当前位置: X-MOL 学术Behavior Modification › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A Clarification of Slope and Scale.
Behavior Modification ( IF 2.692 ) Pub Date : 2020-09-02 , DOI: 10.1177/0145445520953366
Chad E L Kinney 1
Affiliation  

Improvements in the quantification and visual analysis of data, plotted across non-standardized graphs, are possible with the equations introduced in this paper. Equation 1 (an expression of graphic scale variability) forms part of the foundation for Equation 2 (an expansion on the traditional calculation of the tangent inverse of a line’s algebraic slope). These equations provide clarification regarding aspects of “slope” and graphic scaling that have previously confused mathematicians. The apparent lack of correspondence between geometric slope (the angle of inclination) and algebraic slope (the m in y = mx + b) on “non-homogeneous” graphs (graphs where the scale values/distances on the y-axis are not the same as on the x-axis) is identified and directly resolved. This is important because nearly all behavior analytic graphs are “non-homogeneous” and problems with consistent visual inspection of such graphs have yet to be fully resolved. This paper shows how the precise geometric slope for any trend line on any non-homogeneous graph can quickly be determined—potentially improving the quantification and visual analysis of treatment effects in terms of the amount/magnitude of change in slope/variability. The equations herein may also be used to mathematically control for variability inherent in a graph’s idiosyncratic construction, and thus facilitate valid comparison of data plotted on various non-standard graphs constructed with very different axes scales—both within and across single case design research studies. The implications for future research and the potential for improving effect size measures and meta-analyses in single-subject research are discussed.



中文翻译:

斜率和比例的说明。

使用本文中介绍的方程,可以改进跨非标准化图表绘制的数据的量化和可视化分析。等式 1(图形比例可变性的表达式)构成了等式 2(对线的代数斜率的切线倒数的传统计算的扩展)基础的一部分。这些方程提供了有关“斜率”和图形缩放方面的说明,这些方面以前使数学家感到困惑。几何斜率(倾角)和代数斜率(y中的m = mx + b )之间明显缺乏对应关系) 在“非同质”图上(y轴上的比例值/距离与x轴上的比例值/距离不同的图)轴)被识别并直接解决。这很重要,因为几乎所有的行为分析图都是“非同质的”,并且对此类图进行一致的视觉检查的问题尚未完全解决。本文展示了如何快速确定任何非齐次图上任何趋势线的精确几何斜率 - 可能会根据斜率/变异性的变化量/幅度改进治疗效果的量化和可视化分析。本文的方程也可用于数学控制图表的特殊构造中固有的可变性,从而有助于对绘制在以非常不同的轴比例构建的各种非标准图表上的数据进行有效比较——无论是在单一案例设计研究内部还是跨案例设计研究。

更新日期:2020-09-02
down
wechat
bug