Experimental Bias in Number-Line Tasks and How to Avoid Them: Comment on Kim and Opfer (2017) and the Introduction of the Cohen Ray Number-Line Task

Kim and Opfer (2017) report data that demonstrate children produce a negatively accelerating (e.g., logarithmic) response pattern in the unbounded number-line task. This pattern of results is the opposite of those generally reported for the unbounded number-line task (e.g., Cohen & Blanc-Goldhammer, 2011; Cohen & Sarnecka, 2014). We believe Kim and Opfer's (2017) experimental procedure inadvertently biased participants' data in the unbounded task. Here, we (a) outline the factors that induce experimental bias in computerized number-line tasks, (b) identify the likely source of experimental bias in Kim and Opfer (2017) that led to the negatively accelerating pattern of data, (c) introduce a new number-line variation (the universal number-line task), and (d) introduce a publicly available, open source number-line task that provides researchers with a simple, robust, and correct method for collecting data on the unbounded, bounded, and universal number-line tasks. We conclude that Kim and Opfer's (2017) implementation of the unbounded number-line is biased, and therefore cannot provide meaningful support for the log-to-linear shift hypothesis. [For the original article, "A Unified Framework for Bounded and Unbounded Numerical Estimation," see EJ1142527.]