2024-08-10T14:43:17Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00002068
2023-11-09T02:33:24Z
323:350:373:388
ON THE NUMERICAL REPRESENTATIONS AND THE UNIQUENESS PROPERTIES OF ORDERED METRIC SCALES
<原著>順序距離尺度の数値的表現と一意性特性について
村上, 隆
5309
MURAKAMI, Takashi
5310
1977-11-30
Scale values of an ordered metric scale (OMS) derived from a given ordering of differences between two stimuli are not necessarily determined uniquely like an interval scale when the stimulus set is finite. In this study, a method to find the maximum and minimum scale values for all stimuli in any OMS is proposed. The smaller is the range of scale values for any stimulus, the higher is the uniqueness of numerical assignment of OMS. The maximum value of the ranges for all stimuli is called an index of ε-uniqueness for a given OMS. The numerical experiments were carried out to explore the effects of factors affecting the ε-uniqueness. Assumed true scale values were reduced to the orderings of differences between all the pairs of stimuli. Using a modified linear programming algorithm, these orderings were processed to recover the scale values and to calculate the indices of E-uniqueness. Factors investigated in the experiments are the number of stimuli N, and the size of variance of first order differences of the scale values and their permutation. The Main results are as follows; 1) Increase in N and decrease in variance of first order differences raise ε-uniqueness. Unless variance of first order differences is too large or too small, maximum range of scale values decreases in proportion to N^<-2> approximately. 2) While remaining conditions are kept to be constant, ε-uniqueness varies with the permutation of first order differences remarkably.
国立情報学研究所で電子化したコンテンツを使用している。
departmental bulletin paper
名古屋大学教育学部
1977-11-30
名古屋大學教育學部紀要. 教育心理学科
24
43
53
http://hdl.handle.net/2237/3491
03874796
jpn