Algorithms for randomness in the behavioral sciences: A tutorial

Brysbaert, Marc (1991) Algorithms for randomness in the behavioral sciences: A tutorial. [Journal (Paginated)]

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Simulations and experiments frequently demand the generation of random numbera that have specific distributions. This article describes which distributions should be used for the most cammon problems and gives algorithms to generate the numbers.It is also shown that a commonly used permutation algorithm (Nilsson, 1978) is deficient.

Item Type:Journal (Paginated)
Keywords:generation random numbers, simulations, randomisation
Subjects:Psychology > Cognitive Psychology
Psychology > Behavioral Analysis
ID Code:3723
Deposited By: brysbaert, Dr. marc
Deposited On:30 Jul 2004
Last Modified:11 Mar 2011 08:55

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

A. C. (1980). Tests of pseudo-random numbers. Applied

Statistics, 29, 164-171.

BEST, D. J. (1979). Some easily programmed pseudo-random normal

generators. Australian Computer Journal, 11, 60-62.

BISSELL, A. F. (1986). Ordered random selection without replacement.

Applied Statistics, 35, 73-75.

Box, G. E. P., & JENKINS, G. M. (1976). Time series analysis: Forecasting

and control. San Francisco: Holden-Day.

Box, G. E. P., & MULLER, M. E. (1958). A note on the generation

of random normal deviates. Annals of Mathematical Statistics, 29,


BRADLEY, D. R. (1988). DATASIM. Lewiston, ME: Desktop Press.

BRADLEY, D. R., SENKO, M. W., & STEWART, F. A. (1990). Statistical

simulation on microcomputers. Behavior Research Methods, Instruments,

& Computers, 22, 236-246.

BROPHY, A. L. (1985). Approximation of the inverse normal distribution

function. Behavior Research Methods, Instruments, & Computers,

17, 415-417.

DREGER, R. M. (1989). A BASIC program for the Shell-Metzner sort

algorithm. Educational & Psychological Measurement, 49, 6 19-622.

DUDEWICZ, E. J., & RALLEY, T. G. (1981). The handbook of random

number generation and testing with TESTRAND computer code.

Columbus, OH: American Sciences Press.

DWYER, T., & CRITCHFIELD, M. (1978). BASIC and the personalcomputer.

Reading, MA: Addison-Wesley.

EDGELL, S. E. (1979). A statistical check of the DECsystem-10

FORTRAN pseudorandom number generator. Behavior Research

Methods & Instrumentation, 11, 529-530.

ELLIS, J. K. (1985). Distribution counting as a method for sorting test

scores. Behavior Research Methods, Instruments, & Computers, 17,


FISHMAN, G. S., & MooRE, L. R., ifi (1986). An exhaustive analysis

ofmultiplicative congruential random number generators with modulus

2~’—1. SIAM Journal onSciennfic & Statistical Computing, 7, 24-45.

GREEN, B. F. (1963). Digital computers in research: An introduction

for behavioral and social scientists. New York: McGraw-Hill.

GRUENBERGER, F., & JAFFRAY, G. (1965). Problems for computer solution.

New York: Wiley.

HAYS, W. L. (1988). Statistics. New York: Holt, Rinehart and Winston.

KENNEDY, W. J., & GENTLE, J, E. (1980). Statistical computing. New

York: Marcel Dekker.

KNUTH, D. E. (1973), The art ofcomputerprogramming: Vol. 3. Sorting

and searching. Reading, MA: Addison-Wesley.

KNUTH, D. E. (1981). The art of computerprogramming: Vol. 2. Seminumerical

algorithms. Reading, MA: Addison-Wesley.

KRANER, H. C., MOHANTY, S. G., & LYONS, J. C. (1980). Critical

values of the Kolmogorov-Smirnov one-sample test. Psychological

Bulletin, 88, 498-501.

LORDAHL, D. S. (1988). Repairing the Microsoft BASIC RND function.

Behavior Research Methods, Instruments, & Computers, 20,

22 1-223.

MARSAGUA, G. (1962). Random variables and computers. In J. Kozesnik

(Ed.), Information theory, statistical decision fi4nctions, random processes:

Transactions ofthe Third Prague Conference (pp. 499-5 10).

Prague: Czechoslovak Academy of Sciences.

MARSAGUA, G., &BRAY, T. A. (1964). Aconvenient method for generating

normal variables. SIAM Review, 6, 260-264.

MODIANOS, D. T., SCOTT, R. C., & CORNWELL, L. W. (1987). Testing

intrinsic random-number generators. Byte, 12, 175-178.

MOSES, L. E., & OAKFORD, R. V. (1963). Tables of random permutations.

Stanford, CA: Stanford University Press.

NANCE, R. E., & OVERSTREET, C. L. (1972). A bibliography on random

number generators. Computer Review, 13, 495-508.

NII.ssoN, T. H. (1978). Randomization without replacement using

replacement without losing your place. Behavior Research Methods

& Instrumentation, 10, 419.


W. T. (1986). Numerical recipes: The art of scientific computing.

Cambridge, U.K.: Cambridge University Press.

RIPLEY, B. D. (1983). Computer generation of random variables: A

tutorial. International Statistical Review, 51, 301-319.

RIPLEY, B. D. (1987). Stochastic simulation. New York: Wiley.

SAHAI, H. (1979). A supplement to Sowey’s bibliography on random

number generation and related topics. Journal ofStatistical Computation

& Simulation, 10, 31-52.

SOWEY, E. R. (1972). Achronological and classified bibliography on

random number generation and testing. International Statistical Review,

40, 355-371.

SOWEY, E. R. (1978). A second classified bibliography on random number

generation and testing. International Statistical Review, 46,

355-37 1.

SOWEY, E. R. (1986). A third classified bibliography on random number

generation and testing. Journal of the Royal Statistical Society,

149A, 83-107.

STRUBE, M. J. (1983). Tests of randomness for pseudorandom number

generators. Behavior Research Methods & Instrumentation, 15,


VON NEUMANN, J. (1951). Various techniques in connection with random

digits. NBS Applied Mathematics Series, 12, 36-38.

WICHMANN, B. A., & HILL, J. D. (1982). Algorithm AS183: An efficient

and portable pseudo random number generator. Applied Statistics,

31, 188-190.

WICHMANN, B. A., & HILL, J. D. (1984). An efficient and portable

pseudo random number generator: Correction. Applied Statistics, 33,


ZEISEL, H. (1986). A remark on Algorithm A5183: An efficient

and portable pseudo-random number generator. Applied Statistics, 35,


ZELEN, M., & SEvERO, N. C. (1964). Probability functions. In

M. Abramowitz & I. A. Stegun (Eds.), Handbook of mathematical

functions (pp. 925-995). New York: Dover.


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