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A Mean Square Error Comparison of Certain Median Response Estimates for the Up-and-Down Method with Small Samples

R. E. Little
Journal of the American Statistical Association
Vol. 69, No. 345 (Mar., 1974), pp. 202-206
DOI: 10.2307/2285525
Stable URL: http://www.jstor.org/stable/2285525
Page Count: 5
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A Mean Square Error Comparison of Certain Median Response Estimates for the Up-and-Down Method with Small Samples
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Abstract

Mean square errors associated with median response estimates are compared for the normal and logistic distributions, based on both maximum likelihood and minimum chi square analyses. In broad perspective there is little difference among the mean square errors for these four estimates, regardless of sample size and stimulus level spacing. The first three of the median response estimates require an iterative numerical solution, whereas the minimum chi square analysis for the logistic distribution yields an explicit expression for the associated median response estimate. This explicit estimation expression may be particularly convenient when nonuniform spacing of stimulus levels is involved in testing.

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