Applications of Mathematics to Behavioral Sciences: Understanding the Relations between Exploratory Data Analysis and Measurement

The role of mathematics in behavioral sciences is essential for the objective and logical descriptions of the phenomena under consideration. However, the question one must bear in mind is if it is used validly and justifiably. The paper was written in the hope that the basic premises for logical descriptions be well understood and put into practice of data analysis. The views presented here are based on my own observations of current practice in data analysis, and its preliminaries are already discussed in my paper entitled “Generating optimal data as regressions of measurement on data” (Bulletin of Data Analysis of Japanese Classification Society, 2011, Volume 1, No.1, 1-9) and my book “Data analysis for the behavioral sciences: Use of methods appropriate for data” (2010, Baifukan), both in Japanese. The current paper starts with these preliminaries and places special emphasis on the importance of the relations between data and measurement. Through the understanding of their relations, we discover that our data are enormously informative, leading to the important objective of exploratory data analysis: Capture as much information as possible from data in hand.