Behrang,

I am not sure that I understand your question. Cronbach's alpha (in its standardized form) is a function of average inter-item correlation, and number of items. So, I take what you are asking is, if the alpha is unsatisfactorily low, can you ignore one of the determinants of alpha (number of items) and only consider item intercorrelations? Alpha is a sampling estimate of the squared correlation between the sum of observed item scores and the theoretical true score, and this, of course, depends on the number of items sampled. Here, using the domain sampling model, it is adequacy of items sampled rather than subjects that is of interest.

Although alpha is often labeled an "internal consistency" metric of reliability, that is misleading, for as I say, it also depends on the number of items. So, if you are interested in the estimate as specified, you can't ignore the number of items.

As well, with 10 items, alpha can certainly be acceptable given large enough correlations among items. For instance, with an average inter-item intercorrelation of .2, alpha would be > .70, and with an average of .4, it would be near .90. Now, granted, with the limited variability of most items, getting the average intercorrelation up to .4 may be a struggle, but this is the task for efficient scale construction, and is where diagnostics can help. It may be that the "literature" you mention regards examining item intercorrelations, or other related diagnostic statistics to help in increasing alpha through item deletion, rather than examining those itercorrelations instead of alpha.

Now, there is much more one could meander into, and the discussion could be expanded beyond alpha, but this seems to be a rough answer to your Q.

My best wishes on your scale construction,

John

Dear John i really appreciated your help.

I am going to copy here the literature part about it. It says(when there are a small number of items in the scale fewer than 10, Cronbach can be quite small. In this situation it may be better to calculate and report the mean inter-item correlation for the items.Optimal mean inter-correlation value range from .2 to .4 ). As u can see it means if Cronbach is small relay on intert-item correlation instead for reliability ,is that ok?

Behrang,

Did you intend to put a link here, or to just recap that recommendation? I would be interested in where that came from. If you can send a citation, I will try to take a look, but in any case, no is still my answer for the reasons I specified.

I might also say that the "optimal" mean intercorrelatoin among items for alpha is not .2 to .4, but as large as it can be; the larger that average is, the fewer items one needs to achieve the same alpha.

Also, let's follow that recommendation a bit further. Let's say that I have only 2 items in a scale, but the alpha is unsatisfactory. Because alpha is unsatisfactory, we look at the average intercorrelation, herein, a single correlation, and it is .4 -- at the top end of that recommendation. The alpha is .57 and would in general be judged poor. The "large" .4 intercorrelation in no way makes up for the very small number of items. You can expect herein to capture only about 57% of the variance of the true scores from your instrument's observed scores.

I have attached a plot that I sometimes use with psychometric students of the OCs of alpha as a function of average item intercorrelation and number of items; it may help illustrate.

My best,

John

Behrang,

How low is your "low Alpha"? It is true that alpha and reliability measures are related to test size. However, you can have high values with few items and low values with lots of items. Focus your analysis to estructural, content, and construct aspect. Check if you can explain the low reliability, it May give you some clue on how to proceed.

A more avanced option would be to check for response function fit and differential item functioning. I have seem very low alphas explained by heterogeinity in response pattern among subgrups

John,

PALLANT, J. SPSS Survival Manual ****NOT FOR SALE IN AUSTRALIA OR NEW ZEALAND RIGHTS RESTRICTIONS****. Open University Press. this is the book and you can find it on p 6@john morris John Morris

Diego,

Alpha is 5.6 for for items, and inter-item correlation is .245 Diego Fernando Rojas Gualdrón