THE COUNTERNULL VALUE OF AN EFFECT SIZE - A NEW STATISTIC
THE COUNTERNULL VALUE OF AN EFFECT SIZE - A NEW STATISTIC
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DOI：
10.1111/j.1467-9280.1994.tb00281.x
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发表时间：
1994-11-01
影响因子：
8.2
通讯作者：
RUBIN, DB
中科院分区：
文献类型：
--
作者：
ROSENTHAL, R;RUBIN, DB
我们引入了一个新的，容易计算的统计量，counternull值获得的效果大小，这是效果大小的非空幅度，支持的证据量完全相同的支持效果大小的空值。 换句话说，如果将反零值作为零假设，则所得p值将与实际零假设的所得p值相同。 除了p值之外，还报告了反零值，这实际上消除了两个常见的错误：（a）将未能拒绝零值等同于将效应量估计为零;（B）基于显著p值拒绝零假设意味着有科学意义的发现。 在许多具有单自由度效应量的常见情况下，反零值只是所获得效应量大小的两倍，但反零值通常是有定义的，即使对于多自由度效应量也是如此，因此可以在无法使用置信区间时应用。 在荟萃分析中，当评估汇总效应量的科学重要性时，反零值的使用特别有用。
We introduce a new, readily computed statistic, the counternull value of an obtained effect size, which is the nonnull magnitude of effect size that is supported by exactly the same amount of evidence as supports the null value of the effect size. In other words, if the counternull value were taken as the null hypothesis, the resulting p value would be the same as the obtained p value for the actual null hypothesis. Reporting the counternull in addition to the p value, virtually eliminates two common errors: (a) equating failure to reject the null with the estimation of the effect size as equal to zero and (b) taking the rejection of a null hypothesis on the basis of a significant p value to imply a scientifically important finding. In many common situations with a one-degree-of-freedom effect size, the value of the counternull is simply twice the magnitude of the obtained effect size, but the counternull is defined in general, even with multi-degree-of-freedom effect sizes, and therefore can be applied when a confidence interval cannot be. The use of the counternull can be especially useful in meta-analyses when evaluating the scientific importance of summary effect sizes.