程度函数及其可靠性

DEGREE FUNCTION AND IT’S RELIABILITY

通过实验及理论分析，验证并给出了：１．程度函数ａ的可靠性θ的取值范围为：１／ｍ≤θ≤１／ｍ∑ｂｋｙｊｐ。θ值的大小与可靠性呈反向变化：ａ的可靠性大，θ值小，ａ的可靠性小θ值大，一般情况下的θ值，为θ的上界与下界之和的一半；２．采用集值统计模型和一般统计模型处理多级估量法多人次结果，所得到的程度函数平均数几乎相等，而且相关系数高达０．９７７．非常显著．分组数据计算、单一数据计算或全部数据统一计算的程度函数ａ及可靠性θ值也都相等．３．一般统计模型处理多级估量法多人次结果所得到的标准差σ，只反映各被试的程度函数之间的变异，与程度函数可靠性无关（相关系数０．００２４，非常不显著）．如果个人结果中按公式θ＝１／ｍ∑ｅｊ再计算可靠性θ值，然后再求其平均数及标准差，还可进一步了解可靠性θ值的变异情况．

Experiments and theories were used to suggest that: (a) as the reliability of the degree functioned, the value of θsatisfied the relationship: 1/m≤θ≤1/m and changed conversely to the reliability(i,e, if the reliability of a is large, will be small; otherwise, if the reliability of a is small,θ will be large). Usually the value of θ is about half of the upper bound plus lower bound. (b) when the fuzzy statistic model or the probabilistic statistic model was applied to the multi-step rating scale method to deal with group data, the means of degree function were almost the same. Their correlation coefficient, was very conspicuous, reaching high to the value of 0.997. (c)when the probabilistic statistic model was applied to multi-step rating scale method to deal with group data, the standard deviation only reflected the difference among the degree function of the dependants, and showed no relationship to the reliability of degree function. (the correlation coefficient equalled 0.0024 and was not conspicuous). To the personal results, if the value of reliability θwas calculated by using the formula θ=1/m∑θj, following the calculation of the mean and standard variance, how the deviation of θ changed could also be obtained.