九種古典測驗理論信度指標精確性之研究

A Comparison of Precision of Nine Reliability Estimates Based on Classical Test Theory

蔡佩圜(Pei-Huan Tsai) ； 凃柏原(Bor-yaun Twu) ； 吳裕益(Yuh-Yih Wu)

《測驗學刊》 65卷2期 (2018/06) Pp. 217-240

摘要

本研究採用因素結構已知的驗證性因素分析模式來產生模擬資料，探討測驗因素數目、題數、樣本數三個自變項，對ρ_(g1b)、λ_1、λ_2、λ_3(α)、λ_4、λ_5、ω_h、ω_t等九種信度估計方法的偏誤、絕對偏誤、誤差均方根三個依變項之影響，藉以評估不同信度估計指標之精確性。研究結果顯示：(1)傳統最常使用的信度估計值λ_3(α)僅適合用來分析單向度測驗，若為多因素測驗，則會明顯低估信度真值；(2) λ_4及ω_t無論在何種情境其信度估計誤差均極微，建議盡可能採用這兩種信度估計值，當測驗資料之因素結構很明確時，最適合以ω_t來估計整體之信度，若因素結構不明確時，最適合以λ_4來估計整體之信度；(3)除非是分析母群資料，否則ρ_(g1b)有高估信度真值的現象，不適合稱之為最大信度下限；(4)ω_h與ω_t之比值是g因素解釋率占所有共同因素（包括g與所有f）總解釋率之比率，建議以ω_h與ω_t之比值作為評估測驗是否接近單向度的指標。本研究之分析結果可提供給測驗使用人員依不同測驗情境選擇較適切之信度估計指標。

關鍵字

最大信度估計下限 ； 驗證性因素分析

並列摘要

The purpose of this research is mainly to analyze the accuracy of different reliability index by employing ρ_(g1b)、λ_1、λ_2、λ_3(α)、λ_4、λ_5、ω_h、ω_t as the major arguments. Confirmatory Factor Analysis (CFA) is utilized for simulating data in this experiment, basically relying on independent variables (the number of test factors, the number of test items, the number of sample sizes) and dependent variable (bias, absolute mean bias, root mean squared error). The statistical results and analyses are described as following: (1) λ_3(α), the most commonly and traditionally used, only suitable for the analysis of one-dimension test, reliability index value will be significantly underestimated if multi-factor test takes place. (2) ω_t、λ_4 display best values of reliability estimation with extreme little error, it is recommended that these two can be used as much as possible. When the structure of factor of the test data is very clear, ω_t is the most suitable role to estimate the overall reliability. On the other hand, if it is not clear, thenλ_4 is the appropriate candidate to do the work. (3) Unless it is for analyzing the parent group data, then ρ_(g1b) shows a high estimated value of reliability which is not proper to name it as the greatest lower bound reliability. (4) The ratio of ω_h to ω_t is the ratio of the explanatory rate of g factor to the total explanatory rate of all common factors (including g and all f). It is recommended that it can be used as an indicator of whether the undergoing test is close to one dimension. The results of this study can provide testing persons with more appropriate estimates of reliability indicators according to different test scenarios.

並列關鍵字

confirmatory factor analysis ； the greatest lower bound reliability

參考文獻

Sijtsma, K. (2009a). On the use, the misuse, and the very limited usefulness of Cronbach’s alpha. Psychometrika, 74(1), 107-120.

Comrey, A. L., & Lee, H. B. (1992). A first course in factor analysis (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

Sijtsma, K. (2009b). Reliability beyond theory and into practice. Psychometrika, 74(1), 169-173.

Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston, MA: Pearson.

Bollen, K. A. (1989). Structural equations with latent variables. NewYork, NY: JohnWiley & Sons.