Department of Poultry Science, The University of Georgia, Athens 30602-2772., USA.
Poult Sci. 2012 Sep;91(9):2398-404. doi: 10.3382/ps.2011-02098.
Persons conducting research trials often want to be able to declare that treatments, or particularly products, are equivalent (will provide indistinguishable results). However, all research trials can ever provide is the probability that the observed differences in an experiment were due to chance. Also, in trials in which variances are high and there are few replications, it is quite easy to declare no significant differences and equivalency. This paper describes a Microsoft Excel spreadsheet that can be used to easily construct experimental power curves. Such curves predict the proportion of experiments that would yield a given level of significance as the difference between the 2 means increases. The spreadsheet uses the mean and variances from an experiment with the Norm.inv and Rand functions of Excel to simulate outcomes from identical experiments. An experiment that declared GMO and normal feed ingredients to be equivalent was used to illustrate the application of power curves. The experiment had 12 replicate pens of broilers per treatment. The outcomes of 90,000 simulated experiments, each with the same overall variance, but 0 through 8 percent differences in treatment means, were graphed. When the published experiment purported to show equivalence, really it showed that a significant difference in growth (P < 0.05) would be expected to be detected 50% of the time if the means were different by 3.1%; a difference of 4.6% in treatment means could be detected 80% of the time by such an experiment. This Excel spreadsheet enables such a power analysis to be conducted. Easy modifications of the spreadsheet can illustrate the influence of changing the variance or number of replications on the expected power of future experiments. The economic impact of small changes in performance is also discussed.
进行研究试验的人员通常希望能够宣称治疗方法（或特别是产品）是等效的（将提供可区分的结果）。然而，所有研究试验都只能提供观察到的实验差异是由于偶然原因的概率。此外，在方差较高且复制次数较少的试验中，很容易宣布没有显著差异和等效性。本文描述了一个 Microsoft Excel 电子表格，可以用于轻松构建实验功效曲线。这些曲线预测了在 2 个平均值之间的差异增加时，会有多少比例的实验产生给定水平的显著性。该电子表格使用实验的平均值和方差，以及 Excel 的 Norm.inv 和 Rand 函数，模拟来自相同实验的结果。一个宣布转基因生物和正常饲料成分等效的实验被用来举例说明功效曲线的应用。该实验每处理有 12 个重复鸡舍。对 90,000 个模拟实验的结果进行了绘制，每个实验的总体方差相同，但处理平均值的差异为 0 到 8%。当发表的实验声称显示等效性时，实际上它表明，如果平均值相差 3.1%，则预计会有 50%的时间检测到生长的显著差异（P <0.05）；如果处理平均值相差 4.6%，则这样的实验可以 80%的时间检测到。这个 Excel 电子表格可以进行这样的功效分析。对电子表格的简单修改可以说明改变方差或复制次数对未来实验预期功效的影响。还讨论了性能微小变化的经济影响。
