Cronbach's alpha is unidimensional in nature, hence each dimension will have it's individual reliability.

Nevertheless, if dimensions are correlated, the overall alpha is usually also computed.

You should report the alpha for each dimension. It is quite often to report an overall Cronbach alpha. However, an overall alpha should only be reported in case of a second order factor analysis. As Miguel A Ruiz said Cronbach is an one-dimensional in nature. Therefore, you shouldn’t report alpha (overall) for a multidimensional scale

I agree with both answers. You should not compute the alpha for whole scale unless You have strong evidence to do so. Moreover Cronbach's alpha is under strong criticism (especially look at the 74th volume of Psychometrika (issue 1) link: http://link.springer.com/journal/11336/74/1/page/1 ) so it would be wise to look for alternatives.

If You are familiar with R system for statistical computing, the psych and MBESS packages allow to easily compute the McDonald's omega coefficient alongside with 95% confidence intervals.

Thank you all for your reply.

Radoslaw Rogoza, I actually calculated both alpha and omega with R which was quite powerful system. I just wanted to know if I can report just one for example omega for the whole scale(in case if I have different sub-scales/ factors within the whole scale). This was my question as I have seen many journal papers that have a scale with multiple factors, but reported just one alpha/omega for the whole scale in the paper!

That was weird for me!

Alpha is influenced by the number of items and when the assumption of tau-equivalency is violated - the result could be biased. That means, if someone is trying to hide unacceptably low reliability estimate of one factor - then reporting only estimate for the whole scale should work fine. The other reason is just lack statistical consciousness.

Parisa, when there are not provided any evidence for calculating reliability for whole scale (e.g. a bi-factor structure), this is not even weird but bad practice.

Here is a link of an article explaining why and how you should abandon alpha. 

http://www.ehps.net/ehp/issues/2014/v16iss2April2014/4%20%20Peters%2016_2_EHP_April%202014.pdf

There are others suggestions as well. Both article from Psychometrika are very good as well (from Jan and Radoslaw).

Thank you all for your helpful responses.

Does anyone know what is the minimum value for omega of a scale to be reliable? I know it is almost .7 for alpha, but how about omega?

Is there any proper references for that so that I can cite?

Parisa, there are no differences in interpretation between those coefficients since both alpha and omega are just estimates of reliability ranging from 0 to 1. So estimate equal to .7 informs that 30% of responses are due to measurement error.

Beware to use rule of thumbs, it is much better to interpret the results as they are.

I used to proceed (SPSS) in the following way: check unidimensionality through principal components analysis, check reliability using Cronbach's alpha (>.8, if the value drops for one variable, kick it out). Alpha cannot replace PC factor analysis

Thanks Radoslaw and Pat! 

Dear Pariza,

Based on my practice, I normally report the reliability of the construct for the overall items first. Conduct EFA . If there are many Factors emerged, test for the emerged Factors reliability, individually. If the overall reliability is greater than the individual reliability the Factors emerged, then this means that all items measure the construct concerned and it should be reported. If the first Factor reliability is bigger than the overall construct reliability, then report the emerged Factors reliability values. Decide whether to consider one construct or many Factors. Thank you. 

I agree with Pariza, the reliability test for each component has to performed and the Cronbach’s apha values reported.   Second, the KMO and the Bartlett's test of sphericity  (approximate chi-square value) have to reported in most cases

Hi Parisa,

The answer for your question depends whether you are willing to use the whole structure or not. If you found 3 factors, it means that you have 4 sums (scores) to create: 3 on the basis of the factors and 1 for the total. You remember that reliability is a measure for the accuracy and discrimination power of these scores. So, if you are not intended to make the sums for the dimensions, you can publish the reliability for the main sum. But then, why to perform EFA if willing to use only total score. Hence, you actually are willing to profile your cases on the basis of those sub-scores and then you need SOME estimate for reliability for each of those scores.

The real question is What estimator you should use. Most used one in the literature seems to be alpha reliability. But that's intended for raw scores which means that there is no weight of the variables in the sum. On the other hand, it assumes that all the variables have equal variances (even though KR21 is claimed to include that option). When you use factor scores, the score is more accurate than the raw score because of the weighting of the variables in the score. There are specific estimators for factor scores based on the communality of the variables. On of these is Tarkkonen's General Reliability, which, I suppose, is quite unknown. A simplistic one-factor reliability can be obtained in SPSS by selecting the main variables of the factor, run one-factor solution (not PCA) like PAF and, after clicking on Factor Scores, one chooses the option Display factor score coefficient matrix, a by-product of which in the case of one factor is the reliability of the factor score variable. This procedure can be made for all dimensions sepaately. You can check, it's always higher than alpha.  Note that this "sum" is not the same as it would be when using all the variables at the same time in the model. Tarkkonen's procedure takes into account all the factors at the same time.

Hopefully this helped you.

Jari M.

Hi Parisa,

Good question. This is too seldom considered and we see many reports of 'reliability' that are not really appropriate. I will list two sources that I like a lot for guiding EFAs.

As others state, generally researchers should be using subscales (unidimensional measures) of each construct and report the internal consistency scores for them only (with some important exceptions). If you are a colleague uses R, you might try Revelle's procedure for calculating McDonald's omegas - these tell you both internal consistency and a variation on factor analysis which will show you how the items load on the latent factors.

Revelle, W. (2016). psych: Procedures for personality and psychological research (Version 1.6.3) [R package version 1.4.12]. Evanston, IL: Northwestern University. Retrieved from http://cran.r-project.org/web/packages/psych/

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Yes. It is good to report every factor reliability value and do not forget to report the overall reliability value as well. If the overall reliability value is higher than the other factors, individually, then use the overall. Otherwise, select the highest. Thank you.

Yes, you should. Prepare a table for Factor Analysis with Named Factors, Factor Loadings and communalities for all items in descending order. At the bottom of the table, indicate for each Factor its Eigen's value, % variance, and Cronbac'sh alpha; and also indicate the overall value for Eigen's value, % variance and reliability Croncach's alpha. Thank you.