Bimodality revisited

Journal of Modern Applied Statistical Methods

Volumn 6, Issue 1, 2007, Pages 8-20

  Knapp, Thomas R ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

Bimodality; Kurtosis; Moments; Polarization

Indexed keywords

EID: 48249157896     PISSN: 15389472     EISSN: 15389472     Source Type: Journal    
DOI: 10.22237/jmasm/1177992120     Document Type: Article

References (41)

1. Armstrong, R. I. (1987). The midpoint on a five-point Likert-type scale. Perceptual and Motor Skills, 64, 359-362.
2. Ashman, K. M., Bird, C. M., & Zepf, S. E. (1994). Detecting bimodality in astronomical data sets. Astronomical Journal, 108 (6), 2348-2361.
3. Baker, G. A. (1930). Transformations of bimodal distributions. Annals of Mathematical Statistics, 1 (4), 334-344.
4. Balandra, K. P., & MacGillivray, H. L. (1988). Kurtosis: A critical review. The American Statistician, 42(2), 111-119.
5. Barreto, S., Borges, P. A. V., & Guo, Q. (2003). A typing error in Tokeshi's test of bimodality. Global Ecology and Biogeography, 12, 173-174.
6. Beach, S. R. H., Fincham, S. D., Amir, N., & Leonard, K. E. (2005). The taxometrics of marriage: Is marital discord categorical? Journal of Family Psychology, 19(2), 276-285.
7. Chissom, B. S. (1970). Interpretation of the kurtosis statistic. The American Statistician, 24(4), 19-22.
8. Choonpradub, C., & McNeil, D. (2005). Can the box plot be improved? Songklanakarin Journal of Science and Technology, 27(3), 649-657.
9. Darlington, R. B. (1970). Is kurtosis really "peakedness"? The American Statistician, 24(2), 19-22.
10. DeCarlo, L. T. (1997). On the meaning and use of kurtosis. Psychological Methods, 2 (3), 292-307.
11. DiMaggio, P., Evans, J., & Bryson, B. (1996). Have Americans' social attitudes become more polarized? The American Journal of Sociology, 102 (3), 690-755.
12. Doehlert, D. C., McMullen, M. S., Jannink, J-L, Panigrahi, S., Gu, H., & Riveland, N. R. (2004). Evaluation of oat kernel size uniformity. Crop Science, 44, 1178-1186.
13. Esteban, J. M, & Ray, D. (1994). On the measurement of polarization. Econométrica, 62(4), 819-851.
14. Evans, J. H. (2003). Have Americans' attitudes become more polarized? An Update. Social Science Quarterly, 84(1), 71-90.
15. Evans, J. H., Bryson, B., & DiMaggio, P. (2001). Opinion polarization: Important contributions, necessary limitations. The American Journal of Sociology, 106(4), 944-960.
16. Frankland, B. W., & Zumbo, B. D. (2002). Quantifying bimodality, Part I: An easily implemented method using SPSS. Journal of Modern Applied Statistical Methods, 1(1), 157-166.
17. Grandi, C., Tapia, J. L., Marshall, G., and the NEOCOSUR Collaborative Group. (2005). An assessment of the severity, proportionality and risk of mortality of very low birth weight infants with fetal growth restriction: A multicenter South American analysis. Journal de Pedatria, 81(3), 198-204.
18. Greeley, A. M. (1997). Polarizing Catholics?: Don't believe your mail! America, 176(6), 11-15.
19. Guy, R. F., & Norvell, M. (1977). The neutral point on a Likert scale. The Journal of Psychology, 95, 199-204.
20. Haldane, J. B. S. (1952). Simple tests for bimodality and bitangentiality. Annals of Eugenics, 16, 359-364.
21. Hampel, F. R. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69, 383-393.
22. Hartigan, J. A., & Hartigan, P. M. (1985). The dip test of unimodality. The Annals of Statistics, 13(1), 70-84.
23. Hildebrand, D. K. (1971). Kurtosis measures bimodality? The American Statistician, 25(1), 42-43.
24. Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society. Series B (Methodological), 52(1), 105-124.
25. Knapp, T. R. (1959). Two-group classification in the absence of a criterion. Unpublished Ed.D. dissertation, Harvard University.
26. Knapp, T.R. (1970). A measure of bimodality and its sampling distribution for samples from a normal population. Unpublished paper, University of Rochester.
27. Lim, T-O, Bakri, R., Morad, Z., & Hamid, M. A. (2002). Bimodality in blood glucose distribution. Diabetes Care, 25, 2212-2217.
28. Lindner, M. D. (1997). Reliability, distribution, and validity of age-related cognitive deficits in the Morris Water Maze. Neurobiology of Learning and Memory, 68, 203-220.
29. Minnotte, M. C. (1997). Nonparametric testing of the existence of modes. The Annals of Statistics, 25 (4), 1646-1660.
30. Moors, J. J. A. (1986). The meaning of kurtosis: Darlington reexamined. The American Statistician, 40(4), 283-284.
31. Mouw, T., & Sobel, M. E. (2001). Culture wars and opinion polarization: The case of abortion. The American Journal of Sociology, 106(4),913-943.
32. Pearson, K. (1894). Contributions to the mathematical theory of evolution: On the dissection of asymmetrical frequency-curves. Philosophical Transactions of the Royal Society, Series A, Part 1, 185, 71-90.
33. Pearson, K. (1929). Editorial note. Biometrika, 21, 370-375.
34. Reschenhofer, E. (2001). The bimodality principle. Journal of Statistics Education, 9 (1). [Online]
35. Roller, C. M. (2005, February) No child left behind: A survey of its impact on IRA members. 8 pp. Retrieved from the International Reading Association website, www.reading.org.
36. Ruppert, D. (1987). What is kurtosis?: An influence function approach. The American Statistician, 41(1), 1-5.
37. Schilling, M. F., Watkins, M. E., & Watkins, W. (2002). Is human height bimodal? The American Statistician, 56(3), 223-229.
38. 2. Journal of the American Statistical Association, 72(357), 206-211.
39. Spivey, M. J., Grosjean, M., & Knoblich, G. (2005). Continuous attraction toward phonological competitors. PNAS, 102 (29), 10393-10398.
40. Sullivan, R. (2005). The age pattern of first-birth rates among U.S. women: The bimodal 1990s. Demography, 42(2), 259-273.
41. Tokeshi, M. (1992). Dynamics and distribution in animal communities: Theory and analysis. Researches in Population Ecology, 34, 249-273.