多数情况下,α系数可以用来评价测验信度。诸多研究建议,在报告测验信度的时候应当包括其置信区间。通过蒙特卡洛模拟研究,比较了7种α系数区间估计方法,包括Fisher法、Bonett-02法、Bonett-10法、精确Koning—Franses法、渐近ID法、渐近Koning—Franses法和ADF法。结果发现Bonett-10法和精确Koning—Franses法较好,它们的结果相差很小。这两种方法都比较简单,只需要样本的α值、测验题数、被试人数及F临界值,通过简单的运算便可得到α系数的置信区间。
Under the assumption that the item errors in a test are uncorrelated, if coefficient α is high enough to be accepted, then the test reliability is also acceptable. In such a case, using coefficient α to evaluate the test reliability is the first choice, because calculating coefficient α is much easier than calculating composite reliability, even though the latter is more precise in evaluating test reliability. For a test, coefficient α is an unknown population parameter. It is often estimated by the sample coefficient α, a point estimator of the population coefficient α. Point estimate of coefficient α contains limited information and cannot provide information with regard to how far it can be from the population coefficient α The confidence interval of the coefficient α can provide more information. Thus, a better appraisal of the test reliability is the confidence interval of the coefficient α, which provides the precision of the sample coefficient α. We briefed ten methods for estimating confidence intervals of coefficient By excluding three methods that have poor performance revealed in the previous research, we compared the remaining seven methods by a simulation study. The seven methods being compared include : Fisher, Bonett - 02, Bonett - 10, Koning - Franses exact, ID asymptotic, Koning - Franses asymptotic and ADF methods. Four factors were considered in the simulation design: (a) distribution of items (normal, unifbrm, χ^2(3) andχ^2(6) ; (b) the number of items on the test (p = 3, 7, and 14) ; (c) sample size ( n = 50, 100,300,500, and 1000) ; (d) the methods for estimating the confidence interval of coefficient ct (seven methods described above). Totally, 60 treatment conditions were generated in terms of the a- bove 4 - factor simulation design (i. e. , 60 = 4 × 3 × 5). Confidence interval coverage ( % ) and the bias of the lower limit of confidence interval were used to compare the results of the simulation study. A method is better