MANOVA and Its Industrial Application

ANOVA or Analysis of Variance is a group of statistical models to test for a significant difference between the means. It tests whether the means of various groups are equal or not. Multivariate analysis of Variance is called MANOVA. This is similar to ANOVA, which is a one-way Analysis of Variance, except that there is more than one variable or factors involved.

This is used in studies where more than one factors affect the dependent variable. When the various factors affecting the dependent variable, including all their combinations at different levels, are studied and tested, these are called Factorial experiments in MANOVA. No matter which type of MANOVA is being used, the dependent variables are always linearly combined.

If you are trying to tailor your training program based on four different training methods, you would evaluate the employee skill scores and satisfaction testing scores to determine which is the most effective and successful training method. This is what MANOVA, or Multivariate Analysis of Variance, is all about.

When businesses have a problem with two or more variables to work out, MANOVA can help. Many different domains use this technique, such as economics and psychology, and usually, this analysis is performed by data scientists and analysts using highly sophisticated statistical software.

As a business, it’s helpful to have an understanding of MANOVA and how it can help you further your goals as it has numerous applications in marketing, investment, and sales, to name just a few. In the simplest terms, it’s a statistical technique used in testing scenarios to help determine if group differences exist.

MANOVA and Its Applicability

MANOVA is a statistical process that compares multivariate samples means and is commonly used when there are two or more dependent variables. Typically, significance tests that involve separate individual dependent variables follow this procedure.

Since numerous behavioral and educational circumstances have many interrelated factors and can’t be observed by a single variable, a simultaneous analysis is best. MANOVA focuses on the observed outcomes on groups of subjects, and without this technique, you’re limited to only testing two variables at once.

For example, you would not use MANOVA for A/B testing, which only examines two variables, like – ‘Are customers clicking the blue button or the orange button for the webinar registration in our email campaign?’

Instead, you would use this for situations when you’re dealing with a variety of variables, like analyzing different market trends, or figuring out the best packaging designs for your products, or gaining a deeper understanding of market research with your focus group by asking a variety of unique questions.

When it comes to statistical research, MANOVA can be used to ask different questions:

  • What are the core impacts of the independent variables?
  • What are the different interactions between all of the independent variables?
  • What’s the significance of the dependent variables?
  • What’s the level of association among the dependent variables?
  • What is the impact of the covariates, and how can they be used?

The statistical formula is quite complex, which is why this analysis is usually a specialized method performed by researchers, analysts, and data scientists. During standard testing of a hypothesis, a researcher manipulates a non-metric variable and then takes different measurements to determine if objects within one treatment are unique from objects within other treatments. But during many research cases, there are numerous independent variables and measurements, which is the perfect scenario to use MANOVA.

Statistical Depiction of MANOVA

The formula consists of the variance of the model for1, as well as the inverse of the error variance for2.
So, it is implied that the product  for3if the hypothesis of for4is true.

MANOVA in the Business Context

It’s important to keep in mind that MANOVA can often provide outcomes that you want, rather than the outcomes that you need. This is because the answers you receive depends on the analysis and because the way all of these variables are manipulated can skew results. This is yet another reason why MANOVA is a statistical technique often left to industry professionals.

However, for businesses, it can be applied in scenarios across different departments to achieve different objectives, making it a very versatile analytics tool. The outcomes can help inform business actions and decisions to improve the customer experience, or shape social media campaigns, or improve solution development. It also helps businesses consider how scenarios emerge when multiple factors are involved, which is often the case in real-life situations versus controlled environments.

Below are a few examples of how MANOVA is used in the business context:

  • Modifying Services: If a business wants to modify how they deliver services to their customers, for example, they can compare numerous factors to optimize the delivery. For instance, they can compare their new service against the old service in areas like customer satisfaction levels and the time it took for the work to be completed.
  • Understanding Customer Behavior: Companies can use MANOVA to determine the type of interactions between variables to understand customer behaviors and actions in different marketing scenarios. For example, millennials are more likely to visit a website after viewing an ad with an eco-friendly symbol and a green link, while baby boomers visit a website more often if they see an ad for a sale and a blue link.
  • Comparing Solutions: Businesses can use MANOVA to compare how one solution is working across different circumstances. For instance, if a food manufacturer is developing a new type of potato, they can analyze where or not there’s an important difference between the potato’s growth in various soil types that it was planted in during testing, such as clay, salty, or rich dirt, depending on water quantities used, the crop yield, and various herbicides.

Benefits of MANOVA

Using MANOVA has a lot of advantages, both statistically and in a business context. Statistically speaking, MANOVA is a very robust analysis method that has the ability to weed out a wide degree of effects across related variables, as opposed to other methods like ANOVA (analysis of variables), which has a more limited scope. For businesses, MANOVA can help provide answers to the relationships between numerous different scenarios and variables, enabling them to understand the connection between actions customers take, for example, when given certain choices.

  • Saves time: Since MANOVA techniques can test multiple variables at once, it’s a time saver compared to other forms of analysis, which test only two variables, then another two variables, and so forth.
  • Best variable combinations: MANOVA can figure out the best combination of variables, which is perfect for market research. For example, images with groups of businesspeople and red links receive the most click-throughs.
  • Powerful statistics: MANOVA is a strong statistical method that can identify the smaller impact of correlated dependent variables, which typical ANOVA techniques can’t discover.
  • Evaluate patterns: MANOVA can evaluate patterns among multiple dependent variables, uncovering how the elements within a model can impact the connection between dependent variables rather than influencing an individual dependent variable.
  • Reduced likelihood of errors: When you have multiple dependent variables, a series of ANOVA analysis can increase the likelihood of rejecting a null hypothesis. But in a single MANOVA analysis, error rates are equal to the significance levels.

Analytics-Driven Business Decisions Using MANOVA

MANOVA holds the potential to be a valuable asset for businesses in today’s quickly changing markets, where every opportunity, scenario, and decisions need to be carefully examined for strategic advantage.

As a leading market research and analysis service provider, Research Optimus (ROP) has been assisting businesses in the field of data analysis, SWOT analysis, financial research, media monitoring, and more. By refining the approach to statistical analysis, like MANOVA, ROP ensures businesses have the right insights they need to stay on top of their game. Through the skill and specialized expertise of our analysts, we’re able to provide answers to the questions businesses ask of their market, customers, competitors, suppliers, and workforce. Contact us to explore our vast range of research and analysis solutions and start benefiting from our services.

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