메뉴 건너뛰기




Volumn 2, Issue 3, 2011, Pages 528-545

Pearson-fisher chi-square statistic revisited

Author keywords

2 2 contingency table; Chi square distribution; Chi square statistics; Fisher exact test

Indexed keywords

CHI SQUARE STATISTIC; CHI-SQUARE TESTS; COEFFICIENT OF VARIATION; EXPERIMENTAL ERRORS; FISHER EXACT TEST; GOODNESS OF FIT; GOODNESS-OF-FIT TEST;

EID: 84879264436     PISSN: None     EISSN: 20782489     Source Type: Journal    
DOI: 10.3390/info2030528     Document Type: Article
Times cited : (93)

References (52)
  • 1
    • 0040032334 scopus 로고
    • Biometry
    • Fisher, R.A. Biometry. Biometrics 1948, 4, 217-219.
    • (1948) Biometrics , vol.4 , pp. 217-219
    • Fisher, R.A.1
  • 3
    • 0001454867 scopus 로고
    • On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling
    • Pearson, K. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos. Mag. 1900, 50, 157-175.
    • (1900) Philos. Mag , vol.50 , pp. 157-175
    • Pearson, K.1
  • 4
    • 0002386913 scopus 로고
    • 2 from contingency tables, and the calculation of P
    • 2 from contingency tables, and the calculation of P. J. R. Stat. Soc. 1922, 85, 87-94.
    • (1922) J. R. Stat. Soc , vol.85 , pp. 87-94
    • Fisher, R.A.1
  • 5
    • 0002386915 scopus 로고
    • 2 measures the discrepancy between observation and hypothesis
    • 2 measures the discrepancy between observation and hypothesis. J. R. Stat. Soc. 1924, 87, 442-450.
    • (1924) J. R. Stat. Soc , vol.87 , pp. 442-450
    • Fisher, R.A.1
  • 6
    • 34250106763 scopus 로고
    • The components of chi-squared statistics for goodness-of-fit tests
    • Mirvaliev, M. The components of chi-squared statistics for goodness-of-fit tests. J. Sov. Math. 1987, 38, 2357-2363.
    • (1987) J. Sov. Math , vol.38 , pp. 2357-2363
    • Mirvaliev, M.1
  • 7
    • 0006354851 scopus 로고
    • Karl pearson and the Chi-squared test
    • Plackett, R.L. Karl pearson and the Chi-squared test. Int. Statist. Rev. 1983, 51, 59-72.
    • (1983) Int. Statist. Rev , vol.51 , pp. 59-72
    • Plackett, R.L.1
  • 8
    • 77956983837 scopus 로고
    • The fisher/pearson Chi-squared controversary: A turning point for inductive inference
    • Baird, D. The fisher/pearson Chi-squared controversary: A turning point for inductive inference. Br. J. Philos. Sci. 1983, 34, 105-118.
    • (1983) Br. J. Philos. Sci , vol.34 , pp. 105-118
    • Baird, D.1
  • 9
    • 0000642942 scopus 로고
    • Some methods for strengthening the common chi-square tests
    • Cochran, W.G. Some methods for strengthening the common chi-square tests. Biometrics 1954, 10, 417-451.
    • (1954) Biometrics , vol.10 , pp. 417-451
    • Cochran, W.G.1
  • 12
    • 50049128032 scopus 로고
    • On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference, Part I, reprinted at in Neyman, J., Pearson, E.S. Eds.; Cambridge University Press: Cambridge, UK, (originally published in 1928)
    • Neyman, J.; Pearson, E.S. On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference, Part I.; reprinted at pp. 1-66 in Joint Statistical Papers; Neyman, J., Pearson, E.S. Eds.; Cambridge University Press: Cambridge, UK, (originally published in 1928), 1967.
    • (1967) Joint Statistical Papers , pp. 1-66
    • Neyman, J.1    Pearson, E.S.2
  • 13
    • 70350063105 scopus 로고    scopus 로고
    • The Testing of Statistical Hypotheses in Relation to Probabilities a Priori
    • reprinted at in Neyman, J., Pearson, E.S., Eds.; Cambridge University Press: Cambridge, UK, (originally published in 1933), 1967
    • Neyman, J.; Pearson, E.S. The Testing of Statistical Hypotheses in Relation to Probabilities a Priori; reprinted at pp. 186-202 in Joint Statistical Papers; Neyman, J., Pearson, E.S., Eds.; Cambridge University Press: Cambridge, UK, (originally published in 1933), 1967.
    • Joint Statistical Papers , pp. 186-202
    • Neyman, J.1    Pearson, E.S.2
  • 14
    • 0042318390 scopus 로고    scopus 로고
    • On the Problem of Two Samples, reprinted at in Neyman, J., Pearson, E.S., Eds.; Cambridge University Press: Cambridge, UK, (originally published in 1930), 1967
    • Pearson, E.S.; Neyman, J. On the Problem of Two Samples; reprinted at pp. 99-115 in Joint Statistical Papers; Neyman, J., Pearson, E.S., Eds.; Cambridge University Press: Cambridge, UK, (originally published in 1930), 1967.
    • Joint Statistical Papers , pp. 99-115
    • Pearson, E.S.1    Neyman, J.2
  • 15
    • 0003775965 scopus 로고    scopus 로고
    • Chapter 10. Chi-Square Goodness-of-fit, 6th ed.; Thomson Learning Academic Resource Center: Duxbury, MA, USA
    • Rosner, B. Fundamentals of Biostatistics. Chapter 10. Chi-Square Goodness-of-fit, 6th ed.; Thomson Learning Academic Resource Center: Duxbury, MA, USA, 2006, pp. 438-441.
    • (2006) Fundamentals of Biostatistics , pp. 438-441
    • Rosner, B.1
  • 16
    • 0000367077 scopus 로고
    • An investigation of the restraints with respect to sample size commonly imposed on the use of the chi-square statistic
    • Roscoe, J.T.; Byars, J.A. An investigation of the restraints with respect to sample size commonly imposed on the use of the chi-square statistic. J. Am. Stat. Assoc. 1971, 66, 755-759.
    • (1971) J. Am. Stat. Assoc , vol.66 , pp. 755-759
    • Roscoe, J.T.1    Byars, J.A.2
  • 17
    • 0001400362 scopus 로고
    • 2 test of goodness of fit
    • 2 test of goodness of fit. Ann. Math. Stat. 1952, 25, 315-345.
    • (1952) Ann. Math. Stat , vol.25 , pp. 315-345
    • Cochran, WG.1
  • 19
    • 0002033443 scopus 로고
    • The logic of inductive inference
    • Fisher, R.A. The logic of inductive inference. J. R. Stat. Soc. 1935, 98, 39-54.
    • (1935) J. R. Stat. Soc , vol.98 , pp. 39-54
    • Fisher, R.A.1
  • 20
    • 84924532810 scopus 로고
    • An empirical investigation of goodness-of-fit statistics for sparse multinomials
    • Koehler, K.J.; Larntz, K. An empirical investigation of goodness-of-fit statistics for sparse multinomials. J. Am. Stat. Assoc. 1980, 75, 336-344.
    • (1980) J. Am. Stat. Assoc , vol.75 , pp. 336-344
    • Koehler, K.J.1    Larntz, K.2
  • 21
    • 21144483164 scopus 로고
    • Generalized pearson-fisher Chi-square goodness-of-fit tests, with applications to models with life history data
    • Li, G.; Doss, H. Generalized pearson-fisher Chi-square goodness-of-fit tests, with applications to models with life history data. Ann. Stat. 1993, 21, 772-797.
    • (1993) Ann. Stat , vol.21 , pp. 772-797
    • Li, G.1    Doss, H.2
  • 22
    • 0000685721 scopus 로고
    • Unified large-sample theory of general Chi-squared statistics for tests of fit
    • Moore, D.S.; Spruill, M.C. Unified large-sample theory of general Chi-squared statistics for tests of fit. Ann. Stat. 1975, 3, 599-616.
    • (1975) Ann. Stat , vol.3 , pp. 599-616
    • Moore, D.S.1    Spruill, M.C.2
  • 23
    • 0000429529 scopus 로고
    • Chi-square tests for multivariate normality with application to common stock prices
    • Moorea, D.S.; Stubblebinea, J.B. Chi-square tests for multivariate normality with application to common stock prices. Commun. Stat. Theory Methods 1981, 10, 713-738.
    • (1981) Commun. Stat. Theory Methods , vol.10 , pp. 713-738
    • Moorea, D.S.1    Stubblebinea, J.B.2
  • 24
    • 0000863812 scopus 로고
    • Chi-Square Tests of Fit for Type II Censored Data
    • Mihalko, D.P.; Moore, D.S. Chi-Square Tests of Fit for Type II Censored Data. Ann. Stat. 1980, 8, 625-644.
    • (1980) Ann. Stat , vol.8 , pp. 625-644
    • Mihalko, D.P.1    Moore, D.S.2
  • 25
    • 77956059155 scopus 로고    scopus 로고
    • A general family of limited information goodness-of-fit statistics for multinomial data
    • Joe, H.; Maydeu-Olivares, A. A general family of limited information goodness-of-fit statistics for multinomial data. Psychometrika 2010, 75, 393-419.
    • (2010) Psychometrika , vol.75 , pp. 393-419
    • Joe, H.1    Maydeu-Olivares, A.2
  • 26
    • 9844227496 scopus 로고
    • Chi-square tests with one degree of freedom; extension of the mantel-haenszel procedure
    • Mantel, N. Chi-square tests with one degree of freedom; extension of the mantel-haenszel procedure. J. Am. Stat. Assoc. 1963, 58, 690-700.
    • (1963) J. Am. Stat. Assoc , vol.58 , pp. 690-700
    • Mantel, N.1
  • 27
    • 0040477782 scopus 로고
    • On the asymptotic power of tests for independence in contingency tables from stratified samples
    • Nathan, G. On the asymptotic power of tests for independence in contingency tables from stratified samples. J. Am. Stat. Assoc. 1972, 67, 917-920.
    • (1972) J. Am. Stat. Assoc , vol.67 , pp. 917-920
    • Nathan, G.1
  • 28
    • 0018687930 scopus 로고
    • A multiple testing procedure for clinical trials
    • O’Brien, P.C.; Fleming, T.H. A multiple testing procedure for clinical trials. Biometrics 1979, 35, 549-556.
    • (1979) Biometrics , vol.35 , pp. 549-556
    • O’Brien, P.C.1    Fleming, T.H.2
  • 29
    • 0000175291 scopus 로고
    • Estimation of relationship for limited dependent variables
    • Tobin, J. Estimation of relationship for limited dependent variables. Econometrica 1958, 26, 24-36.
    • (1958) Econometrica , vol.26 , pp. 24-36
    • Tobin, J.1
  • 30
    • 0011676998 scopus 로고
    • F-test alternatives to fisher’s exact test and to the Chi-square test of homogeneity in 2 × 2 tables
    • Overall, J.E.; Starbuck, R.R. F-test alternatives to fisher’s exact test and to the Chi-square test of homogeneity in 2 × 2 tables. J. Educ. Behav. Stat. 1983, 8, 59-73.
    • (1983) J. Educ. Behav. Stat , vol.8 , pp. 59-73
    • Overall, J.E.1    Starbuck, R.R.2
  • 31
    • 84973839889 scopus 로고
    • Post hoc pair-wise comparisons for the Chi-square test of homogeneity of proportions
    • Cox, M.K.; Key, C.H. Post hoc pair-wise comparisons for the Chi-square test of homogeneity of proportions. Key Educ. Psychol. Meas. 1993, 53, 951-962.
    • (1993) Key Educ. Psychol. Meas , vol.53 , pp. 951-962
    • Cox, M.K.1    Key, C.H.2
  • 32
    • 73949144163 scopus 로고    scopus 로고
    • Omogeneity/heterogeneity hypotheses for standardized mortality ratios based on minimum power-divergence estimators
    • Pardo, L.; Martín, N. Omogeneity/heterogeneity hypotheses for standardized mortality ratios based on minimum power-divergence estimators. Biom. J. 2009, 51, 819-836.
    • (2009) Biom. J , vol.51 , pp. 819-836
    • Pardo, L.1    Martín, N.2
  • 33
    • 63049089107 scopus 로고    scopus 로고
    • Comments on ‘Tests for the homogeneity of two binomial proportions in extremely unbalanced 2 × 2 contingency tables’
    • Andrés, A.M.; Tejedor, I.H. Comments on ‘Tests for the homogeneity of two binomial proportions in extremely unbalanced 2 × 2 contingency tables’. Stat. Med. 2009, 28, 528-531.
    • (2009) Stat. Med , vol.28 , pp. 528-531
    • Andrés, A.M.1    Tejedor, I.H.2
  • 34
    • 48749139034 scopus 로고
    • Clarification of the use of Chi-square and likelihood functions in fits to histograms
    • Baker, S.; Cousins, R.D. Clarification of the use of Chi-square and likelihood functions in fits to histograms. Nucl. Instrum. Methods Phys. Res. 1984, 221, 437-442.
    • (1984) Nucl. Instrum. Methods Phys. Res , vol.221 , pp. 437-442
    • Baker, S.1    Cousins, R.D.2
  • 35
    • 28144464479 scopus 로고    scopus 로고
    • Alternatives to the Chi-Square Test for Evaluating Rank Histograms from Ensemble Forecasts
    • Elmore, K.L. Alternatives to the Chi-Square Test for Evaluating Rank Histograms from Ensemble Forecasts. Weather Forecast. 2005, 20, 789-795.
    • (2005) Weather Forecast , vol.20 , pp. 789-795
    • Elmore, K.L.1
  • 36
    • 14944341003 scopus 로고    scopus 로고
    • Approximate and asymptotic distributions of Chi-squared-type mixtures with applications
    • Jin-Ting Zhang. Approximate and asymptotic distributions of Chi-squared-type mixtures with applications. J. Am. Stat. Assoc. 2005, 100, 273-285.
    • (2005) J. Am. Stat. Assoc , vol.100 , pp. 273-285
    • Zhang, Jin-Ting1
  • 38
    • 0003632935 scopus 로고
    • 8th ed.; Iowa State University Press: Iowa City, IA, USA
    • Snedecor, G.W.; Cochran, W.G. Statistical Methods, 8th ed.; Iowa State University Press: Iowa City, IA, USA, 1989.
    • (1989) Statistical Methods
    • Snedecor, G.W.1    Cochran, W.G.2
  • 39
    • 0000923503 scopus 로고
    • Asymptotic theory of certain “goodness-of-fit” criteria based on stochastic processes
    • Anderson, T.W.; Darling, D.A. Asymptotic theory of certain “goodness-of-fit” criteria based on stochastic processes. Ann. Math. Stat. 1952, 23, 193-212.
    • (1952) Ann. Math. Stat , vol.23 , pp. 193-212
    • Anderson, T.W.1    Darling, D.A.2
  • 40
    • 0000162341 scopus 로고
    • Confidence limits for an unknown distribution function
    • Kolmogorov, A. Confidence limits for an unknown distribution function. Ann. Math. Stat. 1941, 12, 461-463.
    • (1941) Ann. Math. Stat , vol.12 , pp. 461-463
    • Kolmogorov, A.1
  • 41
    • 54049110614 scopus 로고
    • Studies in crop variation. II. The manurial response of different potato varieties
    • Fisher, R.A.; Mackenzie, W.A. Studies in crop variation. II. The manurial response of different potato varieties. J. Agric. Sci. 1923, 13, 311-320.
    • (1923) J. Agric. Sci , vol.13 , pp. 311-320
    • Fisher, R.A.1    Mackenzie, W.A.2
  • 46
    • 84980082105 scopus 로고
    • Transmission of Information
    • Hartley, R.V.L. Transmission of Information. Bell Sys. Tech. J. 1928, 1928, 535-563
    • (1928) Bell Sys. Tech. J , vol.1928 , pp. 535-563
    • Hartley, R.V.L.1
  • 48
    • 0041954178 scopus 로고    scopus 로고
    • Chi-square goodness-of-fit test (accessed 1 November 2010)
    • Chi-square goodness-of-fit test. In: NIST/SEMATECH e-Handbook of Statistical Methods. Available online: http://www.itl.nist.gov/div898/handbook/prc/section2/prc211.htm (accessed 1 November 2010).
    • NIST/SEMATECH e-Handbook of Statistical Methods
  • 49
    • 0001309764 scopus 로고
    • Classification of the solvent properties of common liquids
    • Snyder, L.R. Classification of the solvent properties of common liquids. J. Chromatogr. A 1974, 92, 223-230.
    • (1974) J. Chromatogr. A , vol.92 , pp. 223-230
    • Snyder, L.R.1
  • 51
    • 0001595204 scopus 로고
    • Table for estimating the goodness of fit of empirical distributions
    • Smirnov, N.V. Table for estimating the goodness of fit of empirical distributions. Ann. Math. Stat. 1948, 19, 279-281.
    • (1948) Ann. Math. Stat , vol.19 , pp. 279-281
    • Smirnov, N.V.1
  • 52
    • 84959801619 scopus 로고
    • Statistical aspects of the analysis of data from retrospective studies of disease
    • Mantel, N.; Haenszel, W. Statistical aspects of the analysis of data from retrospective studies of disease. J. Natl. Cancer Inst. 1959, 22, 719-748.
    • (1959) J. Natl. Cancer Inst , vol.22 , pp. 719-748
    • Mantel, N.1    Haenszel, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.