Cronbach Alpha

Cronbach Alpha is one of the most favored methods for measuring the internal consistency reliability of an aggregation of items. Also known as Cronbach's Alpha coefficient or Cronbach's α(Research Methods and Design in Sport Management). It was described for the first time by Lee Cronbach in 1951.

According to Damon P. S. Andrew, Paul Mark Pedersen, Chad D. McEvoy : "Cronbach's alpha measures how well a set of variables or items measures a single, latent construct. It is essentially a correlation between the item responses in a questionnaire; assuming the statistic is directed toward a group of items intended to measure the same construct. Cronbach's alpha values will be high when the correlations between the respective questionnaire items are high. Cronbach's alpha values range from 0 to 1, and in the social sciences, values at or above 0,7 are desirable, but values well above 0,9 may not be desirable as the scale is likely to be too narrow in focus (Nunnally & Bernstein 1994)."

Interpretting Cronbach's Alpha

"Cronbach's Alpha is an indicator of the internal consistency or homogeneity of a scale. Fundamentally, and perhaps a little simplistically, Cronbach's alpha tells you the extent to which all of the items on the test are "behaving" similarly. A low alpha suggests that there are errors in the selection of items to be included in the measure. If a measure has several subscales, alphas are calculated and reported for each of the individual subscales. It may or may not make sense to report alpha for the scale as a whole as well, depending upon the degree to which the scale as a whole is measuring the same phenomenon" (R. Tappen, 2011, p.131).

The formula from Carmines and Zeller (1979 P.44)

The Cronbach's is often presumed as a simplification of the Spearman-Brown prophecy formula; we measure the mean inter-item correlation (c̄) in order to estimate the degree of agreement amidst individual test items. Next thing we do is to anticipate the reliability coefficient for a n-item test from the correlations amidst all these single-item measures. In addition, other probable perception of the Cronbach's alpha is that it is, originally the average of all possible split half reliabilities (R.M Warner, 2008, p.854).

$\alpha ={\frac {n{\bar {c}}}{1+{\bar {c}}(n-1)}}$

• where "n" remains the number of items
• where "c̄" is the average interitem correlation

(R.M Warner, 2008, p.854)

Cronbach's Alpha's use in health science

Cronbach's Alpha can be use in many different ways. One of the examples is in health science.

"Tests in and outside the health sciences vary enormously in their internal consistency and split-half reliability". Cronbach's alpha is often implemented to divulge these measurements and standards. Split-half reliability is used as an adjust the reliability betwixt the first and the second half of the test.

A brand-new evaluation of nursing competency in the operating theatre developed by researchers at the University of Melbourne presents an thought-provoking instance of utilization of a Cronbach's Alpha. It attain a surprisingly high Cronbach's alpha coefficient of item reliability. A Cronbach's Alpha score between-item of 0,94 was determined for this performance-based heading (S. Mckenzie, 2013, p.201).

Examples of Cronbach Alpha

• Cronbach Alpha is used to measure the reliability of a survey. For example, a survey of student satisfaction with a university course could use Cronbach Alpha to measure how reliable the survey responses are.
• Cronbach Alpha is also used to measure the reliability of a questionnaire. For example, a questionnaire measuring the level of happiness of a group of people could use Cronbach Alpha to measure how reliable the questionnaire responses are.
• Cronbach Alpha can also be used to measure the reliability of a test. For example, a test measuring the cognitive ability of a group of students could use Cronbach Alpha to measure how reliable the test scores are.

Advantages of Cronbach Alpha

Cronbach Alpha is a reliable and popular method for assessing the internal consistency of an aggregation of items. Here are some of the advantages of using Cronbach Alpha:

• It is relatively easy to calculate and interpret, allowing researchers to quickly and accurately measure the reliability of an assessment.
• It is widely accepted in the research community and is seen as a reliable measure of internal consistency.
• It is a good indicator of convergent validity, meaning that it can help assess the correlation between different items.
• It is able to detect small differences in reliability between items, meaning that it can be used to identify poorly performing items in an assessment.
• It can be used to measure the internal consistency of both single-item and multi-item measures.
• It can be used to identify items that are too similar and can be combined to improve the reliability of the assessment.

Limitations of Cronbach Alpha

Cronbach Alpha is a powerful tool for assessing the internal consistency reliability of a set of items, however there are some limitations to consider. These include:

• A low Cronbach Alpha does not necessarily indicate an unreliable measure, as it may just mean that the items are tapping different aspects of the concept being measured.
• The Cronbach Alpha does not take into account the quality of the items included in the measure.
• If the items in the measure are not strongly related, the Cronbach Alpha will be low.
• The Cronbach Alpha may be affected by extreme scores, as a single score can drastically alter the overall result.
• The Cronbach Alpha cannot be used to measure the reliability of a single item.

Other approaches related to Cronbach Alpha

Other approaches that are related to Cronbach Alpha include:

• Split-half reliability - this approach estimates the internal consistency of a test by dividing the test into two halves and then correlating the two halves.
• Spearman-Brown Formula - this approach uses the Spearman-Brown Formula to estimate the internal consistency of a test by correlating the items within the test.
• Kuder-Richardson Formula - this approach uses the Kuder-Richardson Formula to measure the internal consistency of a test by correlating the items within the test.
• Inter-item Correlation - this approach measures the internal consistency of a test by correlating the items within the test.
• Test-retest reliability - this approach measures the internal consistency of a test by administering the same test twice and then correlating the two sets of results.

In summary, there are a number of approaches related to Cronbach Alpha that can be used to measure the internal consistency of a test. These approaches include split-half reliability, the Spearman-Brown Formula, the Kuder-Richardson Formula, inter-item correlation, and test-retest reliability.

Cronbach Alpha — recommended articles

Interval scale — Test validity — Adjusted mean — Statistical power — Anderson darling normality test — Attribute control chart — Residual standard deviation — P chart — Multidimensional scaling

References

• Andrew D.P.S, Pedersen P.M, McEvoy C.D, (1971), Research Methods and Design in Sport Management, Human Kinetics, USA
• Carmines E.G, Zeller R.A, (1979), Reliability and Validity Assessment, Sage Publications, USA
• Mckenzie. S, (2013), Vital Statistics - E-book: An introduction to health science statistics, Churchill Livingstone, Australia
• Nunnnally J.C, Ira H. Bernstein, (1994), Psychometric theory , McGraw-Hill
• Tappen. R, (2011), Advanced nursing research, Jones&Bartlett Learning, USA
• Warner R.M, (2008), Applied Statistics: From Bivariate Through Multivariate Techniques, Sage Publications, USA

Author: Jakub Winiarski