Magnitudes of correlations to assess convergent validity
It is often required in psychometrics to assess the correlation between a test variable subscale total score and a 'gold' standard measure by using a correlation to assess if the two measures are measuring the same construct (convergent validity).
If one treats this correlation as a normal correlation we can use Cohen’s (1988, pp 79-80) rules of thumb as thresholds to assess the degree of convergent validity. Cohen suggests correlations of 0.1 and below are small, correlations between 0.1 and 0.3 are medium and correlations of 0.5 and above are large. These thresholds are also suggested on page 67 of Chapter Five of the below:
Oxford Handbook of Methods in Positive Psychology. Editors Anthony D. Ong and Manfred H.M. Van Dulmen. Oxford University Press:Oxford, 2007. (See this page here.)