关键词: α系数, 置信区间, Bonett-10法, 精确Koning-Franses法

Abstract: Under the assumption that the item errors in a tests are uncorrelated, if coefficient α is high enough to be accepted, then test reliability is also acceptable. In such 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 could not give how far it could be from the population coefficient α. The confidence interval of coefficient α can provide more information. Thus, a better appraisal of the test reliability is confidence interval of coefficient α, which provides the precision of the sample coefficient α. We briefed ten methods for estimating confidence intervals of coefficient α. Having excluded three methods that were poor performance in the previously research, we compared the left 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, uniform, χ２(3) and χ２(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 α (seven methods described above). Totally, 60 treatment conditions were generated in terms of the above 4–factor simulation design (i.e., 60=4×3×5×7). 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 when the corresponding confidence interval coverage is closer to the preset confidence level (e. g., 95%), and when the corresponding lower limit of confidence interval is closer to zero. The results of the simulation study showed that Bonett-10 and Koning-Franses exact methods performed better than the others, whereas Fisher and ADF methods performed worse. Bonett-10 and Koning-Franses exact methods can be easily calculated by using the sample coefficient alpha, the number of items, sample size and F critical value. Therefore, these two methods were recommended for estimating the confidence interval of coefficient α. We used an example of a unidimensional test to illustrate how to calculate confidence interval of coefficient α with Bonett-10 and Koning-Franses exact methods. When confidence interval of coefficient α is considred, Wen and Ye’s (2011) guideline for evaluating test reliability is still valid, with replacing coefficient α by confidence interval of coefficient α.

Key words: coefficient α, confidence interval, Bonett-10 method, Koning-Franses exact method