Multivariate analysis with more than on one dependent variable

By Indra Giri & Priya Chetty on March 14, 2017

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.

EXAMPLE

If the researcher is interested in finding the impact of two different books on the student’s improvement in different subjects such as science and math. In this case, improvement in science and improvement in math are two dependent variables.

If we want to test whether the dependent variable is affected by the difference in the textbook, then MANOVA analysis can opt. 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 an improvement in “Science” and “Mathematics” represents an 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 the reading hours 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
Using multivariate analysis for more than one dependent variables
Multivariate analysis in SPSS

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

multivariate analysis allows to add more than one dependent variable in the anaysis
Selecting dependent and independent variables

Step 2

Once the dialogue box is opened insert the dependent variables (mathematics and science scores) in the “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.

Using multivariate analysis for more than one dependent variable
Selecting the statistics for multivariate analysis
  • Descriptive statistics gives a basic overview of the variables in the model such as mean, median, and 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.
  • A homogeneity test is used to test whether all the groups included in the variable have the 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 the LSD option and click Continue.

Checking the post hoc tests in the multivariate analysis
Adding Post Hoc test for Multivariate analysis
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  • Least Square Difference (LSD) is one of the most powerful ways of finding statistically significant effects. This is because it is able to adjust the types of problems that occurred in the research. Also, the critical difference in LSD is highest as compared to other tests which make it more reliable. Using LSD also helps to reduce Type II errors. 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.

NOTES

Priya is the co-founder and Managing Partner of Project Guru, a research and analytics firm based in Gurgaon. She is responsible for the human resource planning and operations functions. Her expertise in analytics has been used in a number of service-based industries like education and financial services.

Her foundational educational is from St. Xaviers High School (Mumbai). She also holds MBA degree in Marketing and Finance from the Indian Institute of Planning and Management, Delhi (2008).

Some of the notable projects she has worked on include:

  • Using systems thinking to improve sustainability in operations: A study carried out in Malaysia in partnership with Universiti Kuala Lumpur.
  • Assessing customer satisfaction with in-house doctors of Jiva Ayurveda (a project executed for the company)
  • Predicting the potential impact of green hydrogen microgirds (A project executed for the Government of South Africa)

She is a key contributor to the in-house research platform Knowledge Tank.

She currently holds over 300 citations from her contributions to the platform.

She has also been a guest speaker at various institutes such as JIMS (Delhi), BPIT (Delhi), and SVU (Tirupati).

 

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