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Coefficient Alpha

Social science measurement requires scores that are both valid and reliable. Reliability refers to the amount of random fluctuation in a set of scores. One of the most popular methods for estimating the reliability of test scores is coefficient α, which estimates the proportion of observed score variance that is due to true score variance. The coefficient α is widely used in the education and psychosocial literature as an index of reliability of test scores.

Coefficient α was first described by Lee Cronbach in 1951, so it is sometimes termed Cronbach’s α. Coefficient α is used for establishing reliability of test scores from a single administration. However, in spite of the common use of coefficient α in the literature as an index of reliability of test scores, there is a lack of the proper use of coefficient α and its interpretation.

To achieve a greater understanding of coefficient α, this entry discusses these issues. First, the entry offers a more complete definition of reliability and then provides a detailed explanation of coefficient α. The entry then looks at assumptions of coefficient α as well as conceptual issues of this measure of reliability. Finally, the entry demonstrates when the use of alternative methods of reliability, such as ω, may be more appropriate.

Reliability

In 2011, in a study by Tavakol and Dennick, the reliability of a test is concerned with the capability of a test to consistently measure an attribute. A consistent test generates more or less the same results when administered on different occasions. Indeed, reliability refers to the trustworthiness of test scores (McDonald, 2014).

Reliability is based on the classical test theory model. Under the classical test theory model, the observed score is equal to the true score plus the error score (observed score = true score + error score). Researchers are interested in gaining knowledge about the true score and the discrepancy between an observed score and true score (i.e., how strongly the observed score is related to the true score). In other words, researchers want to know how much the differences in observed scores can be directly determined (explained) by the differences in true scores? By answering this question, researchers are in a position to identify the reliability index. Indeed, the reliability index is a correlation between the true score and the observed score (Raykov and Marcoulides, 2011). Given this, reliability is the ratio of the individual differences (variance or variability) of the true score to the individual differences of the observed score. Thus, the greater the ratio of the true score differences to the observed score differences, the more reliable the test.

The Source of Measurement Error and Reliability

As previously pointed out, reliability is the ability of a test to consistently measure an attribute (e.g., students’ competencies). For example, if a student is tested 1,000 times using the same assessment questions, these tests will likely have different scores. The mean of all 1,000 scores produces the true score of the student. However, practically researchers are unable to conduct that many tests in order to obtain the true score of the student. Using a single test administration, the observed score can be cofounded by random or systematic errors, as proposed by the classical test theory.

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