摘要
随着数理统计方法在不同领域的广泛应用,显著性检验中的Ⅱ型错误(即纳伪错误)逐渐得到重视,其可能导致的后果也越来越受到关注。为了有效预测和降低犯Ⅱ型错误的可能性,需要清楚不同条件下犯Ⅱ型错误的概率(β)。通常,计算犯Ⅱ型错误可能性的大小,并不直接计算其概率,而是计算其检验效能(1-β)。传统计算检验效能的方法称为"经典方法",也是目前大多数教科书中介绍的方法,其得到的检验效能被称为"观测效能"(observed power)。但是,经典方法有一个不足,即P值的大小会影响到检验效能的大小,表现为随着P值的增大检验效能逐渐降低。当P值大于显著性水平α时,表明有犯Ⅱ型错误的可能,但此时,使用经典方法计算得到的观测效能通常是小于50%的。观测效能大于50%的情况只有在P值小于α时才能得到,而此时也已经没有犯Ⅱ型错误的可能。因此,经典方法会影响检验效能计算的准确性。本研究介绍了另一种计算检验效能的方法:等效性检验(equivalence testing),该方法能够避免上述经典方法的不足;使用等效性检验的方法对检验效能进行了计算,并与经典方法的结果进行了比较;对等效界值、样本数量、标准差和显著性水平等因子对检验效能计算的影响情况进行了分析。
With an increasing application of statistics in different areas, more attentions are paid on the type II error （ i. e. accept a false null hypothesis） and its potential consequences in the significant test. In order to effectively predict and reduce the possibility of making type II error, we need to calculate the probability of type II errors under different conditions （ J 3）. Instead of calculating the probability of the type II error directly, the statistical power （1-^） is usually calculated. The traditional method for estimating the statistical power is known as ＂classical method＂, which is described in many textbooks. The statistical power calculated using this method is called ＂observed power＂. However, there is a defect for the classical method, i. e., the value of P can affect the value of the statistical power, which decreases with the increase of P value. When P is greater than the significant level a , the type II error may appear, while the value of the observed power calculated using classical method is typically smaller than 50%. The case of the observed power larger than 50 % is obtained only when P is smaller than a , which cannot result in the type II error. Therefore, the classical method may yield inaccurate results of statistical power. In this study, equivalence testing method, which can avoid the above-mentioned defect associated with the classical method, was introduced and used for calculating the sta-tistical power. The results were compared with those from the classical method. The factors, including effect size, sample size, standard deviation and significant level, were also evaluated on their impacts on the calcula-tion of statistical power.
出处
《浙江海洋大学学报（自然科学版）》
CAS
2017年第5期420-425,共6页
Journal of Zhejiang Ocean University：Natural Science
基金
国家重点研究发展计划(2017YFA0604902)
浙江省公益技术应用研究项目(2015C33094)
舟山市科技局项目(2017C41012)
关键词
水产
Ⅱ型错误
检验效能
等效性检验
fisheries
type Ⅱ error
statistical power
equivalence testing
