Previous work has shown that human evaluations in NLP are notoriously under-powered. Here, we argue that there are two common factors which make this problem even worse: NLP studies usually (a) treat ordinal data as interval data and (b) operate under high variance settings while the differences they are hoping to detect are often subtle. We demonstrate through simulation that ordinal mixed effects models are better able to detect small differences between models, especially in high variance settings common in evaluations of generated texts. We release tools for researchers to conduct their own power analysis and test their assumptions. We also make recommendations for improving statistical power.