Interval estimation and inference

M. Edge
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Abstract

Interval estimation is the attempt to define intervals that quantify the degree of uncertainty in an estimate. The standard deviation of an estimate is called a standard error. Confidence intervals are designed to cover the true value of an estimand with a specified probability. Hypothesis testing is the attempt to assess the degree of evidence for or against a specific hypothesis. One tool for frequentist hypothesis testing is the p value, or the probability that if the null hypothesis is in fact true, the data would depart as extremely or more extremely from expectations under the null hypothesis than they were observed to do. In Neyman–Pearson hypothesis testing, the null hypothesis is rejected if p is less than a pre-specified value, often chosen to be 0.05. A test’s power function gives the probability that the null hypothesis is rejected given the significance level γ‎, a sample size n, and a specified alternative hypothesis. This chapter discusses some limitations of hypothesis testing as commonly practiced in the research literature.
区间估计与推断
区间估计试图定义区间,以量化估计中的不确定性程度。估计的标准偏差称为标准误差。置信区间的设计是为了以指定的概率覆盖估计的真实值。假设检验是试图评估支持或反对特定假设的证据程度。频率假设检验的一个工具是p值,或者如果零假设实际上是正确的,那么数据在零假设下偏离预期的概率会比观察到的情况极端或更极端。在内曼-皮尔逊假设检验中,如果p小于预先指定的值(通常选择为0.05),则拒绝原假设。检验的幂函数给出了在给定显著性水平γ,样本量n和指定的备选假设的情况下,零假设被拒绝的概率。本章讨论了研究文献中常见的假设检验的一些局限性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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