I've read elsewhere that Alpha is probably a low-bound estimate of realibility if the tau equivalence is violated (which is often is). An alternative was proposed which is the composite reliability. Let's say that my Cronbach Alpha produced a reliability (or internal consistency) of 0.62. However and using factor loadings (on this calculator) to calculate CR, my CR returned around 0.73. Could that much of a difference really exists? If so, can I safely proceed with my analysis and conclude that my construct or factor is generally reliable?

  • $\begingroup$ Far from a conclusive answer, but see the second comment to this question. As far as I can see, composite reliability is calculated using factor loadings. If Cronbach's alpha and factor loadings are qualitatively different then it doesn't seem surprising that Cronbach's alpha and composite reliability could differ markedly. $\endgroup$ – Ian_Fin Oct 14 '16 at 11:17
  • $\begingroup$ Thanks for the comment. Do you think that one can be on the safe side if one proceeds with a Cronbach of 0.63 but with CR of 0.77? (Results are robust and significance is still found) $\endgroup$ – R. AS. Oct 14 '16 at 11:28
  • $\begingroup$ You probably would need to acknowledge that the reliability of your measurements may not be very good. $\endgroup$ – Ian_Fin Oct 14 '16 at 12:14
  • $\begingroup$ That would definitely be done. However and if significant results are to still be found, can one conclude that despite the weak reliability (since weaker ones increase error and decrease statistical power), measurements were still found to be robust. Am I correct if I write something like this? $\endgroup$ – R. AS. Oct 14 '16 at 12:16
  • $\begingroup$ I'm not sure. Intuitively, it seems like results obtained using an unreliable instrument could be spurious. This seems like a whole other question in itself. $\endgroup$ – Ian_Fin Oct 14 '16 at 12:26

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