My coefficient alpha is negative

Abstract

An essential feature of the definition of a reliability coefficient is that as a proportion of variance, it should in theory range between 0 and 1 in value. Unfortunately, the definitions given here include unobservable true and error scores, and when we turn from theory to practice, our attempts to estimate reliabilities can produce unexpected results. In practice, the possible values of estimates of reliability range from -¥ to 1, rather than from 0 to 1. Though this is the most extreme case, SPSS users occasionally present a values that are negative and have magnitudes greater than 1, and want to know how this can happen. It must be borne in mind that a is actually a lower bound on the true reliability of a test under general conditions, and that it will only equal the true reliability if the items satisify a property known as essential t –equivalence (Lord & Novick), which requires that their true scores are either all the same, or that each item’s true score can be converted to any other item’s true score by adding a fixed constant. This implies that in order for a to be a measure of reliability instead of a lower bound, the items must be measuring the same thing. Note that even if the items do satisfy the essential t –equivalence assumption, if there is a good deal of error in measurement, sample values of a may be negative even though the population values are positive. This becomes less likely as the numbers of cases and items increases, because sampling variability is reduced. If one encounters a negative value for a, implying a negative average covariance among items, the first thing that should be checked is to see whether data or item coding errors are responsible. A common problem of this type is that the scale consists of some items that are worded in opposite directions to alleviate response biases, and the researcher has forgotten to appropriately recode the reverse scored items, resulting in negative covariances where the actual covariances of interest are positive. Another possibility, most likely with small sample sizes and small numbers of items, is that while the true population covariances among items are positive, sampling error has produced a negative average covariance in a given sample of cases. Finally, it may simply be the case that the items do not truly have positive covariances, and therefore may not form a useful single scale because they are not measuring the same thing.