Final answer:
A restriction of range can indeed affect the accuracy of calculated correlations, since it may lead to an underestimation of the true relationship between variables if the full range of scores is not represented.
Step-by-step explanation:
The statement is true. When calculating a correlation between two variables, such as a test and a validating measure, any restrictions of range on the variables can affect the accuracy and generalizability of the correlation coefficient. This phenomenon is known as restriction of range. If the full range of scores is not represented because the sample is limited or has been pre-selected in some way, the correlation may be weaker than it would otherwise be in the full population. This restriction can lead to an underestimation of the true strength of the relationship between the variables.
It is also important to note that a positive correlation simply indicates a direct relationship between two variables and doesn't necessarily suggest health benefits. Correlation does not imply causation; two variables may be associated without one directly causing the other. Finally, the Pythagorean theorem is indeed used to calculate the length of the resultant vector when adding two vectors at right angles to each other.