...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>International Journal of Statistics and Probability >Explaining Lord's Paradox in Introductory Statistical Theory Courses
【24h】

Explaining Lord's Paradox in Introductory Statistical Theory Courses

机译：在介绍性统计理论课程中解释主的悖论

获取原文
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

When two groups are compared in a pre-post study, two different conclusions can be drawn between the two-sample t-test and the analysis of covariance (ANCOVA). It is known as Lord's Paradox, and it occurs because the parameter in the two-sample t-test and the parameter of interest in the ANCOVA model are not the same quantity. The difference between the two parameters can be explained by the covariance of linearly combined random variables which is an important topic in introductory statistical theory courses. Lord's paradox is frequently observed in practice, and it is very important for students (future researchers) to have clear understanding of the paradox. The objective of this article is to explain Lord's Paradox using the covariance of linearly combined random variables. The paradox is explained using three scenarios in the context of educational research. The first scenario is when the average baseline (pre-score) is greater in the treatment group than the control group, the second scenario is when the average baseline is lower in the treatment group than the control group, and the third scenario is when the average baseline is same between the two groups by randomization. This article is written at the level of introductory statistical theory courses for undergraduate and graduate statistics students to help understanding the difference between the parameter of interest in the two-sample t-test and the parameter of interest in the ANCOVA model.
机译：当在后研究中比较两组时，可以在两个样本T检验和协方差分析（ANCOVA）之间绘制两种不同的结论。它被称为主的悖论，它发生的是因为两个样本T检验中的参数和Ancova模型中的感兴趣参数不同。两个参数之间的差异可以通过线性组合随机变量的协方差来解释，这是介绍统计理论课程中的一个重要主题。主的悖论经常在实践中观察，对学生（未来的研究人员）非常重要，以了解对悖论的了解。本文的目标是使用线性组合随机变量的协方差来解释主的悖论。在教育研究的背景下使用三种情景来解释悖论。第一种情况是当治疗组的平均基线（预分数）比对照组更大时，第二种情况是当治疗组的平均基线比对照组较低，第三种情况是当通过随机化平均基线在两组之间相同。本文是在本科和研究生统计学生的介绍性统计理论课程的水平，以帮助了解两个样本T检验参数与ANCOVA模型的兴趣参数之间的差异。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号