Journal of The Japanese Society for Quality Control
Online ISSN : 2432-1044
Print ISSN : 0386-8230
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Volume 10, Issue 3
Displaying 1-8 of 8 articles from this issue
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  • Two-Sample Tests for Ordered Categorical Data and Their Performance
    Hiroyuki UESAKA, Masashi GOTO
    Article type: Contributed Paper
    1980 Volume 10 Issue 3 Pages 36-46
    Published: July 15, 1980
    Released on J-STAGE: March 12, 2019
    DOIhttps://doi.org/10.20684/quality.10.3_36
    JOURNAL RESTRICTED ACCESS
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    Several methods have been proposed to test equality of two population distributions when responses are obtained as ordered categories. Among these , four tests, that is, conditional Wilcoxon test (W), normal test based on preassigned scores (T), cumulative chi-square test (Q) and ordinal chi-square test (X2) are investigated from the following aspects. (1) Large sample approximating distributions and power formulas are obtained. Limiting distributions and limiting power formulas in Pitman's sense are also derived. (2) Powers of the tests against some families of hypotheses are compared based on the model with successive categories on underlying continuum. W has higher powers than Q against the location shift alternatives in normal distributions. In the case of scale shift alternatives in exponential distribution, Q gives higher powers than W for some cases. and conversely W is more superior to Q for another, depending on the form of class alternatives. (3) For the cumulative chi-square test, we have numerically investigated actual limiting sizes of the two and three moment chi-square approximating tests. (4) For the T test, some meaning of equi-spaced scores is considered through optimal scores.
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  • Analysis of Interaction Effects in a Two-way Layout without Replication
    Chihiro HIROTSU
    Article type: Contributed Paper
    1980 Volume 10 Issue 3 Pages 47-53
    Published: July 15, 1980
    Released on J-STAGE: March 12, 2019
    DOIhttps://doi.org/10.20684/quality.10.3_47
    JOURNAL RESTRICTED ACCESS
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    It is usual to assume special structures in interaction effects for analizing two-way layout with interaction and no replication. However, it is also necessary to have another approach unless there is any intrinsic interest in those assumed structures. In this paper an approach is shown to defining the pattern of interaction effects and to estimating σ2, the variance of errors, without assuming any special structures in advance.
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