VALIDITY is the test for precision. Your proposed CFA model is Y(θ) and the theoretical against which the proposed model is measured for precision is Y(θ*) by finding the difference of di = Y(θ) - Y(θ*), you can verify if there is significant difference in di. If there is significant difference, it means that the proposed model fail validity test, i.e. not being accurate of precise when compared to the theoretical model Y(θ*). The Tbar analysis may be obtained by:

T = d^ / (Sd / sqrt(n))

where d^ = mean of the difference series di, Sd is the standard deviation of di series, and n is the number of pairs of di = Y(θ) - Y(θ*).

DIFFERENT CONTEXT is referring to the generalizability of the proposed model. if the model is reliable and valid, if must be usable in different data set and produce consistent results (consistent) and achieve similar level of precision (valid). How to do it? Obtain a new set of data and substitute into the unknown variable, then analyze the resulting Y.

REFERENCE:

See Kanji's book on 100 Statistical tests

https://www.pdfdrive.com/100-statistical-tests-e97177.html

Model-comparispm approach.

Hope this helps

Matt