最大折半信度之計算與估計

Calculation and Estimation of the Maximum of Split-Half Reliabilities

10.6450/ER.200806.0141

馮文俊(Wen-Chun Feng)

信度 ； 折半信度 ； 測驗理論 ； reliability ； split-half reliability ； test theory

教育學刊

30期（2008 / 06 / 01）

141 - 165

繁體中文

Owing to the difficulty to obtain the test-retest reliability coefficient in practice, Flanagan and Gunman proposed using split-half method to estimate test reliability. Under the condition that split-half tests or subtests are essentially τ-equivalent, Flanagan's split-half reliability Fρ(superscript 2 subscript X) and Cronbach's α are exactly equivalent to population reliability, otherwise they estimate a lower bound to the test reliability. Gunman believed that the maximum of Flanagan's split-half reliabilities, denoted by MFρ(superscript 2 subscript X) was the most appropriate estimate for the test reliability, and one should try to split the test in such a manner as to maximize Fρ(superscript 2 subscript X). In contrast to Guttman's notion for finding MFρ(superscript 2 subscript X) Cronbach suggested using α to estimate test reliability, and persuaded people not to spend much time to search for MFρ(superscript 2 subscript X) because in his research the difference between MFρ(superscript 2 subscript X) and α was found too small to be of practical importance. However, he pointed out also that Brownell found substantial difference between MFρ(superscript 2 subscript X) and α. Cronbach thought that the contradictory results they obtained could be explained by the much lower α's for tests in Brownell's study. Following Guttman's proposition, based on two real data sets, this research developed a SAS IML program to calculate Flanagan's all possible split-half reliabilities {Fρ(superscript 2 subscript X)} and their maximum MFρ(superscript 2 subscript X) for a test, and examined the difference magnitude between MFρ(superscript 2 subscript X) and α. Unlike the dependence relation Cronbach thought, the results showed that the difference magnitude between MFρ(superscript 2 subscript X) and α didn't depend on α. For school children intelligence test, when both item number and a were small, for example, with six items and α＜0.35, there were many MFρ(superscript 2 subscript X)-α cases less than 0.05. This result was different from Brownell's having substantial difference result, As for customers' satisfaction data, when item number and α were large, for example, with twenty items and α=0.7, there were many MFρ(superscript 2 subscript X)-α eases falling between 0.13 and 0.18. Such difference magnitudes might not be ignored in practice. This result disagreed with Cronbach's having small difference and not important in practice conclusion.

Owing to the difficulty to obtain the test-retest reliability coefficient in practice, Flanagan and Gunman proposed using split-half method to estimate test reliability. Under the condition that split-half tests or subtests are essentially τ-equivalent, Flanagan's split-half reliability Fρ(superscript 2 subscript X) and Cronbach's α are exactly equivalent to population reliability, otherwise they estimate a lower bound to the test reliability. Gunman believed that the maximum of Flanagan's split-half reliabilities, denoted by MFρ(superscript 2 subscript X) was the most appropriate estimate for the test reliability, and one should try to split the test in such a manner as to maximize Fρ(superscript 2 subscript X). In contrast to Guttman's notion for finding MFρ(superscript 2 subscript X) Cronbach suggested using α to estimate test reliability, and persuaded people not to spend much time to search for MFρ(superscript 2 subscript X) because in his research the difference between MFρ(superscript 2 subscript X) and α was found too small to be of practical importance. However, he pointed out also that Brownell found substantial difference between MFρ(superscript 2 subscript X) and α. Cronbach thought that the contradictory results they obtained could be explained by the much lower α's for tests in Brownell's study. Following Guttman's proposition, based on two real data sets, this research developed a SAS IML program to calculate Flanagan's all possible split-half reliabilities {Fρ(superscript 2 subscript X)} and their maximum MFρ(superscript 2 subscript X) for a test, and examined the difference magnitude between MFρ(superscript 2 subscript X) and α. Unlike the dependence relation Cronbach thought, the results showed that the difference magnitude between MFρ(superscript 2 subscript X) and α didn't depend on α. For school children intelligence test, when both item number and a were small, for example, with six items and α＜0.35, there were many MFρ(superscript 2 subscript X)-α cases less than 0.05. This result was different from Brownell's having substantial difference result, As for customers' satisfaction data, when item number and α were large, for example, with twenty items and α=0.7, there were many MFρ(superscript 2 subscript X)-α eases falling between 0.13 and 0.18. Such difference magnitudes might not be ignored in practice. This result disagreed with Cronbach's having small difference and not important in practice conclusion.

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