Issues and Perspectives Concerning the Development from Descriptive Statistics to Inferential Statistics: From the Point of View of the Negation Theory

Abstract

　　 The purpose of this paper is to clarify curriculum issues concerning the development from descriptive statistics to inferential statistics based on an epistemological perspective of negation, and to refer to perspectives about solving the issues.  For achieving this purpose, three tasks are worked on.  The first task is to analyze history of statistics based on Otaki’s conception model so that the static conception of descriptive and inferential statistics is interpreted.  The second task is to make clear the dynamic conception of descriptive and inferential statistics based on Iwasaki’s framework on the negation theory in concept formation.  A framework about the development to inferential statistics is made by solving these tasks.  The third task is to analyze mathematics textbooks from the perspective of the framework.  As a result, it is found out that the development to inferential statistics is not necessarily intended.  

　　In the development to inferential statistics three steps of negation are required.  The first step is negation of statistic and construction of substance of a statistic, which is not the same of one in descriptive statistics. The next step is analytic negation in which substance of a statistic is negated by viewpoint of decision, and it is regarded as a random variable in inferential statistics.  The final step is synthetic negation in which a random variable is negated by viewpoint of a parameter, and the relation between descriptive and inferential statistics is made clear.  This sequence of negation is shown below (Fig.).

Fig. the development from descriptive statistics to inferential statistic