【作者】 马鹏； 赵守盈；

【Author】 Ma Peng;Zhao Shouying;School of Psychology,Guizhou Normal University;

【机构】 贵州师范大学心理学院；

【摘要】 统计功效是指某检验能够正确地拒绝一个错误的虚无假设的能力,常用1-β表示。在实际测量中,研究者往往会通过扩大样本量来提高统计检验力,以求获得更可靠的结果。研究表明,在使用ML估计时,容易产生较高的不收敛和不适当解比率,参数估计存在边际偏差,衰减标准误,虚假卡方值及基于卡方的I型错误比率,以及非正态进一步提高基于卡方的I型错误的比率。尽管小样本会出现诸多问题,但过度追求样本的绝对数量意义并不大,从时间和物质成本角度出发,有必要从统计功效角度入手,考察适宜样本量。当前实验中通过统计功效考察样本量较多,已成为必不可少的一步,但在测量中还考虑较少,因此研究拟从因子模型入手,通过统计功效来考察样本量,以期能从统计功效角度进一步找到适宜样本量,节省人力物力。研究采用认知失败量表,并根据作者问卷编制的因子载荷值为依据,进行蒙特卡洛模拟。根据前人研究,统计功效达到0.8的标准为:参数及标准误偏差不超过10%,对于所要分析参数的标准估计偏差不超过5%,覆盖率在0.91～0.98之间。研究考察样本量分别设置为50、100、300、600、900、1200,模拟样本量设置为10000,重点检验因子载荷和一阶因子间相关是否达到统计功效标准。结果表明,当样本量为50时,因子载荷估计偏差均d于5%,一阶因子间相关估计偏差比例达到6.09%,超过5%的标准,且覆盖率低于0.91,因此未达到0.8的统计功效;当样本量为100时,因子载荷估计偏差均低于5%,一阶因子间相关估计偏差比例在0.25%～4.42%之间,均小于5%,且覆盖率在0.93～0.95之间,均高于0.91。而其余样本量均达到标准。综上所述,在使用认知失败量表进行施测时,样本量达到100即达到了统计功效,可以进行有效分析。后续研究可以考察多个变量时的样本量,以及进一步扩展到结构方程模型中,统计功效和样本量的应用。更多还原

【Abstract】 Statistical power is the ability which can test to correctly reject a false null hypothesis, often expressed as1-β. In the actual statistical measurement, researchers often improve statistical power by expanding the simple size in order to obtain more reliable results. Studies shows that when ML estimation is used, it is easy to generate many problems, such as: high rates of nonconvergence and inappropriate solution, marginal bias of parameter estimation,attenuation error, false chi-square value and type I error rate based on chi-square, and non-normal conditions further increase the rate of type I error based on chi-square. Although there are many problems in small sample, it is not significant to over-pursue the absolute number of samples. From the perspective of time and material cost, it’s necessary to investigate the appropriate sample size from statistical power. In current experience, it has become an essential step to investigate the statistical power, but it is still less considered in measurement. Therefore, the study intends to start from the factor model and investigate the sample size through the statistical power, in order to further find the appropriate sample size and save manpower and material resources. The cognitive failure scale was used in this study, and Monte Carlo simulation was conducted based on the factor loading values developed by author’s questionnaire. According to previous study, the criteria for statistical power to reach 0.8: the deviation of parameters and standard error is no more than 10%; the deviation of standard estimation of the parameters to be analyzed is no more than 5%; and then the coverage rate is between 0.91 and 0.98. The study investigated the sample size of 50,100,300,600,900,1200, and the simulated sample size of 10000, and focus on testing whether the factor loading and the correlation between the first-factor reached the statistical power standard. The results show that when sample size is 50, the error of factor loading estimation is less than 5%, and the error ratio of correlation estimation among first-order factors reached 6.09%, importantly, the coverage rate was less than 0.91. Therefore, it didn’t reach the statistical power of 0.8. When sample size is 100, the error of factor loading estimation was all lower than 5%, the error ratio of correlation among first-order factors ranged from 0.25% to 4.42%, and the coverage rate ranged from 0.93 to 0.95. In the same way, the rest of samples were up to standard. In conclusion, the statistical power is achieved when the sample size reaches 100, which indicates that the cognitive failure scale can be used for effective analysis.Subsequent studies can examine the sample size in the case of multiple variables, and future extend to structural equation models, and the application of statistical power.更多还原