scholarly journals On a property which holds good for all groupings of a normal distribution of frequency for two variables, with applications to the study of contingency-tables for the inheritance of unmeasured qualities

1906 ◽  
Vol 77 (517) ◽  
pp. 324-336 ◽  
Keyword(s):  
Normal Distribution ◽  
Contingency Table ◽  
Contingency Tables ◽  
Good For

1. Suppose a contingency-table to have been formed for two characters A and B which have been assigned in some way into classes A 1 ...A r , B 1 ...B s , the table having r columns, s rows, and giving the frequencies of occurrence of all combinations like A m B n . Let (A m ) (B n ) denote the frequencies of A m and B n (A m B n ) the frequency of their combination. Extract from the general contingency-table any four adjacent frequencies, say— (A m B n ), (A m + 1 B n ) (A m B n +1 ), (A m + 1 B n + 1 ).

scholarly journals Boolean Monte Carlo Method

2019 ◽  
Author(s):  
Takuma Usuzaki ◽  
Minoru Shimoyama ◽  
Shuji Chiba ◽  
Naoko Mori
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Contingency Table ◽  
Contingency Tables ◽  
Medical Test ◽  
Frequentist Approach ◽  
Large Numbers ◽  
Result Analysis ◽  
Variable Analysis

A medical test and accuracy of diagnosis are often discussed with contingency tables. However, it is difficult to apply a contingency table to multivariate cases because the number of possible categories increases exponentially. We hypothesize that randomly assigning Boolean operators and focusing on frequencies of Boolean operators could explain the outcome correctly, obtain the tendencies of operators, and overcome difficulties in analyzing large numbers of variables and categories. The aims of this paper are introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases. To test this method, we construct two types of data: 1) when variables and outcome were randomly determined and 2) when the outcome depends on one variable. Analysis of the first type of data by this method showed that there was no significant result. Analysis of the second type of data reflected the bias of the data. As far as we know, this is the first attempt to use a frequentist approach to randomly assigned Boolean operators.

scholarly journals Subsymmetry and asymmetry models for multiway square contingency tables with ordered categories

2016 ◽  
Vol 14 (1) ◽  
pp. 195-204
Author(s):  
Serpil Aktaş
Keyword(s):  
Contingency Table ◽  
Contingency Tables ◽  
Ordered Categories ◽  
Square Contingency Table

AbstractThis paper suggests several models that describe the symmetry and asymmetry structure of each subdimension for the multiway square contingency table with ordered categories. A classical three-way categorical example is examined to illustrate the model results. These models analyze the subsymmetric and asymetric structure of the table.

An AID/Logit Procedure for Analyzing Large Multiway Contingency Tables

1978 ◽  
Vol 15 (1) ◽  
pp. 132-136 ◽  
Author(s):  
Paul E. Green
Keyword(s):  
Contingency Table ◽  
Contingency Tables ◽  
Logit Analysis ◽  
Criterion A ◽  
Step Procedure

A two-step procedure is described in which AID is applied first to a multiway contingency table to isolate those variables (and levels within variable) that best account for variance in the criterion. A logit analysis follows for estimating parameters for prediction purposes. The method is described and applied illustratively to a set of data on usage of an AT&T telecommunications service.

A new framework of statistical inferences based on the valid joint sampling distribution of the observed counts in an incomplete contingency table

2015 ◽  
Vol 26 (4) ◽  
pp. 1712-1736 ◽  
Author(s):  
Guo-Liang Tian ◽  
Hui-Qiong Li
Keyword(s):  
Confidence Interval ◽  
Contingency Table ◽  
Contingency Tables ◽  
Sampling Distribution ◽  
Maximum Likelihood Estimates ◽  
Interval Methods ◽  
Simulation Studies ◽  
Underlying Assumption ◽  
Incomplete Observations ◽  
New Framework

Some existing confidence interval methods and hypothesis testing methods in the analysis of a contingency table with incomplete observations in both margins entirely depend on an underlying assumption that the sampling distribution of the observed counts is a product of independent multinomial/binomial distributions for complete and incomplete counts. However, it can be shown that this independency assumption is incorrect and can result in unreliable conclusions because of the under-estimation of the uncertainty. Therefore, the first objective of this paper is to derive the valid joint sampling distribution of the observed counts in a contingency table with incomplete observations in both margins. The second objective is to provide a new framework for analyzing incomplete contingency tables based on the derived joint sampling distribution of the observed counts by developing a Fisher scoring algorithm to calculate maximum likelihood estimates of parameters of interest, the bootstrap confidence interval methods, and the bootstrap testing hypothesis methods. We compare the differences between the valid sampling distribution and the sampling distribution under the independency assumption. Simulation studies showed that average/expected confidence-interval widths of parameters based on the sampling distribution under the independency assumption are shorter than those based on the new sampling distribution, yielding unrealistic results. A real data set is analyzed to illustrate the application of the new sampling distribution for incomplete contingency tables and the analysis results again confirm the conclusions obtained from the simulation studies.

Multiway Contingency Tables: Monte Carlo Resampling Probability Values for the Chi-Squared and Likelihood-Ratio Tests

2010 ◽  
Vol 107 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Michael A. Long ◽  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Monte Carlo ◽  
Likelihood Ratio ◽  
Contingency Table ◽  
Contingency Tables ◽  
Likelihood Ratio Tests ◽  
Ratio Test ◽  
Test Statistics ◽  
Test Statistic ◽  
Resampling Methods ◽  
Chi Squared

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.

scholarly journals A Geometry-Based Multiple Testing Correction for Contingency Tables by Truncated Normal Distribution

2020 ◽  
Vol 12 (1) ◽  
pp. 63-77
Author(s):  
Tapati Basak ◽  
Kazuhisa Nagashima ◽  
Satoshi Kajimoto ◽  
Takahisa Kawaguchi ◽  
Yasuharu Tabara ◽  
...  
Keyword(s):  
Normal Distribution ◽  
Multiple Testing ◽  
Contingency Tables ◽  
Truncated Normal Distribution ◽  
Multiple Testing Correction ◽  
Truncated Normal

scholarly journals Log-normal Distribution Type Symmetry Model for Square Contingency Tables with Ordered Categories

2018 ◽  
Vol 47 (3) ◽  
pp. 39-48
Author(s):  
Kiyotaka Iki
Keyword(s):  
Normal Distribution ◽  
Contingency Tables ◽  
Ordered Categories ◽  
Symmetry Model ◽  
Proposed Model ◽  
Type Symmetry ◽  
The Difference ◽  
Log Normal ◽  
Distribution Type ◽  
Log Normal Distribution

For the analysis of square contingency tables with the same row and column ordinal classications, this article proposes a new model which indicates that the log-ratios of symmetric cell probabilities are proportional to the difference between log-row category and log-column category. The proposed model may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate log-normal distribution. Also, this article gives the decomposition of the symmetry model using the proposed model with the orthogonality of test statistics. Examples are given. The simulation studies based on bivariate log-normal distribution are given.

scholarly journals Correction for detector's specificity and sensitivity in contingency tables

2019 ◽  
Author(s):  
Giorgio Gambirasio
Keyword(s):  
Contingency Table ◽  
Contingency Tables ◽  
Probabilistic Approach ◽  
Disease Status ◽  
Specificity And Sensitivity

A methodology has been developed to correct the influence of detector's specificity and sensitivity on the contingency table used to evaluate how much an effect (like disease status) depends on a given cause (like taking a certain drug). The work is based on a deterministic (non-probabilistic) approach to contingency tables analysis.

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