I suppose that under "repeatability" you understand the test-retest validity, don't you?
There are diffrerent types of validity which all together show that you are measuring the correct construct. Remeber, that reliability indicates that your "correctly measure the construct".
How can one assure that the construct is correct? One can look at similar constructs and show that his measurement is close but slightly differs. This "slightly" indicates the new aspect you added to the science with your new construct.
One can also calculate a convergent validity, showing that he measured (the parts of) the construct correctly. Discriminant validity might indicate that different factors constituting the construct are measured correctly (that the measurements do not overlap). One has also the nomologic validity, where the network of related concepts and theire relationships are analyzed. This validity explains how broad or how specfic your concept is.
Repeated measures belong to the reliability test (I hope I am correct). Reliability tests do not focus on what you measured, but on how you measured it. For example, Cronbach's alpha indicates the internal consistency of the measurement and shows that items which are supposed to measure one factor, correlate. Composite reliability (CR) is similar but allows one to check the reliability if the measures are of a different type (e.g. Likert scales + time variables). Test-retest reliabiliy might show one that the test worked not only ones (by certain conditions), but that it works when repeated. It should indicate that the first obtained results were not a coincidence and to reveal that there are no other confounding conditions.
Validity means if a measure what it is supposed to measure. Relaibility means repeatability. If a study is not valid even though it's reliable the results will not mean anything. There are several ways to establish validity and reliability. The CI on the other hand states that with 95% confidence you could state that true population parameter lies within the given range. A valid study with adequate number of samples would give you precise estimations.
Repeatability of the test is one of the parameter of validation which shows the result of process or product to be precise and should not be more then 2 % while 95 % CL shows range of method (Upper and lower range) where the process or products meets its predetermined procedure. Thus within 95 % Cl we find our method is precise or not precise. so we conclude that the method is precise within the range predicts the high degree of assurance nothing but validity of product or process.
Thank you very much for answering my question. I absolutely agreed with all ideas above. Initially, I though, it might synthesize these validity, reliability and 95%CI in somehow in relationships.