In this letter we study the mean sizes of Hμ clumps in turbulent disk galaxies relative to kinematics, gas fractions, and Toomre Q. We use ∼100 pc resolution HST images, IFU kinematics, and gas fractions of a sample of rare, nearby turbulent disks with properties closely matched to main-sequence galaxies (the DYNAMO sample). We find linear correlations of normalized mean clump sizes with both the gas fraction and the velocity dispersion-to-rotation velocity ratio of the host galaxy. We show that these correlations are consistent with predictions derived from a model of instabilities in a self-gravitating disk (the so-called "violent disk instability model"). We also observe, using a two-fluid model for Q, a correlation between the size of clumps and self-gravity-driven unstable regions. These results are most consistent with the hypothesis that massive star-forming clumps in turbulent disks are the result of instabilities in self-gravitating gas-rich disks, and therefore provide a direct connection between resolved clump sizes and this in situ mechanism.