Cronbach to the future

(This article was originally published at Psychological Statistics, and syndicated at StatsBlogs.)

One fascinating thing about working in the area of psychological statistics is how hard it is to move people away from reliance on bad, inefficient or otherwise problematic methods. My own view - informed to some extent by the literature, by experience and by anecdote is that it isn't sufficient merely to establish than the standard approach is wrong. It isn't even sufficient to provide an obviously superior alternative. You also need to three other things: i) get the message out to the people using the method, ii) reduce barriers to implementing the method (provide user-friendly software, easy to understand tutorial sand so forth), and iii) get the new method taught at undergraduate or masters level. A good illustration is the need to provide confidence intervals (CIs) as well as point estimates of statistics. This has been advocated for decades and has only relatively gradually trickled through to standard practice. In addition, CIs are commonly reported only where popular software such as SPSS reports them by default. For instance, few psychology papers report a CI for the correlation coefficient r (probably because it isn't in many introductory texts and isn't part of the default SPSS output).

A case in point is the problem of internal reliability estimation. There are dozens of papers in the psychometrics literature that have shown that the most popular internal consistency reliability measure, coefficient alpha (or Cronbach's alpha) is seriously flawed. A number of alternative approaches or measures have been proposed that are relatively easy to estimate and have good properties when applied to scales in psychology. However, these measures rarely get used in practice. The main barriers here are probably awareness of the problem and availability of appropriate software. My guess is that once these barriers are reduced then alternatives to alpha will also get into text books and be more widely taught.

Tom Dunn (a former PhD student) has just written a paper (co-authored with myself and Viv Brunsden) aiming to change people's attitude to coefficient alpha. This has just been accepted in the British Journal of Psychology. In it we try to summarize with as little jargon as possible the criticisms of coefficient alpha and recommend a simple alternative: McDonald's coefficient omega (McDonald, 1999). Crucially we also provide a mini-tutorial on calculating omega using R. We chose mainly R because it is free, open source and runs on Mac, PC and linux systems. A further, major advantage is that the MBESS package will estimate a bootstrap CI for omega. A reliability estimate (of any kind) is pretty useless if presented as a point estimate because it could be measured very imprecisely. In many cases the lower bound of the 95% CI is a more useful guide to whether a test is reliable. The lower bound will usually be conservative but it is better to be safe than sorry in most cases.

A pre-print of the paper (links to the online version will be added as soon as they are available) can be found here. The R script that runs the example in the paper can be accessed here. The data sets (in a zipped folder called "omega example") can be downloaded here. Unzip this folder and put it on your desktop. (If you move it elsewhere you need to specify the path in the R code or change the R working directory to the folder where the data files are located. You can also download the .csv formatted data file directly from here.

References

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297–334.

Dunn, T., Baguley, T., & Brunsden, V. (2013, in press). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British Journal of Psychology.

McDonald, R. P. (1999). Test theory: A unified approach. Mahwah, NJ: Lawrence Erlbaum Associates.

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Tags: coefficient alpha, coefficient omega, confidence intervals, internal consistency, psychology, psychometrics, R, reliability, statistics