Often a written test is used as an inexpensive substitute for a per formance measure. A specified minimum performance level or prob ability of successful performance can be translated into a minimum passing score for the written test most efficiently by measuring the performance of students whose written test scores are near the de sired cutoff score. Stochastic approximation methods accomplish this purpose. The up-and-down method and the Robbins-Monro process are presented, discussed, and compared.
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References
1.
Brownlee, K.A., Hodges, J.L., and Rosenblatt, M.The up-and-down method with small samples. Journal of the American Statistical Association, 1953, 48, 202-277.
2.
Cornfield, J. and Mantel, N.Some new aspects of the application of maximum likelihood to the calculation of the dosage response curve. American Statistical Association Journal, 1950, 45, 181-210.
3.
Davis, M.Comparison of sequential bioassays in small samples. Journal of the Royal Statistical Society, Series B, 1971, 33, 78-87.
Dixon, W.J.The up-and-down method for small samples. Journal of the American Statistical Association, 1965, 60, 967-978.
6.
Dixon, W.J. and Mood, A.M.A method for obtaining and analyzing sensitivity data. Journal of the American Statistical Association, 1948, 43, 109-126.
7.
Farrell, R.H.Bounded length confidence intervals for the zero of a regression function . Annals of Mathematical Statistics, 1962 , 33, 237-247.
8.
Hsi, B.P.The multiple-sample up-and-down method in bioassay. Journal of the American Statistical Association, 1969, 64, 147-162.
9.
Robbins, H. and Monro, S.A stochastic approximation method. Annals of Mathematical Statistics, 1951, 22, 400-407.
10.
Sacks, J.Asymptotic distribution of stochastic approximation procedures. Annals of Mathematical Statistics, 1958, 29, 373-405.
11.
Scheber, T.K.Stochastic Approximation: A Survey. Document AD 761 766. Springfield, Virginia: National Technical Information Service, 1973.
12.
Stroup, D.Stopping rules for stochastic approximation procedures. Unpublished Ph.D. thesis, Princeton University Department of Statistics, 1979.
13.
Tsutakawa, R.K.Random walk design in bioassay. Journal of the American Statistical Association, 1967, 62, 842-856.
14.
Venter, J.H.An extension of the Robbins-Monro procedure. Annals of Mathematical Statistics, 1967, 38, 181-190.
15.
Wetherill, G.B.Sequential estimation of quantal response curves. Journal of the Royal Statistical Society, Series B, 1963, 25, 1-48.
16.
Wetherill, G.B.Sequential Methods in Statistics. London: Chapman & Hall (New York: Halsted), 1975.
17.
Wetherill, G.B. and Levitt, H.Sequential estimation of points on a psychometric function. British Journal of Mathematical and Statistical Psychology, 1965, 18, 1-10.