We study the design of contracts that incentivize a researcher to conduct a costly experiment, extending the work of Yoder (2022) from binary states to a general state space. The cost is private information of the researcher. When the experiment is observable, we find the optimal contract and show that higher types choose more costly experiments, but not necessarily more Blackwell informative ones. When only the experiment result is observable, the principal can still achieve the same optimal outcome if and only if a certain monotonicity condition with respect to types holds. Our analysis demonstrates that the general case is qualitatively different than the binary one, but that the contracting problem remains tractable.