Editor's note: Dr. Betsy Goodnow is president of Market ACTION Research Software Inc., a developer and publisher of statistical software and a supplier of research since 1984. In September, Market ACTlON released a perceptual mapping package for both correspondence analysis and dual scaling called MAPWlSE. Clients include Fortune 500 corporations and leading universities, advertising agencies, and research firms around the world. Betsy has taught graduate level marketing research, worked for research suppliers, and published several articles on research techniques.
The purpose of this article is to demonstrate how to apply correspondence analysis to most research projects. It will explain how correspondence analysis is applicable to any type of table or set of tables, and demonstrate the applicability of correspondence analysis to competitive positioning, brand image tracking ,and market segmentation through a simple example. The article also presents other possible applications and closes with an evaluation of correspondence analysis.
"Easy Sophistication" sounds like the title of the latest pop song, but it actually describes the latest research technique - correspondence analysis. Recently most marketing research conferences have offered sessions, tutorials, and/or exhibits on this innovative statistical technique for perceptual mapping, but few researchers know how to apply it to "run-of-the-mill" research projects.
They don't realize that correspondence analysis can simultaneously reduce their work load and increase their sophistication. If you, like most researchers, feel overworked and under appreciated, read on and discover for yourself the practical benefits of correspondence analysis.
Background
The Frenchman Jean Paul Benzecri developed correspondence analysis in 1969 as a geometric display of dual scaling. Although this nonparametric technique is taught to French children, correspondence analysis has been neglected outside of Europe until recently because explanations of the technique were translated into math rather than into English.
The purpose of this statistical technique is to summarize and describe on a perceptual map the correlations among row and column categories in one or more data tables. In other words, correspondence analysis reconciles row and column percentages by weighing categories so their row and column percentages best correspond.
A correspondence analysis map is easier to interpret than other types of multidimensional scaling, now that the algorithm has been refined. Researchers no longer need to name axes or to draw vectors. They can now measure with a ruler or compass the actual distances between each row and/or column category to determine the strength of their correlation.
For example, if the joint occurrence of two categories in a table is much higher than expected, the categories are positioned nearby on the perceptual map and have a strong positive correlation. In contrast, if their joint occurrence is much lower than expected, they are positioned far apart and have a strong negative correlation.
(Sophisticated software for correspondence analysis now reports the correlations among each pair of categories on the first three axes with six digit accuracy.)
Correspondence analysis is bivariate if the categories of only two variables are correlated by their positions on a perceptual map. However, the technique is called multiple correspondence and is multivariate if the categories of more than two variables are correlated.
Data Requirements
The data in the set of tables being analyzed may be nominal (categorical), ordinal (ranking), or equal interval (rating), categorized metric (numeric), or a mixture of the above. "Brands" and "Images" are examples of nominal data. Ordinal data includes such responses as "Strongly Agree," "Agree," "Neither Agree Nor Disagree," "Disagree," and "Strongly Disagree." Equal interval data includes attribute scales, whereas categorized metric data includes income levels and age groups.
In contrast to other types of multidimensional scaling, correspondence analysis does not require ranking or rating data. However, the response categories should represent all possible positive and negative choices. Since correspondence analysis analyzes any type of data, surveys may be quite simple, as shown in Example I.
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In this simplified example using 210 respondents, our research objective is to evaluate the impact of a promotional campaign on the image of Mercedes-Benz and to determine the television show preferences of the target market. We assume that the respondents are representative and that all possible choices are included in the survey.
The data tables being analyzed may cross-tabulate subgroups, markets, brands, or respondents with such attributes as images, features, and demographics. Since the row and column categories are treated equally, both can be either objects or attributes.
The responses to the pre- and post-promotional surveys in Example I are cross-tabulated as shown in Example II. The data are frequency counts which tally the joint occurrences of each row and column category in the table.
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The data in the table or tables may be frequency counts, percentages, probabilities, or the results of any statistical analysis. However, mean scores on attribute ratings are only meaningful if you assume that the responses to each question are normally distributed. Some programs for correspondence analysis compensate for missing data and also permit multiple responses.
Correlations among categories of the two most important variables (active variables) define the axes of the initial map. At least three active categories are required for each active variable. These active categories are usually positioned in the upper left corner of a banner table.
In multiple correspondence analysis, at least one supplemental category is passively superimposed on the initial map. A passive column category is a supplemental banner point whereas a passive row category is a supplemental stub of the same banner. Each passive category must be cross? tabulated with categories of an active variable.
We demonstrate multiple correspondence analysis in this article because we correlate more than two variables. Our variables are "Brands," "Ideal Brand," "Prior Images," "New Images," and "Television Show Preferences." The active variables in Example II are "Brands" and "Prior Images." The passive column categories are "New Images" and "Television Show Preferences," whereas the passive row category is "Ideal Brand."
Axes
The axes in correspondence analysis do not represent variables as in hypothetical diagrams. In sophisticated programs for correspondence analysis, each axis best explains the remaining variance (distances or correlations) among the categories.
Each axis minimizes the distance of each category from the origin. According to a theorem by Pythagoras, this simultaneously minimizes the distances among all the categories. Thus a correspondence map best summarizes on two axes the correlations among all the categories in the data.
In contrast to other types of multidimensional scaling, the axes do not distinguish dimensions for discriminating categories. In direct and derived multidimensional scaling, the more distant from the origin, the stronger (more significant) the attribute. However, in correspondence analysis, such vector analysis is no longer relevant.
In correspondence analysis, the closer to the attribute, the more correlated. Axes need not be named in correspondence analysis because they do not accentuate distinctions between categories as do the axes in other types of multidimensional scaling.
Correspondence analysis of the data in Example II produced the correspondence map in Example III. The horizontal axis explains 90% and the vertical axis explains 10% of the variance (distances or correlations) among the categories.
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In all correspondence analysis maps, each axis best summarizes the remaining correlations among brands and images. When the axes and the map are significant, they distinguish correlations among categories of the active variables.
Interpretation
Correspondence analysis is an effective tool for competitive positioning because brand images are evident from the proximity of brands and images. Since relationships are mutual in correspondence analysis, the map also shows the brands associated with each image.
The images of the three automobiles included in this study are quite distinct. The proximity of Mercedes-Benz and Quality means that Mercedes-Benz has a quality image. The map reveals that Hyundai has an economical image and that Porsche has a power image. Conversely, quality is associated with Mercedes-Benz, economy with Hyundai, and power with Porsche.
Multiple correspondence analysis lets you track the impact of an advertising campaign over time. You merely compare the positions of images relative to the brands both before and after a promotional campaign.
For example, after the promotion, the buyers now perceive Mercedes-Benz as being more economical, Hyundai as being less economical, and Porsche as being less powerful than before the campaign. Thus the promotion by Mercedes-Benz is highly effective and should be continued.
You may enrich the value of your map by analyzing data on the demographic, lifestyle, and buying characteristics of each market segment.
For example, the proximity of television show preferences to brands discloses that Mercedes-Benz buyers prefer 60 Minutes, Hyundai buyers prefer Cheers, and Porsche buyers prefer LA Law. Assuming that only three media possibilities are available for promoting Mercedes-Benz, we conclude that the most effective media for reaching the target market for Mercedes-Benz is the television show 60 Minutes.
You can reposition your brand as more ideal by revising its image to match the image of the ideal brand.
The ideal brand is apparently more similar to Mercedes-Benz than to the other automobiles in the study. However, Mercedes?Benz can become more ideal by gaining a more economical image.
Other Applications
This example demonstrated the application of correspondence analysis to competitive positioning, brand image tracking and market segmentation. However, correspondence analysis visualizes correlations among categories in any type of table or set of tables. For example, secondary research can often be enriched through correspondence analysis. Other popular applications include relating:
1. Corporations and their images for competitive positioning.
2. Advertisements and their rank to evaluate advertising copy.
3. Features preferred by industrial buyers in a focus group to develop new product ideas.
4. Reasons for a purchase and the purchase decision to disclose purchase motivations.
5. Purchases over time and influences on their purchase behavior to track purchase behavior.
6. Marketing expenditures and revenues to evaluate marketing effectiveness.
7. Brands, features, benefits, and values to reveal purchase motivations.
8. Product sales in markets over time to identify market opportunities.
Other applications of correspondence analysis are only limited by the imagination of the researcher.
Evaluation
The latest generation of correspondence analysis software is so sophisticated it's easy - easy to apply, easy to use, easy to understand, and easy to believe.
The software is easy to apply because the data requirements are quite flexible. The program is applicable to any level of data, reads any type of numbers, compensates for multiple responses and missing data, and handles both raw and aggregated data.
However, correspondence analysis is only applicable to tables with up to 100 row and 100 column categories. This limitation is only theoretical because a perceptual map with more than two hundred categories boggles the human mind. Thus correspondence analysis is applicable to virtually any table or set of tables.
Recently a correspondence analysis program has been developed which is easy to use. Jean Paul Benzecri has long recognized the need for a user-friendly program for micro computers. Now software is available which is designed for marketing executives, rather than FORTRAN-literate statisticians. This new software guides the user through the program, prevents mistakes from occurring, and creates presentation graphics.
However, this software has sacrificed speed for the sake of scientific accuracy. The program compensates for this by being able to read up to 10,000 numbers in any ASCII data file, to calculate the significance, to weigh the sizes of subgroups, and to create presentation graphics compatible with most word processing programs.
A perceptual map must also be easy to understand. Executives balk at subjectively naming axes and interpreting vectors. The latest enhancements in correspondence analysis allow the perceptual map to be interpreted at face value. The closer the categories on the map, the more correlated. Now executives can correlate categories in tables by comparing their distances on a map with a ruler or compass and by comparing their numeric correlations relative to the top three axes.
However, researchers steeped in multidimensional scaling often confuse the two techniques. Since they assume that a correspondence map is interpreted like other perceptual maps, they think that the axes are important to understand its meaning. To prevent such an interpretation, the most sophisticated program does not provide a measure of a category's correlation or contribution to the axes.
The results of a statistical technique must be easy to believe. The credibility of a correspondence map can be established by evaluating its significance and the validity of the position of each category on the map. Now correspondence analysis has this capability.
Correspondence analysis is a powerful new technique for describing correlations among categories in table data. Many software packages are now available for micro computer, but they vary widely in the quality. In this article, we've discussed the features and benefits of the Mercedes-Benz of software for multiple correspondence analysis. Now correspondence analysis is so sophisticated, it's easy.