Some previous research found evidence for the predictive validity of a measure. I've done some work and found the measure to be unreliable. Since reliability provides an upper limit for predictive validity (http://psc.dss.ucdavis.edu/sommerb/sommerdemo/intro/validity.htm), how can this be possible?
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I think more information is needed to provide a useful answer here. Can you provide the exact example you are interested in, or a different example that we can use? Also, are there any differences between how you collected your data and the data that indicate predictive validity? The relationship between, and definitions of, reliability and validity are not always clear, so it really depends on your example. For instance, validity for some unobserved or latent measure (e.g. think psychology) is often ascertained through correlations between observed variables. – user3237820 Feb 25 '16 at 15:24
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There is a related question with answers: http://stats.stackexchange.com/q/81098/3277. Please read the answers and the comments to them. – ttnphns Feb 25 '16 at 18:58
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1There is not single understanding of "validity". One is "validity is like unbiasedness". Another is "validity is like precision". In psychometrics, the second understanding prevails. And then may come such things as "reliability provides an upper limit for predictive validity". In general, your question is more psychometrical that proper statistical. – ttnphns Feb 25 '16 at 19:02
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See this as well: http://stats.stackexchange.com/q/82088/3277 – ttnphns Feb 25 '16 at 20:09