Different laboratories have achieved a consensus regarding how well human observers can estimate the average orientation in a set of N objects. Such estimates are not only limited by visual noise, which perturbs the visual signal of each object's orientation, they are also inefficient: Observers effectively use only N objects in their estimates (e.g., S. C. Dakin, 2001; J. A. Solomon, 2010). More controversial is the efficiency with which observers can estimate the average size in an array of circles (e.g., D. Ariely, 2001, 2008; S. C. Chong, S. J. Joo, T.-A. Emmanouil, & A. Treisman, 2008; K. Myczek & D. J. Simons, 2008). Of course, there are some important differences between orientation and size; nonetheless, it seemed sensible to compare the two types of estimate against the same ideal observer. Indeed, quantitative evaluation of statistical efficiency requires this sort of comparison (R. A. Fisher, 1925). Our first step was to measure the noise that limits size estimates when only two circles are compared. Our results (Weber fractions between 0.07 and 0.14 were necessary for 84% correct 2AFC performance) are consistent with the visual system adding the same amount of Gaussian noise to all logarithmically transduced circle diameters. We exaggerated this visual noise by randomly varying the diameters in (uncrowded) arrays of 1, 2, 4, and 8 circles and measured its effect on discrimination between mean sizes. Efficiencies inferred from all four observers significantly exceed 25% and, in two cases, approach 100%. More consistent are our measurements of just-noticeable differences in size variance. These latter results suggest between 62 and 75% efficiency for variance discriminations. Although our observers were no more efficient comparing size variances than they were at comparing mean sizes, they were significantly more precise. In other words, our results contain evidence for a non-negligible source of late noise that limits mean discriminations but not variance discriminations.
展开▼
机译：关于人类观察者在一组N个物体中估计平均方位的能力，不同实验室已经达成共识。这样的估计不仅受到视觉噪声的限制，视觉噪声会扰乱每个对象的方向的视觉信号，而且效率也很低：观察者在估计中仅有效使用了N个对象（例如S.C.Dakin，2001; J.A.Solomon，2010）。更具争议性的是观察者估计一系列圆圈的平均大小的效率（例如，D。Ariely，2001，2008; SC Chong，SJ Joo，T.-A。Emmanouil，和A. Treisman，2008; K （Myczek＆DJ Simons，2008年）。当然，方向和尺寸之间有一些重要的区别。尽管如此，将这两种估计与同一个理想观察者进行比较似乎是明智的。实际上，对统计效率的定量评估需要这种比较（R. A. Fisher，1925）。我们的第一步是测量仅比较两个圆时限制大小估计的噪声。我们的结果（对于84％正确的2AFC性能，Weber分数必须介于0.07和0.14之间）与视觉系统一致，该视觉系统向所有对数转换的圆直径添加了相同量的高斯噪声。我们通过随机改变1、2、4和8个圆的（未拥挤）阵列的直径来夸大这种视觉噪声，并测量其对平均大小之间的区别的影响。从所有四个观察者推断出的效率都大大超过了25％，在两种情况下接近100％。我们对大小差异的明显差异的测量更加一致。后面的结果表明方差判别的效率在62％到75％之间。尽管我们的观察者比较大小差异的效率没有比较平均大小的效率高，但它们的精确度却高得多。换句话说，我们的结果包含了无法忽略的后期噪声源的证据，该噪声源限制了均值判别而不是方差判别。
展开▼
