What is the relation between coefficient alpha and coefficient of precision when a composite test is made up of non-parallel subtests?

Correct option is B

When subtests are non-parallel (tau-equivalent or congeneric rather than strictly parallel), Cronbach's alpha provides a lower bound estimate of reliability. The coefficient of precision (true reliability) will be equal to or greater than coefficient alpha. This is because alpha assumes essentially tau-equivalent measures, and when this assumption is violated with non-parallel tests, alpha underestimates the true reliability.

Information Booster:
1. Coefficient Alpha: Cronbach's alpha estimates internal consistency reliability based on the average inter-correlation among items
2. Parallel Tests Assumption: True parallel tests have equal true score variances and equal error variances, which rarely occurs in practice
3. Non-parallel Tests: When tests are tau-equivalent (equal true scores but unequal error variances) or congeneric (unequal true and error variances), alpha underestimates reliability
4. Lower Bound Property: Alpha is considered a lower bound estimate of reliability, meaning the true reliability is at least as high as alpha
5. Practical Implications: Researchers can be confident that actual test reliability is at least as good as the alpha coefficient indicates