Eye Fitting Straight Lines in the Modern Era

How do statistical regression results compare to intuitive, visually fitted results? Fitting lines by eye through a set of points has been explored since the 20th century. Common methods of fitting trends by eye involve maneuvering a string, black thread, or ruler until the fit is suitable, then drawing the line through the set of points. In 2015, the New York Times introduced an interactive feature, called “You Draw It,” where readers were asked to input their own assumptions about various metrics and compare how these assumptions relate to reality. In this article, we validate “You Draw It” as a method for graphical testing, comparing results to the less technological method used in Mosteller et al. and extending that study with formal statistical analysis methods. Results were consistent with those found in the previous study; when shown points following a linear trend, participants tended to fit the slope of the principal axis over the slope of the least-squares regression line. This trend was most prominent when shown data simulated with larger variances. This study reinforces the differences between intuitive visual model fitting and statistical model fitting, providing information about human perception as it relates to the use of statistical graphics. Supplementary materials for this article are available online.

统计回归结果与直观视觉拟合结果之间存在何种差异？自20世纪以来，学界便已开展针对通过肉眼为一组数据点拟合直线的相关研究。常见的肉眼拟合趋势的方法包括：调整细绳、黑线或直尺至拟合效果合适的状态，随后为该组数据点绘制拟合直线。2015年，《纽约时报》推出了一款名为"You Draw It"（你画即得）的互动功能，邀请读者输入自身对各类指标的预设假设，并对比这些假设与真实情况的契合程度。本文将"You Draw It"验证为一种图形化测试方法，将其结果与Mosteller等人研究中使用的低技术含量方法进行对比，并通过规范的统计分析方法拓展了该研究的范畴。本次研究结果与此前研究保持一致：当向参与者展示呈线性趋势的数据点时，受试者往往会拟合主轴（principal axis）的斜率，而非最小二乘回归线（least-squares regression line）的斜率。当展示方差更大的模拟数据时，这一倾向表现得最为显著。本研究明确了直观视觉模型拟合与统计模型拟合之间的差异，为探究人类感知与统计图形使用之间的关联提供了相关依据。本文的补充材料可在线获取。