Cronbach's alpha

Cronbach’s alpha is a statistical measure used to assess the reliability of a set of test scores. The figure known as alpha is meant to provide a numerical value for the internal consistency of a group of test data. Tests with higher alpha values are considered to be more reliable, while tests with lower values are less reliable. The measure was first developed in the 1950s by Stanford University professor Lee Cronbach. Since that time, Cronbach’s alpha has become the most widely used measure of statistical reliability in psychological and educational testing.

Background

Statistics is a scientific field that examines data to make reliable conclusions about many different topics. These topics can range from the performance of athletes, to the effectiveness of medical treatments, to cultural and social trends in a population. To arrive at a reliable conclusion, statisticians must be able to analyze data that has been properly collected and analyzed. If a statistician examines incomplete or inaccurate data, the conclusion of his or her analysis will almost certainly be wrong.

In statistical terms, the entire number of people or objects a statistician wishes to study is known as a population. This can include smaller numbers, such as a classroom of twenty students, or larger figures, such as the number of senior citizens in the United States. Because entire populations are often too big to study effectively, researchers typically choose a narrow subset of the population called a sample. These samples must be chosen in such a way that they provide an unbiased representation of the entire population.

Even if sample sizes are chosen correctly, the final results can be corrupted by improper testing methods, incorrect analysis of data, or prolonged examination of the data. For example, survey questions meant to test a sample can provide inaccurate results if the questions are misleading or too complicated. Surveys that are too long can lead a respondent to fill in answers just to get the test over with, while surveys that are too short may not provide enough data to give an accurate answer.

Overview

In 1951, Lee Cronbach developed a method to track the internal consistency of an individual’s test scores to gauge their statistical reliability. Internal consistency refers to how well the items, or questions, in a test measure the same concept as a group. Cronbach called his method coefficient alpha, and he published it in a paper titled “Coefficient Alpha and the Internal Structure of Tests.” From his work with coefficient alpha, Cronbach was later able to develop his generalizability theory, a test of reliability meant to identify the sources of errors in data measurement. Other mathematical formulas to determine data reliability were available when Cronbach developed his method. Many of these methods were equally as effective; however, Cronbach’s alpha was considered the most general and was more widely used than the other methods.

Cronbach’s alpha is a method most often used to gauge the reliability of a test before that test can be administered in a real-world setting. Surveys meant to examine employee satisfaction, for example, should generate consistent results if the same person retakes the survey under similar conditions. A test is considered reliable if a person’s satisfaction score is similar on multiple versions of the test. If one score is high and another low, that may indicate the test is flawed and is not an accurate measure of employee satisfaction.

In simple terms, the value of Cronbach’s alpha is a measure of how well a test correlates with itself. This measurement takes into account the total number of test items, the average reliability of the correlation among the items within the test, and the average distance of the data from the mean. In statistics, the mean represents the average score of all the data points. The value of Cronbach’s alpha is most often expressed between 0 and 1; however, negative values can be achieved. If a negative value occurs, it typically means there is a problem with the set of data. In general, an alpha score of .90 or higher means the consistency of the data is excellent. If alpha scores are at .95 or higher, however, that can raise a red flag that the questions may be repetitive. A score between .80 and .89 means the consistency is good; and a score between .70 and .79 means the consistency is acceptable. Any score below .50 is considered unacceptable.

Low alpha scores are usually the result of too few questions, poor correlation between the items, or content that varies too widely. If an alpha value is considered too low, researchers can usually make the test more consistent by adding more related items. If the problem is caused by poor correlation between questions, they can fix the issue by revising the items or discarding the ones that test the lowest. Each alpha value is unique for its particular test and sample size. To achieve accurate results, a new Cronbach’s alpha value should be calculated for every test.

While effective, Cronbach’s method is not perfect and comes with some limitations. If the number of questions on a test is too low, the alpha value may not be a true representation of the test’s consistency. A similar issue may occur if the sample size tested is also too low. If the test has too many concepts or too wide-ranging a scope, the value may not be accurate. In this case, the alpha value can be calculated for parts of the test with similar concepts rather than the test as a whole. At the same time, if Cronbach’s alpha is used improperly, it can lead a researcher to mistakenly discard accurate tests or view reliable values as untrustworthy.

Bibliography

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Barchard, Kimberly A. “Coefficient Alpha.” Encyclopedia of Measurement and Statistics, vol. 1, edited by Neil J. Salkind. Sage Publications, 2007.

Bonett, Douglas G., and Thomas A. Wright. “Cronbach’s Alpha Reliability: Interval Estimation, Hypothesis Testing, and Sample Size Planning.” Journal of Organizational Behavior, vol. 36, no. 1, pp. 3–15, doi.org/10.1002/job.1960. Accessed 20 Nov. 2024.

Brennan, Robert L. Generalizability Theory. Springer, 2013. EBSCOhost, search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=2755579&site=ehost-live&scope=site. Accessed 20 Nov. 2024.

Luh, Wei-Ming. “A General Framework for Planning the Number of Items/Subjects for Evaluating Cronbach’s Alpha: Integration of Hypothesis Testing and Confidence Intervals.” Methodology: European Journal of Research Methods for the Behavioral & Social Sciences, vol. 20, no. 1, Mar. 2024, pp. 1–21, doi.org/10.5964/meth.10449. Accessed 20 Nov. 2024.

Tavakol, Mohsen, and Reg Dennick. “Making Sense of Cronbach’s Alpha.” International Journal of Medical Education, vol. 2, 2011, pp. 53–55, 2011, www.ijme.net/archive/2/cronbachs-alpha.pdf. Accessed 20 Nov. 2024.

“What Does Cronbach’s Alpha Mean?” UCLA Institute for Digital Research and Education, 2019, stats.idre.ucla.edu/spss/faq/what-does-cronbachs-alpha-mean/. Accessed 20 Nov. 2024.