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Автор: Grafiati

Опубліковано: 15 вересня 2021

Оновлено: 10 лютого 2022

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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 (January 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.

2

Mwamba, John Muteba. "On The Persistence Of Selectivity And Market Timing Skills In Hedge Funds." International Business & Economics Research Journal (IBER) 12, no. 12 (November 25, 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.

3

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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4

Ortego, M. I., and J. J. Egozcue. "Bayesian estimation of the orthogonal decomposition of a contingency table." Austrian Journal of Statistics 45, no. 4 (July 28, 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.

5

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 (January 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.

6

Stein, Joël, and Fabien Stoop. "Neighborhood-Based Contingency Tables Including Errors Compensation." Monthly Weather Review 147, no. 1 (January 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.

7

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 (June 11, 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.

8

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 (May 31, 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.

9

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 (December 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.

10

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 (November 1988): 235–49. http://dx.doi.org/10.1111/j.2044-8317.1988.tb00899.x.

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11

BARVINOK, ALEXANDER. "What Does a Random Contingency Table Look Like?" Combinatorics, Probability and Computing 19, no. 4 (February 12, 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.

12

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 (October 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.

13

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 (June 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.

14

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 (June 11, 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.

15

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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16

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 (June 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.

17

Ostrovski, Vladimir. "New Equivalence Tests for Approximate Independence in Contingency Tables." Stats 2, no. 2 (April 23, 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.

18

Dyer, Martin, Ravi Kannan, and John Mount. "Sampling contingency tables." Random Structures and Algorithms 10, no. 4 (July 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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19

Kayibi, Koko K., S. Pirzada, and T. A. Chishti. "Sampling contingency tables." AKCE International Journal of Graphs and Combinatorics 15, no. 3 (December 1, 2018): 298–306. http://dx.doi.org/10.1016/j.akcej.2017.10.001.

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20

Tsumoto, Shusaku. "Contingency matrix theory: Statistical dependence in a contingency table." Information Sciences 179, no. 11 (May 13, 2009): 1615–27. http://dx.doi.org/10.1016/j.ins.2008.11.023.

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21

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

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22

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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23

Brzezińska, Justyna. "Ordinal Log-Linear Models for Contingency Tables." Folia Oeconomica Stetinensia 16, no. 1 (December 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.

24

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 (June 5, 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.

25

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 (September 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.

26

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 (January 1, 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.

27

Uhler, Caroline, and Donald Richards. "Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables." Journal of Algebraic Statistics 10, no. 1 (April 10, 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.

28

Pham, Thi Mui, and Maria Kateri. "Inference for Ordinal Log-Linear Models Based on Algebraic Statistics." Journal of Algebraic Statistics 10, no. 1 (April 10, 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.

29

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

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30

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

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31

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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32

Kateri, Maria. "ϕ-Divergence in Contingency Table Analysis". Entropy 20, № 5 (27 квітня 2018): 324. http://dx.doi.org/10.3390/e20050324.

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33

Govaert, Gérard, and Mohamed Nadif. "Latent Block Model for Contingency Table." Communications in Statistics - Theory and Methods 39, no. 3 (January 13, 2010): 416–25. http://dx.doi.org/10.1080/03610920903140197.

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34

Kern-Isberner, Gabriele, and Heinz Peter Reidmacher. "Interpreting a contingency table by rules." International Journal of Intelligent Systems 11, no. 6 (December 7, 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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35

Hong, Chong Sun, and Tae Gyu Oh. "Correlation plot for a contingency table." Communications for Statistical Applications and Methods 28, no. 3 (May 31, 2021): 295–305. http://dx.doi.org/10.29220/csam.2021.28.3.295.

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36

Pyle, Matthew E., and Keith F. Brill. "A Comparison of Two Methods for Bias Correcting Precipitation Skill Scores." Weather and Forecasting 34, no. 1 (December 26, 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.

37

Kriesniati, Prastika, Desi Yuniarti, and Darnah A. Nohe. "ANALISIS KORELASI SOMERS’D PADA DATA TINGKAT KENYAMANAN SISWA-SISWI SMP PLUS MELATI SAMARINDA." BAREKENG: Jurnal Ilmu Matematika dan Terapan 7, no. 2 (December 1, 2014): 31–40. http://dx.doi.org/10.30598/barekengvol7iss2pp31-40.

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Somers'd correlation is a analysis of correlate is used for data with ordinal scale and formed in a contingency table. Somers'd correlation can be used for symmetric and asymmetric relationships. In this case, will be explained about Somers’d asymmetric correlation. Somers'd dYX correlation for asymmetrical association applied to data from questionnaires about their comfortable level of Students live in dorms of Melati formed into 2 contingency table, the contingency table for boarding facilities with the comfortable level of students and the quality of the food with the comfortable level of students. Based on the analysis of correlation Somers'd dYX, it can be seen that there is relationship between boarding facility with comfortable level of students and quality of food with comfortable level of students, and then correlation coefficient from 2 contingency table is 0,330 and 0,345 respectively

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Hoshino, Nobuaki. "Random partitioning over a sparse contingency table." Annals of the Institute of Statistical Mathematics 64, no. 3 (March 6, 2011): 457–74. http://dx.doi.org/10.1007/s10463-011-0327-8.

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Jammalamadaka, Sreenivasa Rao. "A Contingency Table Approach to Nonparametric Testing." Journal of the American Statistical Association 97, no. 459 (September 2002): 927. http://dx.doi.org/10.1198/016214502760301291.

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Chen, Ming-Hui. "A Contingency Table Approach to Nonparametric Testing." Technometrics 45, no. 1 (February 2003): 105–6. http://dx.doi.org/10.1198/tech.2003.s22.

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41

Zwick, Rebecca, and Elliot M. Cramer. "A MULTIVARIATE PERSPECTIVE ON CONTINGENCY TABLE ANALYSIS." ETS Research Report Series 1986, no. 1 (June 1986): i—15. http://dx.doi.org/10.1002/j.2330-8516.1986.tb00167.x.

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42

Tsumoto, Shusaku, and Shoji Hirano. "Combinatorics of Information Granule in Contingency Table." International Journal of Intelligent Systems 28, no. 9 (July 8, 2013): 892–906. http://dx.doi.org/10.1002/int.21610.

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43

Luck, Stanley. "Factoring a 2 x 2 contingency table." PLOS ONE 14, no. 10 (October 25, 2019): e0224460. http://dx.doi.org/10.1371/journal.pone.0224460.

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Govaert, Gérard, and Mohamed Nadif. "Clustering of contingency table and mixture model." European Journal of Operational Research 183, no. 3 (December 2007): 1055–66. http://dx.doi.org/10.1016/j.ejor.2005.10.074.

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45

Sulewski, Piotr. "Power Analysis of Independence Testing for Three-way Contingency Table 2×2×2." Przegląd Statystyczny 63, no. 4 (December 31, 2016): 431–47. http://dx.doi.org/10.5604/01.3001.0014.1224.

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The first aim of this paper is to present the theory of the proposal of the author in the form of modular statistics for three-way contingency table 2×2×2 and examine its properties in relation to known “chi-squared statistics”. The second aim is to describe the procedure of generating the content of these tables using the bar method. The third aim is to propose the measure of untruthfulness of null hypothesis as well as to compare the quality of independence tests using their power. Critical values for all analyzed statistics were determined by simulation methods of Monte Carlo.

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Iki, Kiyotaka. "Log-normal Distribution Type Symmetry Model for Square Contingency Tables with Ordered Categories." Austrian Journal of Statistics 47, no. 3 (May 27, 2018): 39–48. http://dx.doi.org/10.17713/ajs.v47i3.701.

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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.

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Everitt, B. S. "The Analysis of Contingency Tables." Biometrics 48, no. 3 (September 1992): 977. http://dx.doi.org/10.2307/2532373.

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Schwenke, James R., and B. S. Everitt. "The Analysis of Contingency Tables." American Statistician 47, no. 2 (May 1993): 156. http://dx.doi.org/10.2307/2685204.

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Højsgaard, Søren. "Split models for contingency tables." Computational Statistics & Data Analysis 42, no. 4 (April 2003): 621–45. http://dx.doi.org/10.1016/s0167-9473(02)00119-6.

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Klimova, Anna, Tamás Rudas, and Adrian Dobra. "Relational models for contingency tables." Journal of Multivariate Analysis 104, no. 1 (February 2012): 159–73. http://dx.doi.org/10.1016/j.jmva.2011.07.006.

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