無母數適測方法在心理物理學閾值測量之收斂研究

Convergence of Non-Parametric Adaptive Threshold Estimation in the Yes-No Task

無母數適測方法（non-parametric adaptive method）包含固定與非固定梯級（step size）方法，可應用於心理物理學偵測與區辨作業中有關閾值的測量（見Leek, 2001; Treutwein, 1995之文獻回顧）。近年來，有數名研究者透過模擬方式比較部份適測方法的大樣本與小樣本特質（如Faes et al., 2007; Garcia-Perez, 1998, 2001）。在本篇論文中，我們藉電腦模擬有系統探某些適測方法在「是／否」（yes-no）偵測作業上的適用性。我們系統性地操弄起始值，（相對）梯級（即單一改變量大小），及反應指標三個向度來探討這些方法的收斂情形。結果顯示，不管在大樣本還是小樣本情況下，以快速隨機接近法（ASA）（Kesten, 1958）使用中到大的（原始）梯級表現最佳。而固定梯級方法中，在偏差硬幣投擲設計（BCD）（Durham & Flournoy, 1993, 1995）使用小的梯級亦可被推薦。此外，結果也指出，在小樣本情況下，先使用ASA再接著使用BCD的結合方法是可行的。

In psychophysical research of detection and discrimination, non-parametric adaptive methods, including the fixed and non-fixed step-size methods, have been used extensively for threshold estimation through a combination of decreasing and increasing stimulus steps (see Leek, 2001; Treutwein, 1995, for reviews). In recent years, researchers have focused on the asymptotic and small-sample properties of some of the methods via computer simulations (e.g., Faes et al., 2007; Garcia-Perez, 1998, 2001). In this article we systematically investigate via simulations the large-and small-sample properties of some of the non-parametric adaptive methods in the yes-no detection task. The convergence for different starting values, relative step sizes, and response criteria is systematically investigated. The results show that in both the large-and small-sample conditions, the accelerated stochastic approximation (ASA) (Kesten, 1958) performs well with medium to large (initial) step size. A fixed-step-size method called the biased coin design (BCD) (Durham & Flournoy, 1993, 1995) with small step size is also recommended. Furthermore, our simulation results show that for small sample size, it is also feasible to apply ASA first, then followed by BCD in the sequence as the combined method.