# Discriminant analysis (in marketing)

For the discriminant analysis algorithm, see Linear discriminant analysis.

In marketing, discriminant analysis is a statistical technique for analyzing data. It is applicable when there is only one dependent variable but multiple independent variables (similar to ANOVA and regression analysis). But unlike ANOVA and regression analysis, the dependent variable must be categorical. It is similar to factor analysis in that both look for underlying dimensions in responses given to questions about product attributes. But it differs from factor analysis in that it builds these underlying dimensions based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique : a distinction between independent variables and dependent variables (also called criterion variables) must be made.

## Analysis steps

1. Formulate the problem and gather data - Identify the salient attributes consumers use to evaluate products in this category - Use quantitative marketing research techniques (such as surveys) to collect data from a sample of potential customers concerning their ratings of all the product attributes. The data collection stage is usually done by marketing research professionals. Survey questions ask the respondent to rate a product from one to five (or 1 to 7, or 1 to 10) on a range of attributes chosen by the researcher. Anywhere from five to twenty attributes are chosen. They could include things like: ease of use, weight, accuracy, durability, colourfulness, price, or size. The attributes chosen will vary depending on the product being studied. The same question is asked about all the products in the study. The data for multiple products is codified and input into a statistical program such as SPSS or SAS. (This step is the same as in Factor analysis).
2. Estimate the Discriminant Function Coefficients and determine the statistical significance and validity - Choose the appropriate discimininant analysis method. The direct method involves estimating the discriminant function so that all the predictors are assessed simultaneously. The stepwise method enters the predictors sequentially. The two-group method should be used when the dependent variable has two categories or states. The multiple discriminant method is used when the dependent variable has three or more categorical states. Use Wilks’s Lambda to test for significance in SPSS or F stat in SAS. The most common method used to test validity is to split the sample into an estimation or analysis sample, and a validation or holdout sample. The estimation sample is used in constructing the discriminant function. The validation sample is used to construct a classification matrix which contains the number of correctly classified and incorrectly classified cases. The percentage of correctly classified cases is called the hit ratio.
3. Plot the results on a two dimensional map, define the dimensions, and interpret the results. The statistical program (or a related module) will map the results. The map will plot each product (usually in two dimensional space). The distance of products to each other indicate either how different they are. The dimensions must be labelled by the researcher. This requires subjective judgement and is often very challenging. See perceptual mapping.

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