Ebersbach Mirjam, Lehner Mirjam, Resing Wilma C M, Wilkening Friedrich
University of Zurich, Switzerland.
Acta Psychol (Amst). 2008 Feb;127(2):247-57. doi: 10.1016/j.actpsy.2007.05.005. Epub 2007 Jul 20.
Previous research has demonstrated adults' difficulties with explicitly forecasting exponential processes. Exponential growth is usually grossly underestimated, whereas exponential decline is forecast more accurately. By contrast, the present study examined implicit knowledge about exponential processes and how it is affected by function type (growth versus decline) in samples of 7-, 10-, 14-year-olds, and adults (N=80). Different indicators of the quality of forecasts were investigated. As opposed to previous findings, participants of all age groups estimated exponential decline less adequately than exponential growth. This effect could be attributed mainly to the fact that, in relation to fitted exponential functions, the starting value, or intercept, of the function was approximated well for exponential growth but badly with regard to exponential decline. The accuracy of the non-linear component in forecast functions barely differed between function types within the same age group. Furthermore, even 7-year-olds appeared to have a preliminary understanding of exponential processes, while both intercepts and exponents of forecasts became more accurate with age. Theoretical and practical implications are discussed.
先前的研究表明，成年人在明确预测指数过程方面存在困难。指数增长通常被严重低估，而指数下降的预测则更为准确。相比之下，本研究考察了7岁、10岁、14岁儿童以及成年人（N = 80）样本中关于指数过程的隐性知识，以及函数类型（增长与下降）对其的影响。研究调查了预测质量的不同指标。与先前的研究结果相反，所有年龄组的参与者对指数下降的估计都不如指数增长充分。这种效应主要可归因于这样一个事实，即相对于拟合的指数函数，指数增长函数的起始值或截距能被很好地近似，但指数下降函数的起始值或截距则近似得很差。在同一年龄组内，预测函数中非线性成分的准确性在不同函数类型之间几乎没有差异。此外，即使是7岁的儿童似乎也对指数过程有初步的理解，而且预测的截距和指数都随着年龄的增长而变得更加准确。本文讨论了其理论和实际意义。
