Anderson R B, Tweney R D
Department of Psychology, Bowling Green State University, OH 43403, USA.
Mem Cognit. 1997 Sep;25(5):724-30. doi: 10.3758/bf03211315.
Recent studies of the mathematical relationship between time and forgetting suggest that it is a power function rather than an exponential function, a finding that has important theoretical consequences. Through computational analysis and reanalyses of published data, we demonstrate that arithmetic averaging of exponential curves can produce an artifactual power curve, particularly when there are large and systematic differences among the slopes of the component curves. A series of simulations showed that the amount of power artifact is small when the slopes of the component curves are normally or rectangularly distributed and when the performance measure is noise free. However, the simulations also showed that the artifact can be quite large, depending on the shape of the noise distribution and restrictions in the performance range. We conclude that claims concerning the form of memory functions should consider whether the data are likely to contain artifact caused by averaging or by the presence of range-restricted noise.
近期关于时间与遗忘之间数学关系的研究表明，遗忘是幂函数关系而非指数函数关系，这一发现具有重要的理论意义。通过对已发表数据的计算分析和重新分析，我们证明指数曲线的算术平均会产生人为的幂曲线，尤其是当组成曲线的斜率存在较大且系统的差异时。一系列模拟表明，当组成曲线的斜率呈正态分布或矩形分布且性能指标无噪声时，幂函数假象的量很小。然而，模拟也表明，根据噪声分布的形状和性能范围的限制，这种假象可能会相当大。我们得出结论，关于记忆函数形式的论断应考虑数据是否可能包含由平均或范围受限噪声导致的假象。
