Traditions of statistical significance testing in second language (L2) quantitative research are strongly entrenched in how researchers design studies, select analyses, and interpret results. However, statistical significance tests using "p" values are commonly misinterpreted by researchers, reviewers, readers, and others, leading to confusion regarding the actual findings of primary studies and critical challenges for the accumulation of meaningful knowledge about language learning research. This paper outlines the basic challenges of accurately calculating and interpreting statistical significance tests, explores common examples of incorrect interpretations in L2 research, and proposes strategies for resolving these problems.