Query about reliability coefficient

#1
Hello everyone,

I am trying to grasp a concept but not having any luck.
The statement "reliability places an upper limit on validity" makes a bit of sense to me, for example, a test with r = .70 could not correlate higher than this with any other test.
BUT what would it mean if it did? Say a test of Emotional Intelligence has a reliability coefficient r = .70 but then the test correlates more highly with another test, say at r = .92. What would this mean? My thoughts are...
1. that the original test is not consistent, so not reliable
2. since the original test is not reliable, it is not valid.

Does this make sense or have I gone wrong somewhere? Stats logic not my forte clearly!
Thank you for any help in advance :)
 

spunky

Doesn't actually exist
#2
Given the way theoretical reliability and validity are defined, it's mathematically impossible for a validity coefficient to be greater than the reliability. A formal proof of this statement can be found in Chapter 3, Section 3.9 of Lord & Novick's Statistical Theories of Mental Test Scores.

Notice two important points: (1) This is only true in the population. Sampling variability may contradict this for any given sample but, with a large enough sample it becomes true. (2) The theoretical definition of reliability is different from its (various) quantifiers. That means that although Cronbach's alpha is a quantifier of reliability, it is not the same as true, theoretical reliability which exists only in the abstract.