A fundamental weakness of statistical analyses is the evaluation of probabilities - more so the risk acceptance level which is an individual judgement call. A good hypothesis is best applied when a resounding “NO” is the result. The “yes” is never absolute and it is extremely variable. Values of any statistical test are especially problematic when the evaluation test results are near a “threshhold” value – itself a product of general consensus risk assessment.

Certainly, one must be very careful about claiming causality (or reliability) when the accepted tests result in marginal values. Remember that you should be trying simply to determine IF the results are more like due to some cause instead of random. It is never a good idea to hunt and peck for a test or scenario that supports a preconception! You should evaluate which test to use based on the data – type, format, and amount. Comparing two different test implies that you did not really categorize your data carefully.

After considering that, the Rho-C is often recommended as an alternative to the Rho-A (Cronbach’s Alpha) because “Reliability coefficients based on structural equation modeling (SEM) or generalizability theory are superior alternatives in many situations”.

Again, it is of the utmost importance for scientific integrity that you understand why you are using a specific statistical test, and what the limitations of its results are. Statistically “proving” non-randomness does not necessarily imply causation of an effect, much less proof.

The decision of whether to use composite reliability (rho_c) rather than average inter-item correlation (rho_a) to assess the reliability of constructs in a study depends on several factors. Composite reliability and average inter-item correlation serve different purposes and have different implications for the assessment of reliability. Here's a breakdown of their roles:

Now, to address your specific question:

If composite reliability (rho_c) meets an acceptable threshold (e.g., 0.7 or higher) for a particular construct, but the average inter-item correlation (rho_a) for some of the construct's items is below 0.7, it suggests that, as a whole, the construct exhibits adequate internal consistency. This means that, despite some individual items having weaker correlations with each other, the collective set of items still effectively measures the intended construct when considered together.

In this case, you can rely on the composite reliability as an indicator of the overall reliability of the construct, especially if it meets the predefined threshold. It suggests that the construct, as a whole, is internally consistent and reliable, even if individual item correlations are weaker.

However, it's important to exercise caution and carefully consider the context and purpose of your study. You should also ensure that the items within the construct are theoretically meaningful and that the low inter-item correlations are not due to conceptual issues or measurement problems.

In summary, if composite reliability meets the desired threshold, it generally indicates adequate internal consistency for the construct, and you can rely on it as a measure of reliability, even if individual item correlations (rho_a) are below 0.7 for some items within that construct.

Pandia Vadivu Pandian I think your answer is very well explained and makes sense. Do you have any paper through which I can support this argument? I need it for my own purpose. Your kind help will be highly appreciated.