無母數適測方法在心理物理學與簡單反應時間研究之應用

Abstract

無母數適測方法（non-parametric adaptive method）包含固定與非固定梯級（step size）的方法，可應用於心理物理學中偵測與區辨作業（見Leek, 2001；Treutwein, 1995之文獻回顧）。近來，有多名研究者透過模擬的方式比較部份方法的大樣本與小樣本特質（如García-Pérez, 1998, 2001；Faes et al., 2007）。 在本篇論文中，我將藉電腦模擬探討這些方法在是否（yes-no）的偵測作業與簡單反應時間作業的適用性。其中，應用在簡單反應時間的作業可藉以找到引起某反應時間百分位數的刺激強度。在這兩部份的研究，我系統性地操弄起始值、梯級（單ㄧ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，在兩種作業中，以快速隨機接近法（ASA）（Kesten, 1958）的表現最佳。另一方面，在固定梯級的方法中，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，在兩種作業中使用結合的方法，即先使用ASA接著再使用BCD，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 the estimate of threshold 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 those methods by simulations (e.g., Faes et al., 2007; García-Pérez, 1998, 2001). In this thesis I systematically investigate via simulations the asymptotic and small-sample properties of some of the non-parametric adaptive methods in two experimental situations, one concerns the yes-no detection task and the other the simple reaction time (RT) task. In particular, the application of adaptive methods for RT experiments provides an alternative to estimate signal intensities that elicit certain (fixed) RT percentiles. The convergences for different starting values, step sizes, and response criteria are systematically investigated in both tasks. The results show that the accelerated stochastic approximation (ASA) (Kesten, 1958) is suitable for both tasks. A fixed-step-size method called the biased coin design (BCD) (Durham & Flournoy, 1993, 1995) with small step sizes is also recommended. Furthermore, our simulation results show that for small sample sizes, it is also feasible to apply ASA first, then followed by BCD, as the combined method.