# The Benefits of Performing Discriminant Analysis on Survey Data

February 28, 2018

## What is Discriminant Analysis?

Discriminant analysis is a versatile statistical method often used by market researchers to classify observations into two or more groups or categories. In other words, discriminant analysis is used to assign objects to one group among a number of known groups.

In order to perform any kind of discriminant analysis, you must first have a sample within these known groups.

## When To Use Discriminant Analysis

By performing discriminant analysis, researchers are able to address classification problems in which two or more groups, clusters, or populations are known up front, and one or more new observations are placed into one of the known classifications based on measured characteristics.

Discriminant analysis is also used to investigate how variables contribute to group separation, and to what degree. For this reason, it’s often leveraged to compliment the findings of cluster analysis.

Market researchers are continuously faced with situations in which their goal is to obtain a better understanding of how groups (customers, age cohorts, etc.) or items (brands, ideas, etc.), differ in terms of a set of explanatory or independent variables.

These situations are where discriminant analysis serves as a powerful research and analysis tool.

## Descriptive vs. Predictive Discriminant Analysis

Discriminant analysis can be used for descriptive or predictive objectives.

Descriptive discriminant analysis is used when researchers want to assess the adequacy of classification, given the group memberships of the object under study.

Predictive discriminant analysis is used when researchers want to assign objects to one of a number of known groups of objects.

It’s essential to remember that in both of these cases, some group assignments must be known before conducting the statistical procedure. Due to the fact that these group assignments can be obtained in any way, discriminant analysis is often performed alongside cluster analysis.

Further, if the objective of a researcher is to understand how the groups or items at hand differ, the researcher could conduct a one-way analysis of variance (ANOVA) on each independent variable, such as a brand attribute rating scale, across the group means.

Oftentimes, in practical market research, the independent variables — in this case the brand-rating scales — are correlated to some extent. This means that there’s a possibility that a series of one-way ANOVA’s will show that many of the independent variables maintain group means that are significantly different, when in actuality only one or two non-redundant independent variables do.

If there’s a large number of independent variables, there may be differences between groups that are a result of chance where there really are no differences. This is due to Type I error.

Discriminant analysis helps researchers overcome Type I error.

In discriminant analysis, the intercorrelation of variables is addressed by partitioning correlations between independent variables.

When discriminant analysis uses one independent variable to rationalize differences between the groups, the remaining variables are amended so that any difference that is apparent between groups is not due to correlation that the other independent variables have with the first variable.

For this reason, discriminant analysis only addresses the unduplicated variance between groups.

## The Benefits of Discriminant Analysis

Discriminant analysis provides various benefits.

Ultimately, it aims to answer the following questions:

• Where do the expected and observed classifications differ?
• How statistically significant is the deviation of observed from expected classification?

Discriminant analysis can be closely compared to regression analysis for the ways in which it identifies the degree to which objects adhere to the specifications of certain groups.

As discussed above, discriminant analysis can be leveraged to determine which predictor variables are related to the dependant variable, as well as to predict the value of the dependent variable based on the values of the predictor variables.

Discriminant analysis is also commonly used by marketers to develop perceptual maps.

There are seemingly endless ways to implement discriminant analysis for market research and business purposes.

By conducting this method of data analysis, researchers are able to obtain a much stronger grasp on the products and services they provide, and how these offerings stack up against varying topics and areas of interest.

Have you conducted discriminant analysis for business research purposes? If so, we’d love to hear from you. Drop us a line in the comments below!

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