Although both Fisher’s and Neyman’s tests are for testing “no treatment effects,” they both test fundamentally different null hypotheses. While Neyman’s null concerns the average casual effect, Fisher’s null focuses on the individual causal effect. When conducting a test, researchers need to understand what is really being tested and what underlying assumptions are being made. If these fundamental issues are not fully appreciated, dubious conclusions regarding causal effects can be made.
"Randomization-Based Tests for “No Treatment Effects”." Statist. Sci. 32 (3) 349 - 351, August 2017. https://doi.org/10.1214/16-STS590