Abstract
Suppose we have a population wherein associated with each member of the population is characteristic from the set of r 1 characteristics \(c_{11},\ldots,c_{1r_{1}}\) and a characteristic from the set of r 2 characteristics \(c_{21},\ldots,c_{2r_{2}}\). For example, if the population is that of all adults (age 18 or over) in the United States, then characteristic 1 might be sex, so that r 1 = 2, c 11 = male, and c 12 = female, and characteristic 2 might be age, so that r 2 = 100, and c 21 = 18, c 22 = 19, …, C 2,100 = 117. We can associate with each member of the population the pair (i i , i 2), where i 1, denotes the index of characteristic 1 and i 2 denotes the index of characteristic 2 of that member.
“Old statisticians never die ... they just get broken down by age and sex.”
S. Smith
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Anderson, T. W. 1954. On estimation of, parameters in latent structure analysis. Psychometrika 19 (March): 1–10.
Bartlett, M. S. 1935. Contingency table interactions. Journal of the Royal Statistical Society, Supplement 2 (No. 2): 248–52.
Bishop, Y. M. M. 1967. Multidimensional contingency tables: cell estimates. Ph.D. dissertation, Department of Statistics, Harvard University. Ann Arbor: University Microfilms.
Bishop, Y. M., Fienberg, S. E., and Holland, P. W. 1975. Discrete Multivariate Analysis: Theory and Practice. Cambridge, MA: MIT Press.
Boschloo, R. D. 1970. Raised conditional level of significance for the 2 × 2 table when testing for the equality of two probabilities. Statistica Neerlandica 21 (No. 1): 1–35.
Clogg, C. C. 1977. Unrestricted and restricted maximum likelihood latent structure analysis: a manual for users. Working paper No. 1977-09, Population Issues Research Office, The Pennsylvania State University.
Conover, W. J. 1974. Some reasons for not using the Yates continuity correction on 2 × 2 contingency tables. Journal of the American Statistical Association 69 (June): 374–82.
Darroch, J. N. 1962. Interactions in multi-factor contingency tables. Journal of the Royal Statistical Society, Series B 24 (No. 1): 251–63.
Fienberg, S. E. 1977. The Analysis of Cross-Classified Categorical Data. Cambridge, MA: MIT Press.
Finney, D. J., Latscha, A., Bennett, B. M., and Hsu, P. 1963. Tables for Testing Significance in a 2 × 2 Contingency Table. Cambridge: Cambridge University Press.
Fisher, R. A. 1934. Statistical Methods for Research Workers, 5th edn. Edinburgh: Oliver and Boyd.
Fisher, R. A. and Yates, F. 1948. Statistical Tables for Biological, Agricultural, and Medical Research, 6th edn. New York: Hafner.
Garside, G. R. 1971. An accurate correction for the χ2-test in the homogeneity case of 2 × 2 contingency tables. New Journal of Statistics and Operational Research 7 (Part 1): 1–26.
Garside, G. R. 1972. Further tables of an accurate correction for the χ2-test in the homogeneity case of the 2 × 2 contingency table. New Journal of Statistics and Operational Research 8 (Part 1): 6–25.
Gilula, Z. 1983. Latent conditional independence in two-way contingency tables: a diagnostic approach. British Journal of Mathematical and Statistical Psychology 36 (May): 114–22.
Goodman, L. A. 1964. Simple methods of analyzing three-factor interaction in contingency tables. Journal of the American Statistical Association 59 (June): 319–52.
Goodman, L. A. 1969. On partitioning χ2 and detecting partial association in three-way contingency tables. Journal of the Royal Statistical Society, Series B 31 (No. 3): 486–98.
Goodman, L. A. 1970. The multivariate analysis of qualitative data: Interactions among multiple classifications. Journal of the American Statistical Association 65 (March): 226–56.
Goodman, L. A. 1974. The analysis of systems of qualitative variables when some of the variables are unobservable. Part I: A modified latent structure approach. American Journal of Sociology 79 (March): 1179–1259.
Goodman, L. A. 1978. Analyzing Qualitative Categorical Data: Log Linear Models and Latent Structure Analysis. Cambridge, MA: Abt Books.
Goodman, L. A. 1979. Simple models for the analysis of association in cross-classifications having ordered categories. Journal of the American Statistical Association 34 (September): 537–52.
Goodman, L. A. 1984. The Analysis of Cross-Classified Data Having Ordered Categories. Cambridge, MA: Harvard University Press.
Green, B. F. Jr. 1951. A general solution for the latent class model of latent structure analysis. Psychometrika 16 (June): 151–66.
Grizzle, J. 1967. Continuity correction in the χ2-test for 2 × 2 tables. The American Statistician 21 (October): 28–32.
Haberman, S. J. 1972. Log-linear fit for contingency tables. Applied Statistics 21 (No. 2): 218–25.
Haberman, S. J. 1974. Log-linear models for frequency tables with ordered classifications. Biometrics 30 (December): 589–600.
Haberman, S. J. 1978. Analysis of Qualitative Data, Vol. I: Introductory Topics. New York: Academic Press.
Haberman, S. J. 1979. Analysis of Qualitative Data, Vol. II. Introductory Topics. New York: Academic Press.
Haberman, S. J. 1981. Tests for independence in two-way contingency tables based on canonical correlation and on linear-by-linear interaction. Annals of Statistics 9 (November): 1178–86.
Harter, H. L. 1969. Order Statistics and Their Use in Testing and Estimation, Vol. 2. Washington, DC: U.S. Government Printing Office.
Irwin, J. 0. 1935. Tests of significance for differences between percentages based on small numbers. Metron 12 (No. 2): 83–94.
Kastenbaum, M. A. and Lamphiear, D. E. 1959. Calculation of chi-square to test the no three-factor interaction hypothesis. Biometrics 15 (March): 107–15.
Kendall, M. G. and Stuart, A. 1973. The Advanced Theory of Statistics, Vol. 2, 3rd edn. New York: Hafner.
Lancaster, H. 0. 1949. The derivation and partition of χ2 in certain discrete distributions Biometrika 36 (June): 117–29.
Lancaster, H. 0. 1951. Complex contingency tables treated by the partitioning of χ2. Journal of the Royal Statistical Society, Series B 13 (No. 2): 242–49.
Lazarsfeld, P. F. and Henry, N. W. 1968. Latent Structure Analysis. New York: Houghton Mifflin.
Lehmann, E. L. 1959. Testing Statistical Hypotheses. New York: Wiley.
Lewis, B. N. 1962. On the analysis of interaction in multi-dimensional contingency tables. Journal of the Royal Statistical Society, Series A 125 (Part 1): 88–117.
Lieberman, G. J. and D. B. Owen. 1961. Tables of the Hypergeometric Probability Distribution. Stanford, CA: Stanford University Press.
McHugh, R. B. 1956. Efficient estimation and local identification in latent class analysis. Psychometrika 21 (December): 331–47.
McHugh, R. B. 1958. Note on ‘Efficient estimation and local identification in latent class analysis.’ Psychometrika 23 (September): 273–74.
Madansky, A. 1959. Partitioning methods in latent class analysis. Paper P-1644. Santa Monica, CA: RAND Corporation.
Madansky, A. 1960. Determinantal methods in latent class analysis. Psychometrika 25 (June): 183–98.
Madansky, A. 1978. Latent structure. In International Encyclopedia of Statistics, Vol. I, ed. W. H. Kruskal and J. M. Tanur. New York: Free Press, pp. 499–505.
Pearson, K. 1904. On the Theory of Contingency and Its Relation to Association and Normal Correlation. London: Drapers’ Co. Memoirs, Biometric Series No. 1.
Pearson, E. S. and Hartley, H. 0. 1972. Biometrika Tables for Statisticians, Vol. 2. Cambridge: Cambridge University Press.
Plackett, R. L. 1962. A note on interactions in contingency tables. Journal of the Royal Statistical Society, Series B 24 (No. 1): 162–66.
Plackett, R. L. 1964. The continuity correction in 2 × 2 tables. Biometrika 51 (December): 327–37.
Roy, S. N. and Kastenbaum, M. A. 1956. On the hypothesis of no “interaction” in a multi-way contingency table. Annals of Mathematical Statistics 27 (September): 749–57.
Snedecor, G. W. 1958. Chi-squares of Bartlett, Mood, and Lancaster in a 2 × 2 contingency table. Biometrics 14 (December): 560–62.
Srole, L., Langner, T. S., Michael, S. T., Opler, M. K., and Rennie, T. A. C. 1962. Mental Health in the Metropolis: The Midtown Manhatten Study. New York: McGraw-Hill.
Tocher, K. D. 1950. Extension of Neyman-Pearson theory of tests to discontinuous variates. Biometrika 37 (June): 130–44.
Yates, F. 1934. Contingency tables involving small numbers and the χ2 test. Journal of the Royal Statistical Society, Supplement 1 (No. 2): 217–35.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Madansky, A. (1988). Analysis of Cross-Classified Data. In: Prescriptions for Working Statisticians. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3794-5_9
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3794-5_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8354-6
Online ISBN: 978-1-4612-3794-5
eBook Packages: Springer Book Archive