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References
Bailey, B. J. R. (1980). Accurate normalizing transformations of a Student’st variate.Applied Statistics,29, 304–306.
Brophy, A. L. (1983a). Accuracy and speed of seven approximations of the normal distribution function.Behavior Research Methods & Instrumentation,15, 604–605.
Brophy, A. L. (1983b). Approximation of probabilities near the median of the F distribution.Educational & Psychological Measurement,43, 177–180.
Cadwell, J. H. (1951). The bivariate normal integral.Biometrika,38, 475–479.
Chu, J. T. (1956). Errors in normal approximations to the t, r and similar types of distribution.Annals of Mathematical Statistics,27, 780–789.
Cooper, B. E. (1968). Algorithm AS 3: The integral of Student’s t-distribution.Applied Statistics,17, 189–190.
Dorrer, E. (1968). Algorithm 322: F-distribution.Communications of the ACM,11, 116–117.
Dudewicz, E. J., &Dalal, S. R. (1972). On approximations to thet-distribution.Journal of Quality Technology,4, 196–198.
Dunlap, W. P., &Duffy, J. A. (1975). FORTRAN IV functions for calculating exact probabilities associated with z, x2, t, and F values.Behavior Research Methods & Instrumentation,7, 59–60.
el Lozy, M. (1979). Remark on Algorithm 395 and remark on Algorithm 396.ACM Transactions on Mathematical Software,5, 238–239.
Evans, S., &Gilfillan, L. (1986). APL approximations for common statistical tables.Behavior Research Methods, Instruments, & Computers,18, 337–338.
Federighi, E. T. (1959). Extended tables of the percentage points of Student’s t-distribution.Journal of the American Statistical Association,54, 683–688.
Fisher, R. A. (1935). The mathematical distributions used in the common tests of significance.Econometrika,3, 353–365.
Gaver, D. P., &Kafadar, K. (1984). A retrievable recipe for inverset.American Statistician,38, 308–311.
Hastings, C, Jr. (1955).Approximations for digital computers Princeton, NJ: Princeton University Press.
Hill, G. W. (1970a). Algorithm 395: Student’s t-distribution.Communications of the ACM,13, 617–619.
Hill, G. W. (1970b). Algorithm 396: Student’st-quantiles.Communications of the ACM,13, 619–620.
Hill, G. W. (1981) Remark on Algorithm 395.ACM Transactions on Mathematical Software,7, 247–249.
Jaspen, N. (1965). The calculation of probabilities corresponding to values ofz, t, F, and chi-square.Educational & Psychological Measurement,25, 877–880.
Johnson, N. L., &Kotz, S. (1970).Distributions in statistics: Continuous univariate distributions-2. Boston: Houghton-Mifflin.
Kennedy, W., &Gentle, J. (1980).Statistical computing. New York: Marcel Dekker.
Lackritz, J. R. (1984). Exactp values forF andt tests.American Statistician,38, 312–314.
Levine, D. A. (1969). Algorithm 344: Student’st-distribution.Communications of the ACM,12, 37–38.
Ling, R. F. (1978). A study of the accuracy of some approximations for t, and F tail probabilities.Journal of the American Statistical Association,73, 274–283.
Merrington, M. (1942). Table of percentage points of the t-distribution.Biometrika,32, 300.
Mickey, M. R. (1975). Approximate tail probabilities for Student’st-distribution.Biometrika,62, 216–217.
Morris, J. (1968). Algorithm 321:t-test probabilities.Communications of the ACM,11, 115–116.
Morris, J. (1969). Algorithm 346: F-test probabilities.Communications of the ACM,12, 184–185.
Ogasawara, T. H. (1982). The calculation of the significance level of F, t, and r on the Apple II.Behavior Research Methods & Instrumentation,14, 492–493.
O’Grady, K. E. (1981). Probabilities and critical values for z, chi square, r, t, and F.Behavior Research Methods & Instrumentation,13, 55–56.
Owen, D. B. (1965). The power of Student’st-test.Journal of the American Statistical Association,60, 320–333.
Paulson, E. (1942). An approximate normalization of the analysis of variance distribution.Annals of Mathematical Statistics,13, 233–235.
Peizer, D. B., &Pratt, J. W. (1968). A normal approximation for binomial, F, beta, and other common, related tail probabilities, 1. Journal of the American Statistical Association,63, 1416–1456.
Pratt, J. W. (1968). A normal approximation for binomial, F, beta, and other common, related tail probabilities, II.Journal of the American Statistical Association,63, 1457–1483.
Prescott, P. (1974). Normalizing transformations of Student’st-distribution.Biometrika,61, 177–180.
Selvin, S., &Wong, J. T. (1975). An algorithm for calculating probabilities for the F distribution (including the chi square, t, and nor-mal distributions as special cases).Behavior Research Methods & Instrumentation,7, 482–483.
Smirnov, N. V. (Ed.). (1961).Tables for the distribution and density functions of t-distribution (“Student’s” distribution). New York: Pergamon.
Student. (1908). The probable error of a mean.Biometrika,6, 1–25.
von Collani, G. (1983). Computing probabilities for F, t, chi-square, and z in BASIC.Behavior Research Methods & Instrumentation,15, 543–544.
Wallace, D. L. (1959). Bounds on normal approximations to Student’s and the chi-square distributions.Annals of Mathematical Statistics,30, 1121–1130.
Wilson, E. B., &Hilferty, M. M. (1931). The distribution of chi-square.Proceedings of the National Academy of Sciences,17, 684–688.
Wood, D. L., &Wood, D. (1984). TINT: A Microsoft BASIC t integration program.Behavior Research Methods, Instruments, & Computers,16, 479–480.
Wood, D. L., &Wood, D. (1986). Precise F integration.Behavior Research Methods, Instruments, & Computers,18, 405–406.
Zelen, M., &Severo, N. C. (1964). Probability functions. In M. Abramowitz & I. A. Stegun (Eds.),Handbook of mathematical functions (pp. 925–995). Washington, DC: U.S. Government Printing Office.
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Brophy, A.L. Efficient estimation of probabilities in thet distribution. Behavior Research Methods, Instruments, & Computers 19, 462–466 (1987). https://doi.org/10.3758/BF03205616
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DOI: https://doi.org/10.3758/BF03205616