What type of validity is supported when the correlation between a coin-rotation task and a grip strength task is not statistically significant?

Discriminant validity is established when a measure does not correlate with other measures that it should theoretically be different from. In this case, since the correlation between the coin-rotation task and the grip strength task is not statistically significant, it suggests that these two tasks assess different constructs.

When different measurements are intended to measure distinct characteristics or variables, a lack of correlation supports the idea that they are indeed discriminating effectively between those constructs. For example, the coin-rotation task might measure fine motor skills, while the grip strength task measures physical strength; therefore, it is expected that performance on these tasks would not be strongly related if they assess different abilities.

In scenarios where measures should theoretically relate to each other, such as when assessing the same construct, a significant correlation would be anticipated (which is the case in convergent validity). Thus, the absence of a significant correlation aligns with the definition of discriminant validity, indicating the two tasks are measuring different underlying constructs.