As a guide, anything above 0.7 is considered acceptable*. However, just as a large number of items can artificially inflate Chronbach's alpha, a smaller set of items like yours may artificially deflate the figure (the alpha essentially being a form of self correlation). For a scale of only 8 items, I would say that an alpha of 0.68 is perfectly acceptable, especially given the construct you are attempting to assess, but see what people with better expertise in this area have to say.

*George, D., & Mallery, P. (2003). SPSS for Windows step by step: A simple guide and reference. 11.0 update (4th ed.). Boston: Allyn & Bacon.

I agree with Paul. There are so many issues here. With only 8 items you would need to have a higher item-intercorrelation to move into the so-called acceptable range. Here are some thoughts?

Do you have enough people to perform a principal components analyses and see it there is a tendency for a multidimension? If so, even if the dimensions are correlated and the item pool is small, your alpha can misinform.

Another thing to think about is the signal to noise ratio, of which alpha is a form.

Perhaps the topic you are studying has such a strong signal that you can tolerate more error to signal.

You have what you have and should pursue with a nod to these other issues. Good luck.

Dear Maud,

I'd also add that the Cronbach's alpha coefficient itself is not reliable unless the sample size is sufficiently large or the first eigenvalue of a principal component analysis is sufficiently large or the factor weightings for the individual items for this first factor are sufficiently large. I have recently written a draft study guide on this subject: https://www.researchgate.net/publication/280936182_Advice_on_Reliability_Analysis_with_Small_Samples.

Technical Report Advice on Reliability Analysis with Small Samples

The value of 0·7 is just folklore. Nunally didn't say it, and people who claim he said it (such as the SPSS reference above) are sloppy. In fact, Nunally argues against using a measure with such poor reliability. I quote:

In many applied problems, a great deal hinges on the exact score made by a person on a test. . . . In such instances it is frightening to think that any measurement error is permitted. Even with a reliability of .90, the standard error of measurement is almost one-third as large as the standard deviation of the test scores. In those applied settings where important decisions are made with respect to specific test scores, a reliability of .90 is the minimum that should be tolerated, and a reliability of .95 should be considered the desirable standard

Cited in

Lance, C.E., Butts, M.M. & Michels, L.C., 2006. The Sources of Four Commonly Reported Cutoff Criteria: What Did They Really Say? Organizational Research Methods, 9(2), pp.202–220.

Incidentally, there is a literature on item-deletion strategies. They make reliability worse, not better. I can dig out the references if you are interested.

Thank you all for your precious answers, they were very helpfull to me and I really appreciate such dynamism !