Hypothesis testing has come under fire in the past decade as misuses have become increas- ingly visible. It is common to use tests whose assumptions don’t reflect how the data were collected, and editorial policies of many journals reward “p-hacking” by setting the arbitrary threshold of 0.05 to determine whether a result merits publication. In fact, properly designed hypothesis tests are an invaluable tool for inference and decision-making. Classical nonparametric tests, once reserved for problems that could be worked out with pencil and paper or approximated asymptotically, can now be applied to complex datasets with the help of modern computing power. This dissertation tailors some nonparametric tests to modern applications for social good.Permutation tests are a class of hypothesis tests for data that involve random (or plausibly random) assignment. The parametric assumptions for common tests, like the t-test and linear regression, may not hold for randomized experiments; in contrast, the assumptions of permutation tests are implied by the experimental design. But off-the-shelf permutation tests are not a panacea: tests must be tailored to fit the experimental design, and there are subtle numerical issues with implementing the tests in software. We construct permutation tests and software to address particular questions in randomized and natural experiments, including identifying what, if anything, student evaluations of teaching measure, and whether voting machines malfunctioned in Georgia’s November 2018 election.Risk-limiting post-election audits (RLAs) have existed for a decade, but have not been adopted widely, in part due to logistical hurdles. This thesis uses classical nonparametric techniques, including Fisher’s combination method and Wald’s sequential probability ratio test, to build new RLA methods that accommodate the idiosyncratic logistics of statewide elections. A new, more flexible method for using stratified samples in RLAs makes it easier and more efficient to audit elections conducted on heterogeneous voting equipment. This thesis also develops an RLA method based on Bernoulli sampling, which allows ballots to be audited “in parallel” across precincts on Election Day. The RLA method for stratified samples of ballots was piloted in Michigan to study its performance in the face of real-world constraints
