A Novel Non-Statistical Theory and Its Applications to Hypothesis Testing
Xintao Xia · Jiliang xuebao · 2006
Based on fuzzy-set theory,a novel method of hypothesis testing is proposed to solve some problems of traditional statistics.This method is named as the non-statistical hypothesis testing.Started with small sample data,the membership function of the distribution of a collectivity can be recognized automatically,and the true value including its distribution interval of the collectivity can also be estimated directly by the linear estimation method.The rejected region of hypothesis testing,characterized by a membership degree,is suggested by the use of fuzzy-set theory.Many cases are investigated by comparing with the statistical theory,some good efficacy by dint of the non-statistical hypothesis testing method proposed is validated,and the approximate 95% confidence level is yielded.