Correspondence Analysis

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Correspondence analysis present a graphical display of the relationships between the rows and columns in a crosstab. Consider the crosstab below. A careful examination of the crosstab reveals that:

  • Coke's score of 65% for Older is much higher than any other brand's score on this attribute.
  • Although Pepsi's score on Older is substantially lower than Coke's score in this attribute, a fairly general pattern is that Pepsi generally has very low scores and thus we can conclude that Pepsi is also, in relative terms, strongly associated with Older.
  • Applying the same type of logic that was used to deduce that Pepsi is Older, we can also see that Diet Coke is Feminine, Health-conscious<tt>, <tt>Innocent, etc.

ImageGrid.PNG


Carefully examining a table and identifying all the relationships between the rows and the columns is time consuming. Furthermore, it is difficult to digest. By contrast, the correspondence analysis map shown below makes these type of conclusions more apparent. It allows us to quickly see that:

  • Coke and Pepsi are positioned as being traditional and older.
  • Pepsi Max is positioned as being rebellious and open-to-new experiences.
  • Coke Zero has is a mixture of rebellious and open-to-new experiences as well as being related to health and weight issues.
  • Diet Coke and Diet Pepsi are seen as sleepy, innocent, feminine as well as relating to health and weight issues.

CorrespondenceAnalysisMap.png.

At a very simplistic level we can draw conclusions from such maps by looking at how close together things are on the map. Thus, Coke and Pepsi are similar to each other and are correlated with being traditional and older. At a more nuanced level we can look at the distance between the row and column categories from the center of the map. The further they are from the center of the map the stronger the relationship. Thus, the map above tells us that the association between Coke and Traditional is substantially stronger than the association between Diet Coke and Sleepy (both because Coke and Traditional are further from the map and because Sleepy and Diet Coke are not so close together). The actual correct interpretation is even more complex than this yet; please refer to the SurveyAnalysis.org's pages on Correspondence Analysis for more information).

Software

The main options for using correspondence analysis from surveys are:

  • SPSS. Note that to use SPSS to create correspondence analysis maps from grids or multiple response questions it is necessary to 'trick' the program by creating a dummy data file.
  • Q.
  • DataCracker.
  • xlStat.