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1

Beh, Eric J. "Confidence circles for correspondence analysis using orthogonal polynomials." Journal of Applied Mathematics and Decision Sciences 5, no. 1 (2001): 35–45. http://dx.doi.org/10.1155/s1173912601000037.

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An alternative approach to classical correspondence analysis was developed in [3] and involves decomposing the matrix of Pearson contingencies of a contingency table using orthogonal polynomials rather than via singular value decomposition. It is especially useful in analysing contingency tables which are of an ordinal nature. This short paper demonstrates that the confidence circles of Lebart, Morineau and Warwick (1984) for the classical approach can be applied to ordinal correspondence analysis. The advantage of the circles in analysing a contingency table is that the researcher can graphically identify the row and column categories that contribute or not to the hypothesis of independence.
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2

Mokhtari, Mohamed, and Islam Bousri. "Comparaison entre les retenus en utilisant deux schémas de convection : PCMT et Bougeault (1985)." JAMA 4 (June 5, 2020): 61–65. https://doi.org/10.5281/zenodo.10939488.

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Une étude comparative entre les cumuls de précipitations simulés par ALADIN en utilisant deux schémas de convection a été réalisé. La première version utilise le schéma de convection de Bougeault [1] qui fonctionne actuellement en opérationnel dans la chaîne ALADIN-Algérie et la deuxième version utilise le schéma PCMT. La comparaison est faite par rapport aux observations enregistrées par les 84 stations de l'ONM durant la période qui s'étale du 01er janvier 2018 au 30 juin 2019 en utilisant la table de contingence. Les premiers résultats montrent que les scores obtenus avec le schéma PCMT sont les meilleurs que ceux obtenus avec celui de Bougeault [1], notamment pour des situations pluvieuses intenses.
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3

Mwamba, John Muteba. "On The Persistence Of Selectivity And Market Timing Skills In Hedge Funds." International Business & Economics Research Journal (IBER) 12, no. 12 (2013): 1575. http://dx.doi.org/10.19030/iber.v12i12.8251.

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This paper investigates the persistence of hedge fund managers skills during periods of boom and/or recession. We consider a data set of monthly investment strategy indices published by Hedge Fund Research group. The data set spans from January 1995 to June 2010. We divide this sample period into four overlapping sub-sample periods that contain different economic cycles. We define a skilled manager as a manager who can outperform the market consistently during two consecutive sub-sample periods. We first estimate outperformance, selectivity and market timing skills using both linear and quadratic Capital Asset Pricing Model-CAPM. Persistence in performance is carried out in three different fashions: contingence table, chi-square test and cross-sectional auto-regression technique. The results show that fund managers have the skills to outperform the market during periods of positive economic growth only. This market outperformance is due to both selectivity and market timing skills. These results contradict the Efficient Market Hypothesis-EMH due to limited arbitrage opportunity.
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4

JAQUET, Chantal, André CHARRAK, Fabien CHAREIX, and Pierre‑François MOREAU. "Table ronde autour du livre d’André Charrak : Contingence et nécessité des lois de la nature au XVIIIe siècle. La philosophie seconde des Lumières." Philonsorbonne, no. 2 (April 15, 2008): 131–54. http://dx.doi.org/10.4000/philonsorbonne.196.

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5

Ortego, M. I., and J. J. Egozcue. "Bayesian estimation of the orthogonal decomposition of a contingency table." Austrian Journal of Statistics 45, no. 4 (2016): 45–56. http://dx.doi.org/10.17713/ajs.v45i4.136.

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In a multinomial sampling, contingency tables can be parametrized by probabilities of each cell. These probabilities constitute the joint probability function of two or more discrete random variables. These probability tables have been previously studied from a compositional point of view. The compositional analysis of probability tables ensures coherence when analysing sub-tables. The main results are:(1) given a probability table, the closest independent probability table is the product of their geometric marginals;(2) the probability table can be orthogonally decomposed into an independent table and an interaction table;(3) the departure of independence can be measured using simplicial deviance, which is the Aitchison square norm of the interaction table.In previous works, the analysis has been performed from a frequentist point of view. This contribution is aimed at providing a Bayesian assessment of the decomposition. The resulting model is a log-linear one, which parameters are the centered log-ratio transformations of the geometric marginals and the interaction table.Using a Dirichlet prior distribution of multinomial probabilities, the posterior distribution of multinomial probabilities is again a Dirichlet distribution. Simulation of this posterior allows to study the distribution of marginal and interaction parameters, checking the independence of the observed contingency table and cell interactions.The results corresponding to a two-way contingency table example are presented.
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6

Ahmed, S. El Touny, H. Ibrahim Ahmed, and I. Amer Mohmed. "Estimating Cost Contingency for Highway Construction Projects Using Analytic Hierarchy Processes." IJCSI International Journal of Computer Science Issues 11, no. 6 (2014): 73–84. https://doi.org/10.5281/zenodo.4762112.

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Winning a bid at a price that yields a profit, is one of the contractor's major goals from bidding. One of the significant components of markup is the risk allowance (contingencies). Therefore, contractors should be wise to consider the likelihood that a particular risk will occur, identify the potential financial impact, and determine the suitable contingency allowance if the risk was to be mitigated through contingencies. Based on previous research, usually, most of the contractors set a percentage of the cost as contingencies. This approach of setting the contingency percentage intuitively could either lead to losing the bid or leaving money on the table. Therefore, the objective of the presented research in this paper is to identify the financial impacts of the risk factors during the bidding stages that affect cost contingency and develop a fast and reliable model to estimate the expected cost contingency of highway construction projects. A survey was conducted on ninety construction companies and experts in Egypt. The data obtained from the survey was then processed using Analytic Hierarchy Processes (AHP) technique on the most important fourteen factors out of 175 ones that affect cost contingency. The developed model was tested using historical completed projects and results show that the predicted cost contingency matches with (96.31%) the average estimated contingency for real case projects.  The developed cost contingency model showed robust results.
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7

Stein, Joël, and Fabien Stoop. "Neighborhood-Based Contingency Tables Including Errors Compensation." Monthly Weather Review 147, no. 1 (2019): 329–44. http://dx.doi.org/10.1175/mwr-d-17-0288.1.

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Some specific scores use a neighborhood strategy in order to reduce double penalty effects, which penalize high-resolution models, compared to large-scale models. Contingency tables based on this strategy have already been proposed, but can sometimes display undesirable behavior. A new method of populating contingency tables is proposed: pairs of missed events and false alarms located in the same local neighborhood compensate in order to give pairs of hits and correct rejections. Local tables are summed up so as to provide the final table for the whole verification domain. It keeps track of the bias of the forecast when neighborhoods are taken into account. Moreover, the scores computed from this table depend on the distance between forecast and observed patterns. This method is applied to binary and multicategorical events in a simplified framework so as to present the method and to compare the new tables with previous neighborhood-based contingency tables. The new tables are then used for the verification of two models operational at Météo-France: AROME, a high-resolution model, and ARPEGE, a large-scale global model. The comparison of several contingency scores shows that the importance of the double penalty decreases more for AROME than for ARPEGE when the neighboring size increases. Scores designed for rare events are also applied to these neighborhood-based contingency tables.
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8

Ando, Shuji. "An index for discriminating the direction of anti-sum-asymmetry for square contingency tables." Biometrical Letters 62, no. 1 (2025): 49–63. https://doi.org/10.2478/bile-2025-0003.

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Abstract A square contingency table is a special case of a two-way contingency table wherein the row and column variables consist of the same classification. In square contingency tables, observations tend to be concentrated in the main diagonal cells of the table or nearby, and independence between row and column variables often does not hold. The anti-sum-symmetry model has a symmetrical structure with respect to the anti-diagonal cells of the table. The anti-sum-symmetry model should be applied to square contingency tables with ordered categories. The existing index, which can measure the degree of departure from the anti-sum-symmetry model, cannot discriminate between perfect upper and lower anti-sum-asymmetries. To address this issue, we propose here a directional index which can discriminate between the two types of anti-sum-asymmetries. The proposed index can be interpreted as an index for measuring the degree of perfect anti-sum-asymmetry. We derive an approximately unbiased estimator and an approximate confidence interval for the proposed index. The utility of the proposed index is demonstrated through a real data analysis.
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9

Raynaud, Dominique. "Inside the Ghetto - Using a Table of Contingency and Cladisitic Methods for Definitional Purposes." Bulletin of Sociological Methodology/Bulletin de Méthodologie Sociologique 133, no. 1 (2017): 5–28. http://dx.doi.org/10.1177/0759106316681419.

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This article aims at clarifying sociological definitions with the help of an original tool, the logical table of contingency, which has characteristics in common with both the statistical table of contingency and Carroll’s bilateral diagram. The unclear notion of ghetto is taken as a test-case. Successive tables of contingency are applied to various defining properties and various sociohistorical situations. Cladistic methods are then used to make the relationships between all ghetto-like situations explicit.
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10

Yamamoto, Kouji, Yuya Matsuda, and Sadao Tomizawa. "Collapsed Double Symmetry Model and Its Decomposition for Square Contingency Tables." International Journal of Statistics and Probability 5, no. 4 (2016): 31. http://dx.doi.org/10.5539/ijsp.v5n4p31.

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For a square contingency table with ordinal categories, there may be a case that one wants to analyze several collapsed tables obtained by combining some adjacent categories of the original table. This paper proposes some new models which indicate double symmetry, quasi double symmetry and marginal double symmetry for the collapsed square tables. It also gives a decomposition of the double symmetry model for collapsed tables. Two kinds of occupational mobility data are analyzed using new models.
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11

Shahzad, Shakeel, Saud Ahmed Khan, and Atiq Ur Rehman. "Most Stringent Test of Independence in W× K Contingency Tables for Nominal Data Using Monte Carlo Simulations." Sustainable Business and Society in Emerging Economies 4, no. 1 (2022): 45–62. http://dx.doi.org/10.26710/sbsee.v4i1.2145.

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 Purpose: This study aims to analyze the performance of tests of independence for nominal data. Tests of independence is one of the most used statistical techniques in econometrics. A principal interest in many studies regarding contingency tables is to test if the variables are independent in contingency table (CT’s). Many standard tests are available for nominal data. However, there is no clarity about choice of tests for various kinds of Data Generating Process (DGP) of nominal data. 
 Design/Methodology/Approach: This study used stringent criteria (SC) for evaluation of optimal test of independence among a large numbers of tests of independence in w × k contingency tables using Monte Carlo simulations.
 Findings: The most stringent test of independence is Logarithmic Minimum Square (LMS) in w × k contingency table for nominal data. 
 Implications/Originality/Value: This Paper gives very clear guidance to practitioner about use of tests of independence for nominal data. Results recommends based on solid estimation of Monte Carlo Simulation and algorithm for a variety of Data Generating Process (DGP) in w × k contingency tables. We came to conclusion and recommended clearly that Logarithmic Minimum Square (LMS) is the optimal and most stringent test, and no other test can beat it for nominal data in w × k contingency tables. 
 
 
 
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12

Slezák, Peter, Pavol Bokes, Pavol Námer, and Iveta Waczulíková. "Microsoft Excel add-in for the statistical analysis of contingency tables." International Journal for Innovation Education and Research 2, no. 5 (2014): 90–100. http://dx.doi.org/10.31686/ijier.vol2.iss5.188.

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This paper introduces “Contingency table analysis”, a freely available menu-driven add-in program for Microsoft EXCEL, written in Visual Basic for Applications (VBA), for basic univariate and bivariate statistical analyses of contingency tables. The program provides modules for the statistical analysis of proportions, 2 × 2 tables, stratified 2 × 2 tables, and R × C tables. We compare the results of the analyses performed using our software with those obtained by commercially available statistical software. The comparison shows that our software performs equally well. The use of the add-in facilitates the convenient prosecution of basic statistical analyses on contingency tables from within EXCEL, sparing us the additional cost, or the inconvenience of alternating between multiple platforms, often incurred in using a commercial statistical package.
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13

Dagne, Getachew A., C. Hendricks Brown, and George W. Howe. "Bayesian Hierarchical Modeling of Heterogeneity in Multiple Contingency Tables: An Application to Behavioral Observation Data." Journal of Educational and Behavioral Statistics 28, no. 4 (2003): 339–52. http://dx.doi.org/10.3102/10769986028004339.

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Intervention studies often rely on microcoded data of social interactions to provide evidence of change due to development or treatment. Traditionally these data have been collapsed into small contingency tables. Such an approach can introduce spurious findings. Instead of treating each unit’s contingency table independently, or collapsing the tables into single aggregate table, it is more efficient to analyze associations in all units simultaneously using hierarchical models. This article presents Bayesian hierarchical models to analyze several two-way categorical data with random effects that allow different levels of variation across several events. To illustrate this approach, the authors present an analysis of couples’ interaction data from a recent study investigating how couples cope when one partner has become unemployed.
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14

Chatterjee, Sangit, and Nancy Jo Delaney. "Contingencies for analysis of contingency tables: More on the chi-squared test." British Journal of Mathematical and Statistical Psychology 41, no. 2 (1988): 235–49. http://dx.doi.org/10.1111/j.2044-8317.1988.tb00899.x.

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15

BARVINOK, ALEXANDER. "What Does a Random Contingency Table Look Like?" Combinatorics, Probability and Computing 19, no. 4 (2010): 517–39. http://dx.doi.org/10.1017/s0963548310000039.

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Let R = (r1, . . ., rm) and C = (c1, . . ., cn) be positive integer vectors such that r1 + ⋯ + rm = c1 + ⋯ + cn. We consider the set Σ(R, C) of non-negative m × n integer matrices (contingency tables) with row sums R and column sums C as a finite probability space with the uniform measure. We prove that a random table D ∈ Σ(R, C) is close with high probability to a particular matrix (‘typical table’) Z defined as follows. We let g(x) = (x + 1)ln(x + 1) − x ln x for x ≥ 0 and let g(X) = ∑i,jg(xij) for a non-negative matrix X = (xij). Then g(X) is strictly concave and attains its maximum on the polytope of non-negative m × n matrices X with row sums R and column sums C at a unique point, which we call the typical table Z.
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16

Long, Michael A., Kenneth J. Berry, and Paul W. Mielke. "Multiway Contingency Tables: Monte Carlo Resampling Probability Values for the Chi-Squared and Likelihood-Ratio Tests." Psychological Reports 107, no. 2 (2010): 501–10. http://dx.doi.org/10.2466/03.pr0.107.5.501-510.

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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.
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17

Mielke, Paul W., and Kenneth J. Berry. "Exact Probabilities for First-Order, Second-Order, and Third-Order Interactions in 2 × 2 × 2 × 2 Contingency Tables." Perceptual and Motor Skills 86, no. 3 (1998): 760–62. http://dx.doi.org/10.2466/pms.1998.86.3.760.

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A FORTRAN program to calculate exact probabilities for first-, second-, and third-order interactions in 2×2×2×2 contingency tables with fixed marginals is presented. Computational speed and accuracy are assured with the use of an arbitrary constant for the initial table and recursively defined values for all subsequent tables.
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18

Iki, Kiyotaka, Akira Shibuya, and Sadao Tomizawa. "Diagonal Exponent Conditional Symmetry Model for Square Contingency Tables with Ordered Categories." International Journal of Statistics and Probability 5, no. 4 (2016): 38. http://dx.doi.org/10.5539/ijsp.v5n4p38.

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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.
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Saigusa, Yusuke, Tomomasa Takada, Aki Ishii, Tomoyuki Nakagawa, and Sadao Tomizawa. "Measure of departure from cumulative local symmetry for square contingency tables having ordered categories." Biometrical Letters 57, no. 1 (2020): 23–35. http://dx.doi.org/10.2478/bile-2020-0003.

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SummaryFor square contingency tables with nominal categories, a local symmetry model which indicates the symmetric structure of probabilities for only one pair of symmetric cells is proposed. For ordinal square tables, the present paper proposes (1) another local symmetry model for cumulative probabilities from the upper-right and lower-left corners of the table, and (2) a measure to represent the degree of departure from the proposed model. The measure has the form of a weighted harmonic mean of the diversity index, which includes the Shannon entropy as a special case. Examples are given in which the proposed method is applied to square table data on decayed teeth in Japanese women patients.
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Teuscher, Friedrich. "The quantification of Simpson’s paradox and other contributions to contingency table theory." PLOS ONE 17, no. 2 (2022): e0262502. http://dx.doi.org/10.1371/journal.pone.0262502.

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The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium parameter as a measure of two-way interactions applied to three-way tables makes it possible to quantify Simpson’s paradox by a simple formula. With tests on three-way interactions, there is only one that determines whether the partial interactions of all variables agree or whether there is at least one variable whose partial interactions disagree. To date, there has been no test available that determines whether the partial interactions of a certain variable agree or disagree, and the presented work closes this gap. This work reveals the relation of the multiplicative and the additive measure of a three-way interaction. Another contribution addresses the question of which cells in a contingency table are fixed when the first- and second-order marginal totals are given. The proposed procedure not only detects fixed zero counts but also fixed positive counts. This impacts the determination of the degrees of freedom. Furthermore, limitations of methods that simulate contingency tables with given pairwise associations are addressed.
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Sulewski, Piotr. "Wielowymiarowe uogólnienie testu niezależności." Wiadomości Statystyczne. The Polish Statistician 2013, no. 12 (2013): 27–41. http://dx.doi.org/10.59139/ws.2013.12.2.

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This paper discusses the theory of contingency tables with particular emphasis on three-dimension-tables. Their use in statistical surveys is stressed in the article. The three-dimension-table is presented as a chi-square test of independence and its implementation in VBA (Visual Basic for Applications) language. In this way, users are provided ready-made procedures and functions for carrying out surveys in Microsoft Excel. It has been examined also the ability of the three-dimension-table to detect the relationship between the measured traits, referred to as the power of the test.
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22

Tahata, Kouji. "Advances in Quasi-Symmetry for Square Contingency Tables." Symmetry 14, no. 5 (2022): 1051. http://dx.doi.org/10.3390/sym14051051.

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Contingency tables highlight relationships between categorical variables. Typically, the symmetry or marginal homogeneity of a square contingency table is evaluated. The original symmetry model often does not accurately fit a dataset due to its restrictions. Caussinus proposed a quasi-symmetry model which served as a bridge between symmetry and marginal homogeneity in square contingency tables. This study significantly influenced methodological developments in the statistical analysis of categorical data. Herein recent advances in quasi-symmetry are reviewed with an emphasis on four topics related to the author’s results: (1) modeling based on the f-divergence, (2) the necessary and sufficient condition of symmetry, (3) partition of test statistics for symmetry, and (4) measure of the departure from symmetry. The asymmetry model based on f-divergence enables us to express various asymmetries. Additionally, these models are useful to derive the necessary and sufficient conditions of symmetry with desirable properties. This review may be useful to consider the statistical modeling and the measure of symmetry for contingency tables with the same classifications.
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23

Ostrovski, Vladimir. "New Equivalence Tests for Approximate Independence in Contingency Tables." Stats 2, no. 2 (2019): 239–46. http://dx.doi.org/10.3390/stats2020018.

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We introduce new equivalence tests for approximate independence in two-way contingency tables. The critical values are calculated asymptotically. The finite sample performance of the tests is improved by means of the bootstrap. An estimator of boundary points is developed to make the bootstrap based tests statistically efficient and computationally feasible. We compare the performance of the proposed tests for different table sizes by simulation. Then we apply the tests to real data sets.
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Tsumoto, Shusaku. "Contingency matrix theory: Statistical dependence in a contingency table." Information Sciences 179, no. 11 (2009): 1615–27. http://dx.doi.org/10.1016/j.ins.2008.11.023.

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Brzezińska, Justyna. "Ordinal Log-Linear Models for Contingency Tables." Folia Oeconomica Stetinensia 16, no. 1 (2016): 264–73. http://dx.doi.org/10.1515/foli-2016-0017.

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Abstract A log-linear analysis is a method providing a comprehensive scheme to describe the association for categorical variables in a contingency table. The log-linear model specifies how the expected counts depend on the levels of the categorical variables for these cells and provide detailed information on the associations. The aim of this paper is to present theoretical, as well as empirical, aspects of ordinal log-linear models used for contingency tables with ordinal variables. We introduce log-linear models for ordinal variables: linear-by-linear association, row effect model, column effect model and RC Goodman’s model. Algorithm, advantages and disadvantages will be discussed in the paper. An empirical analysis will be conducted with the use of R.
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Kayibi, Koko K., S. Pirzada, and T. A. Chishti. "Sampling contingency tables." AKCE International Journal of Graphs and Combinatorics 15, no. 3 (2018): 298–306. http://dx.doi.org/10.1016/j.akcej.2017.10.001.

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27

Dyer, Martin, Ravi Kannan, and John Mount. "Sampling contingency tables." Random Structures and Algorithms 10, no. 4 (1997): 487–506. http://dx.doi.org/10.1002/(sici)1098-2418(199707)10:4<487::aid-rsa4>3.0.co;2-q.

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IHLENFELD, JANET T. "Log-Linear Contingency Table Analysis." Nursing Research 37, no. 4 (1988): 252???253. http://dx.doi.org/10.1097/00006199-198807000-00017.

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Töwe, J., J. Bock, and G. Kundt. "Interactions in Contingency Table Analysis." Biometrical Journal 27, no. 1 (1985): 17–24. http://dx.doi.org/10.1002/bimj.4710270103.

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30

Kumar, Pranesh. "ANALYSIS OF MULTIFACTOR IMPRECISE DATA USING NEUTROSOPHIC STATISTICS." jnanabha 54, no. 01 (2024): 134–40. http://dx.doi.org/10.58250/jnanabha.2024.54117.

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In multifactor experiments, data collected may correspond to the categorical variables, which place individuals/items into one of several groups (categories). The values of a categorical variable are levels for the categories and distribution of a categorical variable lists the count or percent of individuals/items falling into each category. For example, a two-way table describes two categorical variables by arranging counts according to a row variable and a column variable and each combination of values for two variables is called a cell. However, sometimes a few or every cell counts may be imprecise numbers because of missing or incomplete information on the sample individuals, or investigators negligence, or any other reasons. In such situations, data need to be analyzed using neutrosophic logic and neutrosophic statistics. Generally, the objective of contingency table analysis is to study goodness of model fit for discrete or continuous distributions, testing for homogeneity, and testing for independence. In this paper, we consider neutrosophic analysis of categorical data, which is arranged in contingency tables. We discuss results obtained from the neutrosophic contingency table analysis using data observed in various applications.
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31

Tian, Guo-Liang, and Hui-Qiong Li. "A new framework of statistical inferences based on the valid joint sampling distribution of the observed counts in an incomplete contingency table." Statistical Methods in Medical Research 26, no. 4 (2015): 1712–36. http://dx.doi.org/10.1177/0962280215586591.

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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.
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Tomizawa, Sadao, Nobuko Miyamoto, Obuko Miyamoto, and Ryotaro Yajima. "Proportional Reduction in Variation Measure for Normal-Ordinal Contingency Tables." Calcutta Statistical Association Bulletin 53, no. 3-4 (2002): 167–84. http://dx.doi.org/10.1177/0008068320020301.

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For a two-way contingency table with a nominal explanatory and a nominal response variables, Goodman and Kruskal (1954), and Theil (1970) proposed the measures which describe the proportional reduction in variation (PRV) from the marginal distribution to the conditional distributions of the response. Tomizawa, Seo and Ebi {1997) proposed a generalization of those measures. This paper proposes a PRV measure for a two-way contingency table with a nominal explanatory and an ordinal response variables (instead of those with a nominal response variable). The proposed measure is expressed using the Patil and Taillie's (1982) diversity index, defined for the cumulative probabilities that an observation will fall in the response category j or below (or, j + 1 or above). The measure depends on the order of listing the response categories. It is useful for comparing the degrees of PRV in several tables with ordered response categories.
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Iki, Kiyotaka, and Sadao Tomizawa. "Parsimonious Bivariate T-distribution Type Symmetry Models for Square Contingency Tables." International Journal of Statistics and Probability 11, no. 5 (2022): 44. http://dx.doi.org/10.5539/ijsp.v11n5p44.

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For square contingency tables with ordered categories, Iki, Ishihara and Tomizawa (2013) considered the t-distribution type symmetry model and Iki, Okada and Tomizawa (2018) extended this model. These models are appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution having any degrees of freedom. This study proposes three kinds of parsimonious models for these models. Additionally, this paper provides the decompositions of the parsimonious symmetry model using the proposed model. Some simulation studies based on bivariate t-distribution show the performances of the proposed models.
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López-Chau, Asdrúbal, Lisbeth Rodriguez-Mazahua, Farid García-Lamont, Maricela Quintana-López, and Carlos A. Rojas-Hernández. "Dichotomization of Multilevel Variables to Detect Hidden Associations." Applied Sciences 12, no. 24 (2022): 12929. http://dx.doi.org/10.3390/app122412929.

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A test of independence is commonly used to determine differences (or associations) between samples in a nominal level measurement. Fisher’s exact test and Chi-square test are two of the most widely applied tests of independence used in the data analyses in different areas such as information technologies, biostatistics, psychology and health sciences. In some cases, contingency tables with null entries (also called random zeros) arise, particularly if the number of samples is small, and the variables analyzed are multilevel. This situation becomes a problem because if one or more entries in a contingency table are zero or have small values, then the tests of independence produce unreliable results. In this paper, we propose a method to address that issue. The method merges one or more levels of the variables analyzed to create contingency tables with only one degree of freedom, avoiding applying a test of independence on contingency tables with random zeros. The source code (Python) of the method is publicly available for use. The results obtained using our method give a complete panorama of the associations between the variables of a data set. To show the effectiveness of our approach to find dependencies between variables, we use four data sets publicly available on the Internet.
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35

Saigusa, Yusuke, Yuta Teramoto, and Sadao Tomizawa. "Measure of Departure from Conditional Symmetry Based on Cumulative Probabilities for Square Contingency Tables." Symmetry 13, no. 10 (2021): 1897. http://dx.doi.org/10.3390/sym13101897.

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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.
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36

Macak, Tomas. "Stability of Dependencies of Contingent Subgroups with Merged Groups: Vaccination Case Study." Mathematics 9, no. 22 (2021): 2917. http://dx.doi.org/10.3390/math9222917.

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The answers to extreme phenomena both in nature and in business sectors are the constructions of the distribution of random variables with extreme values. Another area in which appropriate theoretical research is conducted regarding the influence of suppressor (third) variables in categorical data. When examining dependencies in PivotTables, we often find it necessary to merge data into larger sets (e.g., due to a greater number of theoretical frequencies lower than their critical value). A phenomenon many exist wherein the partial relation is stronger than the zero relation. For example, in such a combination, instability may occur, which indicates contingent subgroups with the merged group. The dependence of dependencies is practically manifested because the data of contingent subgroups indicate inconsistent (inverted) conclusions compared to the associated group. For this reason, this paper aimed to find the critical ratios of partial probabilities in the contingency table of subgroups of the original variables, and to determine the conditions of result consistency and contingency stability, including the proof. For practical use and for the ease of repeating the proposed procedure, the solution is based on a case study that compares the effectiveness of vaccination.
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37

Beh, Eric J., and Pamela J. Davy. "A non-iterative alternative to ordinal Log-Linear models." Journal of Applied Mathematics and Decision Sciences 8, no. 2 (2004): 67–86. http://dx.doi.org/10.1155/s1173912604000057.

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Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The technique, based on orthogonal polynomials, provides a much simpler method of model fitting than the conventional approach of maximum likelihood estimation, as it does not require iterative calculations nor the fitting and re-fitting to search for the best model. Another advantage is that quadratic and higher order effects can readily be included, in contrast to conventional log-linear models which incorporate linear terms only.The focus of the discussion is the application of the new parameter estimation technique to multi-way contingency tables with at least one ordered variable. This will also be done by considering singly and doubly ordered two-way contingency tables. It will be shown by example that the resulting parameter estimates are numerically similar to corresponding maximum likelihood estimates for ordinal log-linear models.
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38

Pham, Thi Mui, and Maria Kateri. "Inference for Ordinal Log-Linear Models Based on Algebraic Statistics." Journal of Algebraic Statistics 10, no. 1 (2019): 30–50. http://dx.doi.org/10.18409/jas.v10i1.74.

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Tools of algebraic statistics combined with MCMC algorithms have been used in contingency table analysis for model selection and model fit testing of log-linear models. However, this approach has not been considered so far for association models, which are special log-linear models for tables with ordinal classification variables. The simplest association model for two-way tables, the uniform (U) association model, has just one parameter more than the independence model and is applicable when both classification variables are ordinal. Less parsimonious are the row (R) and column (C) effect association models, appropriate when at least one of the classification variables is ordinal. Association models have been extended for multidimensional contingency tables as well. Here, we adjust algebraic methods for association models analysis and investigate their eligibility, focusing mainly on two-way tables. They are implemented in the statistical software R and illustrated on real data tables. Finally the algebraic model fit and selection procedure is assessed and compared to the asymptotic approach in terms of a simulation study.
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39

Uhler, Caroline, and Donald Richards. "Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables." Journal of Algebraic Statistics 10, no. 1 (2019): 1–12. http://dx.doi.org/10.18409/jas.v10i1.71.

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We consider the lattice, $\mathcal{L}$, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, $n(\cdot)$, on $\mathcal{L}$. We derive from the supermodularity of $n(\cdot)$ some generalized Fr\'echet inequalities complementing and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from $n(\cdot)$, and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequality of Ky Fan to derive a new approach to Fr\'echet inequalities for multidimensional contingency tables.
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40

Bismarck, Malte, Christel Deutschmann, and Dana Králová. "Simulation studies on model search in $3$-dimensional contingency tables. Preliminary results." Applications of Mathematics 35, no. 1 (1990): 1–15. http://dx.doi.org/10.21136/am.1990.104383.

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41

WATASE, Kazunori. "Knowledge Acquisition from the Contingency Table." Journal of Japan Society for Fuzzy Theory and Systems 12, no. 2 (2000): 286–94. http://dx.doi.org/10.3156/jfuzzy.12.2_78.

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42

Hong, Chong Sun, and Tae Gyu Oh. "Correlation plot for a contingency table." Communications for Statistical Applications and Methods 28, no. 3 (2021): 295–305. http://dx.doi.org/10.29220/csam.2021.28.3.295.

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43

Govaert, Gérard, and Mohamed Nadif. "Latent Block Model for Contingency Table." Communications in Statistics - Theory and Methods 39, no. 3 (2010): 416–25. http://dx.doi.org/10.1080/03610920903140197.

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44

Kateri, Maria. "ϕ-Divergence in Contingency Table Analysis". Entropy 20, № 5 (2018): 324. http://dx.doi.org/10.3390/e20050324.

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45

Kern-Isberner, Gabriele, and Heinz Peter Reidmacher. "Interpreting a contingency table by rules." International Journal of Intelligent Systems 11, no. 6 (1998): 327–46. http://dx.doi.org/10.1002/(sici)1098-111x(199606)11:6<327::aid-int1>3.0.co;2-p.

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46

Vorkauf, Helmut. "Uncoupling Multidimensional Contingency Tables." Mathematics and Statistics 4, no. 3 (2016): 76–80. http://dx.doi.org/10.13189/ms.2016.040302.

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47

Bezáková, Ivona. "Sampling Binary Contingency Tables." Computing in Science & Engineering 10, no. 2 (2008): 26–31. http://dx.doi.org/10.1109/mcse.2008.62.

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48

Radavičius, Marijus, and Jurgita Židanavičiūtė. "Statistinė struktūrų analizė: kai kurios jos taikymo problemos." Lietuvos matematikos rinkinys 45 (December 18, 2005): 354–62. http://dx.doi.org/10.15388/lmr.2005.27388.

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The work is based on data about the prevalence of congenital anomalies among newborns in Lithuania. The log-linear model is used to assess dependence structure of a subset of categorical variables. It is shown that fitting the log-linear model with just three categorical variables can be a rather complicated task due to large number of unknown parameters and cells in the contingency table. The classical chi-squre test and the bootstrap technique are compared for testing goodness-of-fit. The results demonstrate that the number of cells of even nonsparse contingency tables has significant impact on the tail distribution of the likelihood ratio statistics.
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Pyle, Matthew E., and Keith F. Brill. "A Comparison of Two Methods for Bias Correcting Precipitation Skill Scores." Weather and Forecasting 34, no. 1 (2018): 3–13. http://dx.doi.org/10.1175/waf-d-18-0109.1.

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Abstract A fair comparison of quantitative precipitation forecast (QPF) products from multiple forecast sources using performance metrics based on a 2 × 2 contingency table with assessment of statistical significance of differences requires accounting for differing frequency biases to which the performance metrics are sensitive. A simple approach to address differing frequency biases modifies the 2 × 2 contingency table values using a mathematical assumption that determines the change in hit rate when the frequency bias is adjusted to unity. Another approach uses quantile mapping to remove the frequency bias of the QPFs by matching the frequency distribution of each QPF to the frequency distribution of the verifying analysis or points. If these two methods consistently yield the same result for assessing the statistical significance of differences between two QPF forecast sources when accounting for bias differences, then verification software can apply the simpler approach and existing 2 × 2 contingency tables can be used for statistical significance computations without recovering the original QPF and verifying data required for the bias removal approach. However, this study provides evidence for continued application and wider adoption of the bias removal approach.
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WAHYUNI, NI LUH PUTU SRI, I. NYOMAN WIDANA, and KARTIKA SARI. "Perhitungan Premi Asuransi Menggunakan Model Select Table Pada Asuransi Joint Life." E-Jurnal Matematika 13, no. 1 (2024): 1. http://dx.doi.org/10.24843/mtk.2024.v13.i01.p434.

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Asuransi jiwa merupakan perjanjian antara penanggung (perusahaan asuransi) dan tertanggung (peserta asuransi) untuk mengatasi masalah finansial yang timbul akibat kematian pihak tertanggung. Asuransi jiwa dibagi menjadi beberapa macam salah satunya adalah asuransi jiwa joint life yang merupakan asuransi jiwa gabungan dimana uang pertanggungan diberikan apabila salah satu tertanggung meninggal. Sebaliknya, peserta asuransi memiliki kewajiban untuk membayar sejumlah uang yang disebut premi ke perusahaan asuransi sesuai dengan kontrak yang telah disepakati. Model select table inilah yang akan digunakan dalam menghitung besar premi yang akan ditanggung oleh pihak tertanggung. Tujuan penelitian untuk menghitung premi dengan menggunakan model select table dan tanpa select table pada asuransi joint life berjangka untuk dua orang tertanggung. Tabel yang digunakan adalah Select Life Table with a two-year select period dalam buku Actuarial Mathematicts for Life Contingent Ris (Dickson, et al., 2009) dan Tabel Mortalitas Indonesia. Hasil yang diperoleh adalah nilai premi yang dihitung menggunakan model select table lebih kecil dari pada tanpa menggunakan select table, dimana jika perusahaana asuransi menggukana model select table dalam perhitungan premi, pihak tertanggung dapat membayar premi lebih kecil ke perusahaan asuransi
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