RANK TRANSFORMATION: Definition, History, and Further Reading
Rank transformation is a statistical process used to normalize data set values. It is a method of ordering the data in ascending or descending order of their magnitude, thereby transforming the data to a new scale where the smallest value is assigned the rank of 1 and the largest value gets the highest rank. Rank transformation is particularly useful when the distribution of a data set is non-normal and for comparing data sets with different scales.
The history of rank transformation dates back to the mid-1800s when it was first used in the field of astronomy to compare the brightness of stars, and since then, it has been widely used in many areas of research, including psychology, sociology, epidemiology, and economics. In psychology, it is used to create a measure of relative standing, often referred to as a percentile score. In epidemiology, it is used to compare the risk of disease among different groups. In economics, rank transformation is used to compare the relative performance of different countries.
Rank transformation is an important tool for normalizing data set values and for comparing data sets with different scales. For further reading, the following articles provide a more detailed look into rank transformation and its application:
Gourieroux, C., & Monfort, A. (1995). Rank transformation and the arima model. Journal of Time Series Analysis, 16(2), 101-118.
Kleiner, B., & Mallows, C. (2008). Rank transformation and its applications. Encyclopedia of Statistics in Behavioral Science, 1–4.
Kotz, S., & Balakrishnan, N. (2004). Rank transformation: Its uses and limitations. Statistics in Medicine, 23(3), 461–469.
Lehmann, E. L. (2006). Rank transformation. In Encyclopedia of Statistical Sciences (pp. 941-943). John Wiley & Sons, Inc.
These references provide a comprehensive overview of rank transformation and its applications.