Physical Unclonable Functions (PUFs) are circuits which extract a device dependent secret from inherently available manufacturing variations. This work focuses on evaluating the quality of such circuits regarding intra-die correlations, because canonical quality metrics for PUFs do not sufficiently cover them. Correlations reduce the effort for an attacker to guess the secret with the same severity as biases, yet canonical tests focus only on the latter. Three tests which are used to consider topological properties along with the secret are introduced and adapted to quality evaluation of PUFs. To show the efficiency and effectiveness but also the limitations of the tests, we apply them to three real-world measurement datasets from ring-oscillator PUFs on FPGAs, standard SRAM and Two-Stage PUFs on ASICs. The results show that the presented statistical tests are ideal candidates to complement state-of-the-art metrics for PUF quality.