On the Hypothesis of No "Interaction" In a Multi-way Contingency Table

Roy, Sasanka; Kastenbaum, Marvin A.

doi:10.1214/aoms/1177728181

Cited by 113 publications

(54 citation statements)

References 2 publications

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“…Norton [21] extended the definition to test a 2 × 2 × K table. Roy and Kastenbaum [27] constructed a likelihood ratio test for testing no second-order interaction in the full table I × J × K , that is to say…”

Section: Further Hypotheses Of Interest In Three-way Tablesmentioning

confidence: 99%

An approach to multiway contingency tables based on ϕ-divergence test statistics

Pardo

2010

Journal of Multivariate Analysis

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Section: Further Hypotheses Of Interest In Three-way Tablesmentioning

confidence: 99%

An approach to multiway contingency tables based on ϕ-divergence test statistics

Pardo

2010

Journal of Multivariate Analysis

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“…. , s; k = 1, 2, ..., t. Roy and Kastenbaum [15] suggested that the generalization to r X s X t case, as an extension of the criterion for zero second-order interaction in a 2 X 2 X 2 case due to Bartlett, is to test the hypothesis H : Aijk = A ; j t ; 2 = 1, 2, ' * * , r -1;…”

Section: R X S X T Contingency Tablementioning

confidence: 99%

“…Odoroff compares small sample hypothesis of no interaction in 2 x 2 x 2 tables. Roy properties of tests for interactions in 2 X 2 X 2 and and Kastenbaum [15] proposed an extension of Bartlett's 3 X 2 X 2 tables. He examined each of the three tests, definition for T X s x t tables.…”

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confidence: 99%

Interaction Test for Three-Dimensional Contingency Tables

Patil

1974

Journal of the American Statistical Association

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A test for the hypothesis of zero second-order interaction is proposed. The test is obtained by making use of conditional reference sets which are derived in Zelen [lq. This permits the derivation of an exact conditional test of significance for testing the hypothesis of zero secondorder interaction. The techniques used, in approximating the large sample distribution of this test, are extensions of those due to Gart [5] and Zelen [la. The test is applied to a numerical example. and his co-workers. This method is equivalent to like& hood ratio test and, like the classical chi-square and likelihood ratio test, it is based on asymptotic distribution theory. The method is described in [lo].The study of small sample properties in situations where asymptotic theory is used for obtaining the distributions of test criterion is very valuable. This needed and useful work, in the present context, is done by Odoroff Bartlett [l] proposed a significance test for the [la] and Berkson [ 2 ] . Odoroff compares small sample hypothesis of no interaction in 2 x 2 x 2 tables. Roy properties of tests for interactions in 2 X 2 X 2 and and Kastenbaum [15] proposed an extension of Bartlett's 3 X 2 X 2 tables. He examined each of the three tests, definition for T X s x t tables. These authors used the minimum logit chi-square, Pearson's chi-square and Pearson's chi-square statistic and suggested obtaining the likelihood ratio test with four methods of estimathe required maximum likelihood estimates iteratively. tion, the iterative maximum likelihood estimation and This involves rather excessive computations. Plackett three variants of non-iterative minimum logit chi-square [13] developed a statistic, for the purpose, which did estimates. The exact levels of the minimum logit chinot need to obtain estimates of the parameters under the square tests and Pearson's chi-square test are better restrictions imposed by the hypothesis. The easily approximated by the tabular chi-square distribution than obtained unrestricted maximum likelihood estimates are are the levels of the likelihood ratio test. The exact levels required to compute the statistic. Goodman [6] sug-of tests based on minimum logit chi-square estimates are gested a variation of Plackett's statistic that requires better approximated than levels of tests based on less computations. maximum likelihood estimates. Interactions in contingency tables are compared with Berkson [a] considered the problem of "no interaction" interactions in the analysis of variance by Darroch [4],under two situations, one in which the prevalent model and this has led to a comparatively simple method of is of logit additivity and the other of linear additivity. constructing the likelihood ratio test statistic for the I n the logit model he investigated the effect of two hypothesis of zero second-order interaction in three-estimation procedures, unrestricted minimum discrimidimensional contingency tables. Goodman [7] has given nation information (UMDI) and maximum likelihood a different definition of intera...

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“…For some further discussion of the analysis of multi-way cross classifications, the reader is also referred to reference [28] and to the literature cited there. APPENDIX Let us assume that the time series considered are of the general type defined in Section 3 herein.…”

Section: The Relation Between Three or More Time Seriesmentioning

confidence: 99%

Some Nonparametric Tests for Comovements between Time Series

Goodman

Grunfeld²

1961

Journal of the American Statistical Association

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The test, proposed by Moore and Wallis [23], of the existence of correlation between the movements in two time series (eliminating at least the primary effects of trends) was justified by them in "the special case of randomly arranged [signs of the] first differences" in both series. Moore and Wallis also noted that the signs of the first differences in a time series will have a negative serial correlation if the time series is a purely random process (or if it is a particular kind of generalization of a purely random process). It is therefore necessary to modify the Moore-Wallis test when applying it to such time series in order to take into account this serial correlation. In the present article, a simple modified form of the Moore-Wallis test is suggested, which can be applied to such time series. Somewhat similar modifications are also suggested for testing the existence of correlation between some more general kinds of time series. The importance of taking into account the effects of trends in the time series and the effects of the serial correlations (between the signs of the first differences) is illustrated by means of two numerical examples. Finally, the study of the movements in three or more time series is briefly discussed.

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On the Hypothesis of No "Interaction" In a Multi-way Contingency Table

Cited by 113 publications

References 2 publications

An approach to multiway contingency tables based on ϕ-divergence test statistics

An approach to multiway contingency tables based on ϕ-divergence test statistics

Interaction Test for Three-Dimensional Contingency Tables

Some Nonparametric Tests for Comovements between Time Series

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