Statistically nonsignificant results (p > .05) are often wrongly seen as proof of no effect, but this is often due to low statistical power. Even with high power, assuming the null hypothesis is true is flawed. Instead of relying on p values, we should focus on effect sizes and confidence intervals. In biological anthropology, methods exist to assess meaningful effects beyond just zero differences. Much of what we think we know about differences between sexes, populations, or treatments is based on faulty statistical interpretations.