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应如何进行对比分析？针对一组散点进行目视直线拟合的方法自20世纪起便已得到研究与探索。常见的目视趋势拟合方法包括调整细绳、黑线或直尺直至拟合效果达标，随后沿该工具穿过该组散点绘制直线。2015年，《纽约时报》推出了一款名为“你画我猜（You Draw It）”的交互式功能，邀请读者输入自身对各类指标的预判，并对比这些预判与实际情况的契合程度。本文验证了“你画我猜（You Draw It）”作为图形化测试方法的有效性，将其结果与莫斯利（Mosteller）等人研究中采用的低技术拟合方法进行对比，并通过规范的统计分析方法拓展了该研究的边界。本研究结果与既往研究结论一致：当向参与者展示呈线性趋势的散点时，他们更倾向于拟合主轴斜率，而非最小二乘回归线的斜率。该倾向在展示方差更大的模拟数据集时表现最为显著。本研究进一步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应用的关联提供了实证依据。本文的补充材料可通过在线渠道获取。