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| [http://www.bmj.com/cgi/content/full/314/7080/572 Bland JM, Altman DG (1997) Statistics notes: Cronbach's alpha. BMJ 314 572] | [http://www.bmj.com/cgi/content/full/314/7080/572 Bland JM, Altman DG (1997) Statistics notes: Cronbach's alpha.] BMJ '''314''' 572. |
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| The above article suggests rules of thumb for Cronbach's alpha and examples of its use. | The above article suggests rules of thumb for Cronbach's $$\alpha$$ and examples of its use. In particular a value of 0.70 is deemed to be 'satisfactory'. |
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| $$ \frac{k}{k-1} 1 - \frac{1}{\mbox{Variance of total scores}} \mbox{Sum of item variances} $$ |
$$\frac{k}{k-1} (1 - \frac{\mbox{Sum of k item variances}}{\mbox{Variance of total scores}} )$$ In particular Bland and Altman (1997) note that ''Cronbach's alpha has a direct interpretation. The items in our test are only some of the many possible items which could be used to make the total score. If we were to choose two random samples of k of these possible items, we would have two different scores each made up of k items. The expected correlation between these scores is'' $$\alpha$$. R code is available from [http://tolstoy.newcastle.edu.au/R/help/06/06/28590.html here] for obtaining confidence intervals for Cronbach's alpha. You just need to run this [:FAQ/cafun: function]. An EXCEL [attachment:cronbachci.xls spreadsheet] also computes in the same way a confidence interval for alpha. This method is the ''exact'' method of Koning AJ and Franses PH (2003). This paper also gives R code in how to compare a pair of Cronbach alphas from two different studies. __Reference__ Koning AJ and Franses PH (2003) [attachment:koning.pdf Confidence intervals for Cronbach's coefficient alpha values.] ERIM Report Series Research in Management. ERIM Report Series reference number ERS-2003-041-MKT. |
A note on Cronbach's alpha
[http://www.bmj.com/cgi/content/full/314/7080/572 Bland JM, Altman DG (1997) Statistics notes: Cronbach's alpha.] BMJ 314 572.
The above article suggests rules of thumb for Cronbach's $$\alpha$$ and examples of its use. In particular a value of 0.70 is deemed to be 'satisfactory'.
Cronbach's alpha is defined as
$$\frac{k}{k-1} (1 - \frac{\mbox{Sum of k item variances}}{\mbox{Variance of total scores}} )$$
In particular Bland and Altman (1997) note that
Cronbach's alpha has a direct interpretation. The items in our test are only some of the many possible items which could be used to make the total score. If we were to choose two random samples of k of these possible items, we would have two different scores each made up of k items. The expected correlation between these scores is $$\alpha$$.
R code is available from [http://tolstoy.newcastle.edu.au/R/help/06/06/28590.html here] for obtaining confidence intervals for Cronbach's alpha. You just need to run this [:FAQ/cafun: function]. An EXCEL [attachment:cronbachci.xls spreadsheet] also computes in the same way a confidence interval for alpha. This method is the exact method of Koning AJ and Franses PH (2003). This paper also gives R code in how to compare a pair of Cronbach alphas from two different studies.
Reference
Koning AJ and Franses PH (2003) [attachment:koning.pdf Confidence intervals for Cronbach's coefficient alpha values.] ERIM Report Series Research in Management. ERIM Report Series reference number ERS-2003-041-MKT.