A class of exact UMP unbiased tests for conditional symmetry in small-sample square contingency tables

2005 ◽  
Vol 32 (4) ◽  
pp. 333-340
Author(s):  
Rolf Aaberge ◽  
Li-chun Zhang
Keyword(s):  
Contingency Tables ◽  
Small Sample ◽  
Conditional Symmetry

scholarly journals A discussion on significance indices for contingency tables under small sample sizes

PLoS ONE ◽  
2018 ◽  
Vol 13 (8) ◽  
pp. e0199102 ◽  
Author(s):  
Natalia L. Oliveira ◽  
Carlos A. de B. Pereira ◽  
Marcio A. Diniz ◽  
Adriano Polpo
Keyword(s):  
Contingency Tables ◽  
Small Sample ◽  
Sample Sizes ◽  
Small Sample Sizes

The impact of uneven filling two-way contingency tables on the critical value of the test statistics

2016 ◽  
Vol 61 (4) ◽  
pp. 1-16
Author(s):  
Piotr Sulewski ◽  
Antoni Drapella
Keyword(s):  
Statistical Modeling ◽  
Contingency Tables ◽  
Critical Value ◽  
Small Sample ◽  
Test Statistics ◽  
Chi Square ◽  
Independent Verification ◽  
Power Of The Test ◽  
The Impact ◽  
Measures Of Inequality

The article concerns two-way (2×2) contingency tables. When the H0— hypothesis of independence of features is correct, very often — because of the small sample — the distribution of the test statistics differ from the chi-square. Quantile of the chi-square is therefore not a correct critical value. With the current performance of computers, designation of critical value by statistical modeling of Monte Carlo method is not a problem, but a problem is H0 modeling. The H0 modeling is generating such arrays, which feature value assigned rows are independent of the characteristics of the assigned columns. Suitable for such modeling are tables — uniform of the same probability of belonging to cells and uneven having equal probability in all rows of a given column or in all columns of a given row. Analysis of the results of statistical modeling revealed that even when H0 is right, the distribution of the test statistics significantly depends on the uneven array. The article shows that in order to maximize the power of the test should be set critical value, taking into account measures of inequality array. The final result of the study is offered the reader a ready tool for independent verification of the H0 hypothesis.

scholarly journals Diagonal Exponent Conditional Symmetry Model for Square Contingency Tables with Ordered Categories

2016 ◽  
Vol 5 (4) ◽  
pp. 38
Author(s):  
Kiyotaka Iki ◽  
Akira Shibuya ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Main Diagonal ◽  
Test Statistics ◽  
Conditional Symmetry ◽  
Exponential Form ◽  
Ordered Categories ◽  
Expected Frequency ◽  
Symmetry Model ◽  
Proposed Model ◽  
New Models

For square contingency tables with ordered categories, this article proposes new models which indicate that in addition to the structure of asymmetry of the probabilities with respect to the main diagonal of the table, the expected frequency has an exponential form along every subdiagonal of the table. Also it gives the new three kinds of decompositions using the proposed model and proves the orthogonality of the test statistics.

Small-sample tests for homogeneity of response probabilities in 2 × 2 contingency tables.

1987 ◽  
Vol 102 (2) ◽  
pp. 307-314 ◽  
Author(s):  
John E. Overall ◽  
Howard M. Rhoades ◽  
Robert R. Starbuck
Keyword(s):  
Contingency Tables ◽  
Small Sample

scholarly journals Measure of Departure from Conditional Symmetry Based on Cumulative Probabilities for Square Contingency Tables

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1897
Author(s):  
Yusuke Saigusa ◽  
Yuta Teramoto ◽  
Sadao Tomizawa
Keyword(s):  
Social Mobility ◽  
Contingency Tables ◽  
Occupational Status ◽  
Main Diagonal ◽  
Asymmetric Structure ◽  
Conditional Symmetry ◽  
Ordered Categories ◽  
Symmetry Model ◽  
Status Data ◽  
Cumulative Probabilities

For the analysis of square contingency tables with ordered categories, a measure was developed to represent the degree of departure from the conditional symmetry model in which there is an asymmetric structure of the cell probabilities with respect to the main diagonal of the table. The present paper proposes a novel measure for the departure from conditional symmetry based on the cumulative probabilities from the corners of the square table. In a given example, the proposed measure is applied to Japanese occupational status data, and the interpretation of the proposed measure is illustrated as the departure from a proportional structure of social mobility.

Sign in / Sign up

Export Citation Format

Share Document