In this article, we present a statistical significance test for necessary conditions. This is an elaboration of necessary condition analysis (NCA), which is a data analysis approach that estimates the necessity effect size of a condition X for an outcome Y. NCA puts a ceiling on the data, representing the level of X that is necessary (but not sufficient) for a given level of Y. The empty space above the ceiling relative to the total empirical space characterizes the necessity effect size. We propose a statistical significance test that evaluates the evidence against the null hypothesis of an effect being due to chance. Such a randomness test helps protect researchers from making Type 1 errors and drawing false positive conclusions. The test is an “approximate permutation test.” The test is available in NCA software for R. We provide suggestions for further statistical development of NCA.