Two-by-Two: Categorical Thinking About Continuous Bivariate Data

Most variables that companies care about are continuous in nature, but they are often analyzed categorically. For instance, consider Rogers’ (1962) innovation adoption curve, one of the most celebrated ideas in marketing. Though there are no natural boundaries on the continuum of innovativeness, customers are classified into five categories (innovators, early adopters, early majority, late majority, and laggards) based on arbitrary cutoffs, in this case defined by the mean and standard deviation (e.g., the cutoff for innovators is two standard deviations above the mean). Similarly, many companies ask customers to indicate their recommendation likelihood on a 0-10 scale, where 0 means “not at all likely” and 10 means “extremely likely.” Instead of analyzing the data continuously, customers are grouped into three categories—detractors (scoring between 0 and 6), passives (scoring 7 or 8), and promoters (scoring 9 or 10). The percentage of detractors is then subtracted from the percentage of promoters to compute a Net Promoter Score. We propose that the ubiquity of such analyses is not just statistical convention, but rather reflects a natural tendency of the mind. Just like our perceptual system automatically divides the continuous spectrum of wavelengths into distinct colors, or separates continuous differences in voice onset time into discrete phonemes, decision-makers tend to simplify and structure continuous data by discretizing it, a strategy we call “categorical thinking.” Categorical thinking can be advantageous in that it facilitates communication. But categorical thinking can also harm judgment quality. One downside has been well-noted: Categorical treatment of continuous variables ignores meaningful variation, leading to flawed inferences.