# Multivariate analysis with more than on one dependent variable

The normal linear regression analysis and the ANOVA test are only able to take one dependent variable at a time. So one cannot measure the true effect if there are multiple dependent variables. In such cases multivariate analysis can be used. Thus, multivariate analysis (MANOVA) is done when the researcher needs to analyze the impact on more than one dependent variable.

For example, if the researcher is interested in finding the impact of two different books on the students improvement in different subject such as science and math. In this case the improvement in science and improvement in math are two dependent variables.

If we want to test whether the both the dependent variable are affected by the difference in the textbook, then MANOVA analysis can be opted. It helps to analyze three things:

• impact of change in independent variables on dependent variables,
• interaction among the dependent variables and
• interaction among the independent variables

## Procedure for multivariate analysis in SPSS

One can perform the MANOVA analysis in SPSS using the following steps:

For the purpose of understanding, the researcher has undertaken a problem wherein the scores in subjects, Mathematics and Science are dependent on two books i.e. Book A and Book B. So, the two dependent variables in this case would be “Science” and “Mathematics” where science represents improvement in “Science” and “Mathematics” represents improvement in mathematics. The improvement in both the subjects has been measured by scores in each subject where 1 is the lowest score and 5 is the highest score. Similarly, two independent variables namely Book A and Book B. The independent variables are measured in terms of reading hour for each book which lies between 1 and 5. Here, 1 means less than 2 hours per day and 5 means more than 5 hours per day.

### Step 1

##### Analyse > General Linear model > Multivariate

Once you click on that new dialogue box will open as shown in figure below:

### Step 2

Once the dialogue box is opened insert the dependent variables (mathematics and science scores) in “Dependent Variables” box and the independent variables in the “Fixed Factor list”. In this case the independent variables are Book A and Book B.

### Step 3

Descriptive statistics, Estimates of effect size, Observed power and Homogeneity tests.

• Descriptive statistics gives a basic overview about the variables in the model such as mean, median,  standard deviation.
• Estimates of effect size will give the impact of independent variables for each dependent variable.
• Observed power shows the results to reduce the Type I error. The Type I error occurs when we reject the null hypothesis even though it is true.
• Homogeneity test is used to test whether all the groups included in the variable have same similar variance or not.

### Step 4

Similarly in the Post Hoc, insert the independent variables in the Post Hoc Test for box and select LSD option and click Continue.

• Least Square Difference (LSD) is one of the most powerful way of finding statistically significant effects. This is because it is able to adjust the types of problems occurred in the research. Also the critical difference in LSD is highest as compared to other test which makes it more reliable. Using LSD also helps to reduce the Type II error. This error occurs when we fail to reject the null hypothesis even when it is not true.

### Step 5

Leave the other options as it is and click OK.

In the next article we will discuss the interpretations for the case study.

### Indra Giri

Senior Analyst at Project Guru
He completed his Masters in Development Economics from South Asian University, New Delhi. His areas of interest includes various socio development issues like poverty, inequality and unemployment in South Asia. Apart from writing for Project Guru he loves to travel and play football in his spare time.

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