This opinion piece summarizes the epistemic benefits of using robust statistical tests in the falsificationist tradition over standard tests such as the t-test, ANOVA, and tests in ordinary least squares regression. I demonstrate this with robust linear regression which does not hinge on normally distributed errors with equal variances and the inconsequentiality of extreme values and outliers. Tests with these broad robustness features act against nonreplication that can occur solely because data anomalies arise differently across studies. Using such a test from the outset sidesteps the pitfalls of making a data-based decision about whether a standard test is applicable. The common practice of conducting a robust test in addition, commonly in response to data inspection, yields multiple test results. I argue that these should be avoided when a binary decision must be reached, for example, whether to conduct further research on the basis on the assumption that an effect exists. Practically, using a single test simplifies analysis. While R offers numerous robust methods, the ones that provide broad robustness are largely restricted to linear models.