MANCOVA in SPSS

Introduction

MANCOVA is a similar test to the ANCOVA test which is present in SPSS, where ANCOVA deals with one dependent variable but MANCOVA deals with more than one dependent variable, along with a covariate variable. Where the covariate variable plays a role of linearity between the dependent variables and also brings out differences in the groups of independent variables. Therefore, MANCOVA is used to estimate the statistical differences between multiple dependent continuous variables by an independent grouping variable controlled by a third variable called a covariate. Covariates can also be multiple based on the sample size used. The need for covariates to be indulged in the testing process is to eliminate the covariance effect between the dependent variables (continuous variables) and independent variables (grouping variables) and to reduce the error terms. There is one important point to remember when we use MANCOVA i.e., it might not show the difference between the specific group, unless and until the post hoc test has been selected from the options. 

In order to view that our data justifies the assumptions of MANCOVA, the basic assumptions of MANCOVA are stated below

Assumption of MANCOVA:

1. Random Sampling

Under the MANCOVA analysis, it is stated that the observations are independent i.e., there is no selection of sample pattern, it is completely random.

2. Type of Variables

MANCOVA induces different types of variables in the analysis. where the dependent variables should be continuous (like a Likert scale score or any other kind of score); independent variables should be categorical (nominal or ordinal variables); and the covariates are meant to be continuous, ordinal, or dichotomous. 

3. Multicollinearity

The dependent variables should not be correlated with each other.

4. Relationship between variables

The dependent variables should be statistically correlated with the covariate variables

5. Homogeneity 

The presence of homogeneity between variances and covariances is needed. MANCOVA assumes that variances and covariances of dependent variables are equal in all groups of independent variables.

6. Normality

Multivariate normality should be checked when MANCOVA is used.

A simple example of where we can use MANCOVA is shown graphically below:

In the below example, we are checking for a correlation between the dependent variables and independent variables. For, example a researcher wanted to analyze the relationship between which Gender supports the statements of “Change to be brought in the work structure”, controlling Years of working experience among the respondent's population.

To analyze this objective let's use one-way MANCOVA here. 

Variables taken are

1. Dependent variables: Statements concerning changes to be done in the work structure (Likert scale variables)

2. Independent variable: Gender

3. Covariate: Years of experience

Let us look use this example and perform MANCOVA in SPSS

The procedure to apply MANCOVA in SPSS :-

1. After setting up the data in Variable view & Data view by uploading the data in the SPSS software. In the Data view section, click Analyze > General Linear Model > Multivariate

 Click the Multivariate option as shown:

2. Place the variables in the given boxes as per their roles.

• Dependent variables: Statements concerning changes to be done in the work structure i.e., Honesty, Positive thinking, Communication, Learning new skills, and Support
• Independent variable: Gender
• Covariate: Years of working experience

3. To find out the statistical significance use Multivariate: Estimated Marginal Means and Multivariate: Options dialogue boxes

4. Click the options as given below, and click continue:

5. The output has been processed by SPSS:

 The output tables to be taken to report MANCOVA are:

Interpretation of Multivariate test:

1. Box test of equality of covariance matrices: 

This table represents the variation in the multivariate samples, it checks if two or more covariance matrices are equal. 

The null hypothesis considered in this test of MANCOVA is that when the p-value is larger than the significance level (0.050), it is stated to possess equal covariance matrices. 

In this case, our p-value (.319 >0.050). Therefore we can state that covariance matrices are equal, through the generated test statistic Box’s M Statistic.

2. Multivariate Tests: 

In this table, we refer to the “Wilk’s Lambda” value present in the table, it explains the strength between the variables considered in the test. The value of this test lies between 0 and 1. But the preferred ideal value is close to 0.

In this case from the table attached below, we see different types of multivariate tests such as “Pillai's Trace, Wilks' Lambda, Hotelling's Trace, and Roy's Largest Root”. these tests represent each different calculation providing probability (p-value) of getting F- statistic value. The most common test referred to in the multivariate analysis table is “Wilk’s Lambda”

As highlighted in the below table “Wilk’s Lambda” values of the independent variable. The statistical significance level will have a p-value less than 0.05 (p<0.05), and vice versa if the p-value is greater than 0.05 (p>0.05), then there is an insignificance level found in the analysis.

In this case, it can be found that as the p >0.05, (.539), there is an insignificant difference between Gender on agreeableness levels of statements related to  “Changes to be brought in the workplace” after controlling for “years of work experience” 

Therefore, we can state that both the independent variable and covariate variable are said to be insignificantly related to the statements about “Changes to be brought in the workplace”. 

Concluding that gender and years of working experience do not play a significant role in the level of agreeableness responses recorded to the statements in relation to “Changes to be brought in the workplace”.        

3. Tests of between-subject effects: it portrays a similar test to ANOVA, where the differences between the dependent variable from an independent variable are analyzed. 

             In this case, we can see that the significant value of gender is more than 0.05  in all the changes to be                                 brought in the work structure statements. This shows that the variables are not different. 

From the MANCOVA results, we can see that there are no significant differences between the level of agreeableness responses recorded to the statements in relation to “Changes to be brought in the workplace”, in relation to gender and years of working experience. Therefore the level of agreeableness received on the statements cannot be defined by the differences between gender and years of working experience but based on their views.