Journal of the Japan Statistical Society, Japanese Issue

k-MULTIPLE CHART AND ITS APPLICATION TO THE TEST FOR HOMOGENEITY AGAINST ORDERED ALTERNATIVES

Kazumasa Wakimoto

1981 Volume 11 Issue 1 Pages 1-7
Published: 1981
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.1

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The paper explains how a k-multiple chart in two dimensions can be constructed as a descriptive tool for the k-samples. This chart is regarded as an extention to the k-sample problem of the pair chart discussed by Quade for the two-sample problem. The area S_k lying below the path on the k-multiple chart is applied to the non-parametric test for homogeneity against ordered alternatives. The Pitman efficiency of S_k with respect to the well-known test statistic W_k of Terpstra and Jonckheere is shown, and its value is illustrated for k=4, 5, …, 15. As the results, though S_k and W_k are nearly equivalent test statistics, S_k may be superior to W_k in terms of the test statistic with some graphical characteristics.

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A NOTE ON THE EFFICIENCY OF THE PAIRWISE INDIVIDUAL MATCHING DESIGN IN A CASE-CONTROL STUDY IN EPIDEMIOLOGY

Takashi Yanagawa

1981 Volume 11 Issue 1 Pages 9-14
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.9

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Miettinen [3] has pointed out that when matching factor was unrelated to exposure, no gain or loss of either validity or efficiency was possible through matching, i.e. matching is futile. However, this is not true in the case of pairwise individual matching design; it is shown in the present note, by employing a mathematical model, that matching factors which are unrelated to exposure leads to the loss of efficiency.

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TEST STATISTICS FOR A SEQUENCE OF RANDOM NUMBERS BASED ON THE DISTRIBUTION FUNCTION OF THREE-DIMENSIONAL RANDOM DISTANCE

Eiji Yamamoto, Osamu Sugano

1981 Volume 11 Issue 1 Pages 15-25
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.15

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The distribution function of a three-dimensional random distance is given and some new three-dimensional d²-tests of randomness are proposed. It is shown by numerical experiments that our test statistics are uncorrelated with the usual test statistics.

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RANK TESTS FOR ORDERED ALTERNATIVES IN RANDOMIZED BLOCKS

Takaharu Araki, Shingo Shirahata

1981 Volume 11 Issue 1 Pages 27-42
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.27

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In a randomized block design with n blocks, c treatments and n_ij observations in the (i, j) cell, we consider two classes of rank tests for homogeneity against ordered alternatives. Both classes consist of weighted sums of n block statistics based on rankings within blocks, but one uses the simple linear rank statistics based on ranks of the whole observations in i-th block as the i-th block statistic [Simple linear type], the other uses the sum of c(c-1)/2 two sample rank statistics based on ranks of combined observations of two cells in the i-th block [Two sample type]. We consider asymptotic properties of these statistics and compare the two types by their Pitman efficiencies. It is shown that Simple linear type is n-asymptotically more efficient than Two sample type and that Simple linear type and Two sample type are n_ij- or c-asymptotically equally efficient.

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EXPLICIT EXPRESSIONS OF PROJECTORS ON CANONICAL VARIABLES AND DISTANCES BETWEEN CENTROIDS OF GROUPS

Haruo Yanai

1981 Volume 11 Issue 1 Pages 43-53
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.43

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Generalized expressions of canonical correlation analysis and partial canonical correlation analysis are introduced, in which the sum of the squared canonical and partial canonical correlation coefficients for each are given as the traces of the product of two orthogonal projectors and that of two oblique projectors respectively.
Following the result, some explicit expressions of projectors are obtained in connection with the product of two projectors defined in terms of canonical variables arising in canonical correlation analysis, partial canonical correlation analysis and part canonical correlation analysis, and the results are applied for showing that the Euclidian distance based on canonical variables turns out to be Mahalanobis' generalized distance with a slight modification.

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[title in Japanese]

[in Japanese], [in Japanese]

1981 Volume 11 Issue 1 Pages 55-56
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.55

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The Teaching of Statistics in Japanese Universities and Colleges

Koichi Ito

1981 Volume 11 Issue 1 Pages 57-59
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.57

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[title in Japanese]

[in Japanese]

1981 Volume 11 Issue 1 Pages 59-66
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.59

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[title in Japanese]

[in Japanese]

1981 Volume 11 Issue 1 Pages 66-72
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.66

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[title in Japanese]

[in Japanese]

1981 Volume 11 Issue 1 Pages 72-80
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.72

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The Dose-Response Relationship

Kazuo Fukutomi

1981 Volume 11 Issue 1 Pages 80-82
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.80

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[title in Japanese]

[in Japanese]

1981 Volume 11 Issue 1 Pages 82-88
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.82

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[in Japanese]

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[title in Japanese]

[in Japanese], [in Japanese], [in Japanese]

1981 Volume 11 Issue 1 Pages 88-94
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.88

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[title in Japanese]

[in Japanese], [in Japanese], [in Japanese], [in Japanese]

1981 Volume 11 Issue 1 Pages 94-101
Published: 1981
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.11.94

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