Comparison and Application of Cumulative Correspondence Analysis
Ordinal data is a common occurrence in almost every discipline. Ordinal data exist on an ordinal scale, this means that the value given to any particular quantity establishes a rank amongst the data points. A common approach to analyzing ordinal data is to use the Pearson Chi-Squared Test. This however, is flawed. In 1967, Frederick Mosteller, the then president of the American Statistical Association expressed concern as to how statisticians deal with contingency tables, "I fear that the first act of most social scientists upon seeing a contingency table is to compute chi-square for it. Sometimes this process is enlightening, sometimes wasteful, but sometimes it does not go quite far enough," (Agresti, 1989). The chi-squared test was designed for contingency tables; however, when there is an inherent order, when the variable(s) are ordinal, the Pearson chi-squared test is inappropriate. Different techniques have been developed to deal with ordinal data.
Smith, Matthew Joseph, "Comparison and Application of Cumulative Correspondence Analysis" (2013). ETD Collection for Fordham University. AAI13853369.