Nowy test niezależności dla tablic dwudzielczych 2×2

Autor

  • Piotr Sulewski Pomeranian University in Słupsk, Faculty of Mathematics and Natural Sciences, Institute of Mathematics

DOI:

https://doi.org/10.18778/0208-6018.330.04

Słowa kluczowe:

test niezależności, tablica dwudzielcza 2×2, statystyka logarytmiczno‑minimalna, statystyka modułowa, statystyki power divergence, metoda Monte Carlo

Abstrakt

W literaturze statystycznej istnieje wiele miar do ujawniania niezależności dwóch zmiennych jakościowych w tabelach kontyngencji, w szczególności w tabelach dwudzielczych 2×2. W niniejszym artykule porównano cztery testy niezależności. Są to: test chi‑kwadrat, jako najbardziej znany przedstawiciel statystyk power divergence, test modułowy oraz test d‑kwadrat, jako modyfikacje testu Pearsona, test logarytmiczno‑minimalny, będący nową propozycją. Wartości krytyczne dla wyżej wymienionych testów zostały wyznaczone metodami Monte Carlo. W celu porównania testów zaproponowano miarę nieprawdziwości H0 i wyznaczono ich moc.

Pobrania

Brak dostępnych danych do wyświetlenia.

Bibliografia

Agresti A. (2002), Categorical Data Analysis, Wiley, New Jersey.
Google Scholar

Albert J.H. (1990), A Bayesian test for a two‑way contingency table using independence, “Prior. Canadian Journal of Statistics”, vol. 18, no. 4, pp. 347–363.
Google Scholar

Andrés A.M., Tejedor I.H., Mato A.S. (1995), The Wilcoxon, Spearman, Fisher, χ2, Student and Pearson Tests and 2x2 Tables, “The Statistician”, pp. 441–450.
Google Scholar

Beh E.J., Farver T.B. (2009), An evaluation of non‑iterative methods for estimating the linear‑by‑linear parameter of ordinal log‑linear models, “Australian & New Zealand Journal of Statistics”, vol. 51, no. 3, pp. 335–352.
Google Scholar

Berry K.J., Mielke P.W. (1988), Monte Carlo comparisons of the asymptotic chi‑square and likelihood‑ratio tests with the no asymptotic chi‑square tests for sparse r×c tables, “Psychological Bulletin”, vol. 103, no. 2, p. 256.
Google Scholar

Blitzstein J., Diaconis P. (2011), A sequential importance sampling algorithm for generating random graphs with prescribed degrees, “Internet Mathematics”, vol. 6, pp. 489–522.
Google Scholar

Campbell I. (2007), Chi‑squared and Fisher‑Irwin tests of two‑by‑two tables with small sample recommendations, “Statistics in Medicine”, vol. 26, no. 19, pp. 3661–3675.
Google Scholar

Ceyhan E. (2010), Directional clustering tests based on nearest neighbor contingency tables, “Journal of nonparametric Statistics”, vol. 22, no. 5, pp. 599–616.
Google Scholar

Chang C.H., Lin J.J., Pal N. (2011), Testing the equality of several gamma means: a parametric bootstrap method with applications, “Computational Statistics”, vol. 26, no. 1, pp. 55–76.
Google Scholar

Chang C.H., Pal N. (2008), A revisit to the Behrens–Fisher problem: comparison of five test methods, “Communications in Statistics – Simulation and Computation”, vol. 37, no. 6, pp. 1064–1085.
Google Scholar

Chen Y., Diaconis P., Holmes S.P., Liu J.S. (2005), Sequential Monte Carlo methods for statistical analysis of tables, “Journal of the American Statistical Association”, vol. 100, pp. 109–120.
Google Scholar

Chen Y., Dinwoodie I.H., Sullivant S. (2006), Sequential importance sampling for multiway tables, “The Annals of Statistics”, pp. 523–545.
Google Scholar

Clogg C.C., Eliason S.R. (1987), Some common problems in log‑linear analysis, “Sociological Methods & Research”, vol. 16, no. 1, pp. 8–44.
Google Scholar

Cochran W.G. (1952), The χ2 test of goodness of fit, “The Annals of Mathematical Statistics”, pp. 315–345.
Google Scholar

Cochran W.G. (1954), Some methods for strengthening the common χ2 tests, “Biometrics”, vol. 10, no. 4, pp. 417–451.
Google Scholar

Cohen J., Nee J.C. (1990), Robustness of Type I Error and Power in Set Correlation Analysis of Contingency Tables, “Multivariate Behav. Res.”, vol. 25, no. 3, pp. 341–350.
Google Scholar

Cressie N., Read T. (1984), Multinomial Goodness‑of‑Fit Tests, “J. R. Stat. Soc. Ser. B. Stat. Methodol.”, vol. 46, pp. 440–464.
Google Scholar

Cressie N., Read T.R. (1989), Pearson’s χ2 and the log likelihood ratio statistics G2: a comparative review, “International Statistical Review/Revue Internationale de Statistique”, pp. 19–43.
Google Scholar

Cryan M., Dyer M. (2003), A polynomial‑time algorithm to approximately count contingency tables when the number of rows is constant, “Journal of Computer and System Sciences”, vol. 67, pp. 291–310.
Google Scholar

Cryan M., Dyer M., Goldberg L.A., Jerrum M., Martin R. (2006), Rapidly mixing Markov chains for sampling contingency tables with a constant number of rows, “SIAM Journal on Computing”, vol. 36, pp. 247–278.
Google Scholar

Cung C. (2013), Crime and Demographics: An Analysis of LAPD Crime Data, “M. sc. Thesis”, UCLA, Department of Statistics, Los Angeles.
Google Scholar

Davis C.S. (1993), A new approximation to the distribution of Pearson’s chi‑square, “StatisticaSinica”, pp. 189–196.
Google Scholar

Desalvo S., Zhao J.Y. (2016), Random Sampling of Contingency Tables via Probabilistic Divide‑and‑Conquer, “ArXiv preprint”, ArXiv, 1507.00070v4.
Google Scholar

Diaconis P., Efron B. (1985), Testing for independence in a two‑way table: new interpretations of the chi‑square statistics, “The Annals of Statistics”, pp. 845–874.
Google Scholar

Diaconis P., Sturmfels B. (1998), Algebraic algorithms for sampling from conditional distributions, “The Annals of Statistics”, vol. 26, pp. 363–397.
Google Scholar

Dickhaus T., Straßburger K., Schunk D., Morcillo‑Suarez C., Illig T., Navarro A. (2012), How to analyze many contingency tables simultaneously in genetic association studies, “Statistical Applications in Genetics and Molecular Biology”, vol. 11, no. 4, pp. 1544–6115.
Google Scholar

Egozcue J.J., Pawlowsky‑Glahn V., Templ M., Hron K. (2015), Independence in contingency tables using simplicial geometry, “Communications in Statistics‑Theory and Methods”, vol. 44, no. 18, pp. 3978–3996.
Google Scholar

El Galta R., Stijnen T., Houwing‑Duistermaat J.J. (2008), Testing for genetic association: a powerful score test, “Stat Med.”, vol. 27, no. 22, pp. 4596–4609.
Google Scholar

Fisher R.A. (1922), On the interpretation of χ2 from contingency tables, and the calculation of P, “Journal of the Royal Statistical Society”, vol. 85, no. 1, pp. 87–94.
Google Scholar

Fishman G.S. (2012), Counting contingency tables via multistage Markov chain Monte Carlo, “Journal of Computational and Graphical Statistics”, vol. 21, pp. 713–738.
Google Scholar

García J.E., González‑López V.A. (2014), Independence tests for continuous random variables based on the longest increasing subsequence, “Journal of Multivariate Analysis”, vol. 127, pp. 126–146.
Google Scholar

García J.E., González‑López V.A. (2016), Independence test for sparse data, “International Conference of Numerical Analysis and Applied Mathematics 2015”, AIP Publishing, vol. 1738, no. 1, p. 140002.
Google Scholar

Garcia‑Perez M.A., Nunez‑Anton V. (2009), Accuracy of the power‑divergence statistics for testing independence and homogeneity in two‑way contingency tables, “Commun. Stat. – Simul. Comput.”, vol. 38, pp. 503–512.
Google Scholar

Garside G.R., Mack C. (1976), Actual type 1 error probabilities for various tests in the homogeneity case of the 2×2 contingency table, “The American Statistician”, vol. 30, no. 1, pp. 18–21.
Google Scholar

Haber M. (1987), A comparison of some conditional and unconditional exact tests for 2x2 contingency tables: A comparison of some conditional and unconditional exact tests, “Communications in Statistics – Simulation and Computation”, vol. 16, no. 4, pp. 999–1013.
Google Scholar

Haberman S.J. (1981), Tests for independence in two‑way contingency tables based on canonical correlation and on linear‑by‑linear interaction, “The Annals of Statistics”, vol. 9, no. 6, pp. 1178–1186.
Google Scholar

Hall P., Wilson S.R. (1991), Two guidelines for bootstrap hypothesis testing, “Biometrics”, pp. 757–762.
Google Scholar

Hui‑Qiong L., Guo‑Liang T., Xue‑Jun J., Nian‑Sheng T. (2016), Testing hypothesis for a simple ordering in incomplete contingency tables, “Computational Statistics & Data Analysis”, vol. 99, pp. 25–37.
Google Scholar

Iossifova R., Marmolejo‑Ramos F. (2013), When the body is time: spatial and temporal deixis in children with visual impairments and sighted children, “Research in Developmental Disabilities”, vol. 34, no. 7, pp. 2173–2184.
Google Scholar

Irwin J.O. (1935), Tests of significance for differences between percentages based on small numbers, “Metron”, vol. 12, no. 2, pp. 84–94.
Google Scholar

Jeong H.C., Jhun M., Kim D. (2005), Bootstrap tests for independence in two‑way ordinal contingency tables, “Computational Statistics & Data Analysis”, vol. 48, no. 3, pp. 623–631.
Google Scholar

Koehler K.J., Larntz K. (1980), An empirical investigation of goodness‑of‑fit statistics for sparse multinomials, “Journal of the American Statistical Association”, vol. 75, no. 370, pp. 336–344.
Google Scholar

Lawal H.B., Uptong G.J.G. (1984), On the use of χ2 as a test of independence in contingency tables with small cell expectations, “Australian Journal of Statistics”, vol. 26, pp. 75–85.
Google Scholar

Lawal H.B., Uptong G.J.G. (1990), Comparisons of Some Chi‑squared Tests for the Test of Independence in Sparse Two‑Way Contingency Tables, “Biometrical Journal”, vol. 32, no. 1, pp. 59–72.
Google Scholar

Lin J.J., Chang C.H., Pal N. (2015), A revisit to contingency table and tests of independence: bootstrap is preferred to Chi‑Square approximations as well as Fisher’s exact test, “Journal of Biopharmaceutical Statistics”, vol. 25, no. 3, pp. 438–458.
Google Scholar

Lipsitz S.R., Fitzmaurice G.M., Sinha D., Hevelone N., Giovannucci E., Hu J.C. (2015), Testing for independence in J×K contingency tables with complex sample survey data, “Biometrics”, vol. 71, no. 3, pp. 832–840.
Google Scholar

Lydersen S., Fagerland M.W., Laake P. (2009), Recommended tests for association in 2×2 tables, “Statistics in Medicine”, vol. 28, no. 7, pp. 1159–1175.
Google Scholar

Meng R.C., Chapman D.G. (1966), The power of chi square tests for contingency tables, “Journal of the American Statistical Association”, vol. 61, no. 316, pp. 965–975.
Google Scholar

Nandram B., Bhatta D., Bhadra D. (2013), A likelihood ratio test of quasi‑independence for sparse two‑way contingency tables, “Journal of Statistical Computation and Simulation”, vol. 85, no. 2, pp. 284–304.
Google Scholar

Pearson K. (1904), On the theory of contingency and its relation to association and normal correlation, “K. Pearson, Early Papers”.
Google Scholar

Shan G., Wilding G. (2015), Unconditional tests for association in 2×2 contingency tables in the total sum fixed design, “Statistica Neerlandica”, vol. 69, no. 1, pp. 67–83.
Google Scholar

Sulewski P. (2009), Two-by-two Contingency Table as a Goodness-of-Fit Test, “Computational Methods in Science and Technology”, vol. 15, no. 2, pp. 203–211.
Google Scholar

Sulewski P. (2013), Modyfikacja testu niezależności [Modification of the independence test], “Statistical News – Central Statistical Office”, vol. 10, pp. 1–19.
Google Scholar

Sulewski P. (2014), Statystyczne badanie współzależności cech typu dyskretne kategorie [The statistical study of features interdependence of discrete categories type], Pomeranian University, Slupsk.
Google Scholar

Sulewski P., Motyka R. (2015), Power analysis of independence testing for contingency tables, “Scientific Journal of Polish Naval Academy”, vol. 56, no. 1, pp. 37–46.
Google Scholar

Sulewski P. (2016a), Moc testów niezależności w tablicy dwudzielczej [Power of independence test in the contingency tables], “Statistical News – Central Statistical Office”, vol. 8, pp. 1–17.
Google Scholar

Sulewski P. (2016b), Moc testów niezależności w tablicy dwudzielczej większej niż 2x2 [Power of independence test in the 2´2 contingency tables bigger than 2x2], “Statistical Review”, vol. 63, no. 2, pp. 191–209.
Google Scholar

Taneichi N., Sekiya Y. (2007), Improved transformed statistics for the test of independence in r×s contingency tables, “Journal of Multivariate Analysis”, vol. 98, no. 8, pp. 1630–1657.
Google Scholar

Vélez J.I., Marmolejo‑Ramos F., Correa J.C. (2016), A Graphical Diagnostic Test for Two‑Way Contingency Tables, “RevistaColombiana de Estadística”, vol. 39, no. 1, pp. 97–108.
Google Scholar

Wickens T.D. (1969), Multiway Contingency Tables Analysis for the Social Sciences, Psychology Press, United States.
Google Scholar

Yenigün C.D., Székely G.J., Rizzo M.L. (2011). A Test of Independence in Two‑Way Contingency Tables Based on Maximal Correlation, “Communications in Statistics‑Theory and Methods”, vol. 40, no. 12, pp. 2225–2242.
Google Scholar

Yoshida R., Xi J., Wei S., Zhou F., Haws D. (2011), Semigroups and sequential importance sampling for multiway tables, “ArXiv preprint”, ArXiv, 1111, p. 6518.
Google Scholar

Yu Y. (2014), Tests of independence in a single 2×2 contingency table with random margins, Doctoral dissertation, Worcester Polytechnic Institute, Worcester.
Google Scholar

Zelterman D. (1987). Goodness‑of‑fit tests for large sparse multinomial distributions, “J. Am. Stat. Assoc.”, vol. 82, pp. 624–629.
Google Scholar

Opublikowane

2017-11-15

Jak cytować

Sulewski, P. (2017). Nowy test niezależności dla tablic dwudzielczych 2×2. Acta Universitatis Lodziensis. Folia Oeconomica, 4(330), [55]-75. https://doi.org/10.18778/0208-6018.330.04

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