Click OK to run the analysis.

Interpreting the SPSS Output

Let’s interpret the key sections of the SPSS output.

Box’s Test of Equality of Covariance Matrices

Box’s M	F	df1	df2	Sig.
15.987	2.345	6	1002.56	.021

Box’s M test assesses the equality of covariance matrices. In this example, the test is significant (p = .021),
indicating a violation of the assumption of homogeneity of covariances. While MANCOVA is robust to some violations,
this should be noted when interpreting results.

Levene’s Test of Equality of Error Variances

F	df1	df2	Sig.
1.234	3	196	.297

Levene’s test checks the homogeneity of variances for each dependent variable. Here, the test is not significant
(p > .05), suggesting the assumption is met for both dependent variables.

Multivariate Tests

Effect	Value	F	Hypothesis df	Error df	Sig.	Partial Eta Squared
Teaching Method	Pillai’s Trace	3.456	2	194	.034	.034

The multivariate tests (e.g., Pillai’s Trace, Wilks’ Lambda, Hotelling’s Trace, Roy’s Largest Root) evaluate
the overall effect of the independent variable on the combined dependent variables. In this case, Pillai’s
Trace is significant (p = .034), indicating that teaching method has a significant effect on the combination
of mathematics and science scores.

Tests of Between-Subjects Effects

Dependent Variable	Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
Mathematics	Teaching Method	234.56	2	117.28	4.567	.012	.045
Science	Teaching Method	321.45	2	160.73	3.678	.025	.037

The between-subjects effects table shows the results for each dependent variable separately. Both mathematics
and science scores are significantly affected by the teaching method (p = .012 for mathematics and p = .025 for
science), with moderate effect sizes (partial eta squared = .045 and .037, respectively).

Conclusion

This tutorial covered the key steps and interpretation for conducting a one-way MANCOVA in SPSS Statistics.
By understanding and checking the assumptions, performing the analysis, and correctly interpreting the output,
you can effectively use MANCOVA to investigate the influence of categorical variables on multiple dependent
variables while controlling for covariates. For further details on MANCOVA and other SPSS-related tutorials,
explore our other posts on Mastering SPSS.