First, since you have binary data, its typically referred instead to the K-R 20 coefficient, which Cronbach’s Alpha is based.
As for why it’s negative. The sum of your item variances is greater than that of the scale variance. Another way of thinking about it is that the average covariance of the items is negative.
As for the causes. First, the most common cause is that an item calculated in the reliability is worded negatively or is negatively associated with the other items, and thus
needs to be reverse coded. I would check for this first, it’s the most likely, and see what this nets you. I have found that people will argue items should all be positively associated with each other and the wording is positive, yet one item clearly stands out as negatively associated with all other times. We often find that there was an interpretation mistake that was possible with the item, or even how most or all respondents interpreted the item. If the item wasn’t correlated as expected and it appears to be an error in interpretation, since this can never be known or proven, I suggest removing it. This issue can also lead to the second possibility.
If the negative coefficient is small, it may mean nothing more than a great deal of error variance. This often arises when the population is small or the items were hard to interpret, and thus interpreted differently by many of the respondents. Again, if this is clear, my suggestion would be to either remove the item, or if bad enough, scrap the entire collection effort and reword the items to be more clearly and easily understandable. Even if you choose to scrap it, given that there was a cost and time placed on collecting the data in the first place, you may find that you can salvage a few items from the original scale (at least 3 remember) which reflect the core latent construct well enough for an initial measurement of reliability. It’s also possible that additional analysis could be done to
help in reconstructing the survey for the next round.
Matthew J Poes
Research Data Specialist
Center for Prevention Research and Development
University of Illinois
510 Devonshire Dr.
Champaign, IL 61820
Phone: 217-265-4576
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Eins Bernardo
Sent: Monday, October 01, 2012 2:44 AM
To: [hidden email]
Subject: Negative Cronbach's alpha for 0/1 values
Hope someone can help solve my problem pertaining to the negative Cronbach's alpha. I have 10 items and each item is coded 0 and 1, where 1 is the correct
answer. Please suggest what shall be done when Cronbach's alpha is negative for 0/1 values.