We apply Hoeffding’s inequality directly to weighted estimators of Pauli-expanded witnesses to obtain finite-sample tests for mixed-state nonstabilizerness. With witnesses and shot allocations fixed in advance, the tests control false positives under independent sampling. We also derive sufficient shot counts for a specified positive violation margin and target detection probability. A separate plug-in Gaussian diagnostic is used for comparison. Examples include the single-qubit stabilizer-octahedron criterion, a fixed two-qubit Pauli-correlation Triangle witness, and a previously proposed two-copy Clifford circuit with postselection. For this circuit, we construct eight linear contrasts of the four-qubit input state for each prescribed output threshold. When the postselection probability is positive, the threshold is exceeded if and only if at least one contrast is positive. These contrasts involve 31 nonidentity Pauli observables covered by 15 local product-Pauli bases. Using independent measurement batches, we obtain ratio-free threshold tests and explicit sufficient bounds on shots and input copies. For two identical, independent copies of a two-qubit state, we establish a sharp upper bound on the unnormalized contrast margin at the thresholds considered. An explicit state family attains every positive margin up to this bound. Finite-shot simulations assess detection probabilities for a bound-attaining input and its noisy extension. Separate null checks cover boundary and interior states, as well as inputs with zero postselection probability.