The LMS for testing independence in two-way contingency tables

Albert, J.H. (1990): A Bayesian test for a two-way contingency table using independence. Prior, Canadian Journal of Statistics 18(4): 347–363.10.2307/3315841Search in Google Scholar

Amiri, S., Modarres, R. (2017): Comparison of tests of contingency tables, Journal of Biopharmaceutical Statistics: 1–13.10.1080/10543406.2016.126978627936354Search in Google Scholar

Amiri, S., von Rosen, D. (2011): On the efficiency of bootstrap method into the analysis contingency table. Computer Methods and Programs in Biomedicine 104(2): 182–187.10.1016/j.cmpb.2011.01.00721458876Search in 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: 441–450.10.2307/2348893Search in 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 103(2): 256.10.1037/0033-2909.103.2.256Search in Google Scholar

Campbell, I. (2007): Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations, Statistics in Medicine 26(19): 3661–3675.10.1002/sim.283217315184Search in Google Scholar

Cochran, W.G. (1952): The χ² test of goodness of fit, The Annals of Mathematical Statistics 23(3): 315–345.10.1214/aoms/1177729380Search in Google Scholar

Cochran, W.G. (1954): Some methods for strengthening the common χ² tests, Biometrics 10(4): 417–451.10.2307/3001616Search in 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. 25(3): 341–350.10.1207/s15327906mbr2503_6Search in Google Scholar

Cressie, N., Read, T. (1984): Multinomial Goodness-of-Fit Tests, J R Stat Soc Ser B Stat Methodol 46: 440–464.10.1111/j.2517-6161.1984.tb01318.xSearch in 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: 19–43.10.2307/1403582Search in Google Scholar

Davis, C.S. (1993): A new approximation to the distribution of Pearson’s chi-square, Statistica Sinica: 189–196.Search in Google Scholar

D’Agostino, R.B., Chase, W., Belanger, A. (1988): The Appropriateness of Some Common Procedures for Testing Equality of Two Independent Binomial Proportions. The American Statistician 42(3): 198–202.10.1080/00031305.1988.10475563Search in 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 13(3): 845–874.10.1214/aos/1176349634Search in 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 85(1): 87–94.10.2307/2340521Search in 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 30(1): 18–21.10.1080/00031305.1976.10479127Search in 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 9(6): 1178–1186.10.1214/aos/1176345635Search in Google Scholar

Irwin, J.O. (1935): Tests of significance for differences between percentages based on small numbers, Metron 12(2): 84–94.Search in Google Scholar

Koch, G., Edwards, S. (1988): Clinical efficiency trials with categorical data. In K.E. Peace (Ed.), Biopharmaceutical Statistics for Drug Development. New York, NY: Marcel Dekker: 403–451.Search in 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 75(370): 336–344.10.1080/01621459.1980.10477473Search in 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 26: 75–85.10.1111/j.1467-842X.1984.tb01270.xSearch in 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 32(1): 59–72.10.1002/bimj.4710320111Search in Google Scholar

Liddell, D. (1976): Practical tests of 2x2 contingency tables. The Statistician 25(4): 295–304.10.2307/2988087Search in 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 25(3): 438–458.10.1080/10543406.2014.92085124905809Search in 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 71(3): 832–840.10.1111/biom.12297456752525762089Search in Google Scholar

Lydersen, S., Fagerland, M.W., Laake, P. (2009): Recommended tests for association in 2×2 tables, Statistics in Medicine 28(7): 1159–1175.10.1002/sim.353119170020Search in Google Scholar

Marcotorchino F. (1984): Utilisation des Comparaisons par Paires en Statistique des Contingences, Partie (1), Etude IBM F069, France.Search in Google Scholar

Meng, R.C., Chapman, D.G. (1966): The power of chi square tests for contingency tables, Journal of the American Statistical Association 61(316): 965–975.10.1080/01621459.1966.10482187Search in Google Scholar

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

Shan, G., Wilding, G. (2015): Unconditional tests for association in 2×2 contingency tables in the total sum fixed design, Statistica Neerlandica 69(1): 67–83.10.1111/stan.12047Search in Google Scholar

Sulewski, P. (2013): Modyfikacja testu niezależności [Modification of the independence test], (The paper is in Polish. The abstract in English is available on scholar.google.pl), Statistical News – Central Statistical Office 10: 1–19.Search in Google Scholar

Sulewski, P. (2014): Statystyczne badanie współzależności cech typu dyskretne kategorie, (in Polish), Akademia Pomorska, Słupsk.Search in Google Scholar

Sulewski, P., Motyka, R. (2015): Power analysis of independence testing for contingency tables, Scientific Journal of Polish Naval Academy 56(1): 37-46.10.5604/0860889X.1161260Search in Google Scholar

Sulewski, P. (2016): Moc testów niezależności w tablicy dwudzielczej większej niż 2x2 [Power of independence test in the 2×2 contingency tables bigger than 2x2], (The paper is in Polish. The abstract in English is available on scholar.google.pl), Statistical Review 63(2): 191–209.10.5604/01.3001.0014.1159Search in Google Scholar

Sulewski, P. (2017): A new test for independence in 2x2 contingency tables, Acta Universitatis Lodziensis. Folia Oeconomica 4(330): 55–75.10.18778/0208-6018.330.04Search in Google Scholar

Sulewski, P. (2018): Power analysis of independence testing for the three-way contingency tables of small sizes, Journal of Applied Statistics 45(13): 2481–2498.10.1080/02664763.2018.1424122Search in Google Scholar

Vélez, J.I., Marmolejo-Ramos, F., Correa, J.C. (2016): A Graphical Diagnostic Test for Two-Way Contingency Tables, Revista Colombiana de Estadística 39(1): 97–108.10.15446/rce.v39n1.55142Search in 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 40(12): 2225–2242.10.1080/03610921003764274Search in Google Scholar

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