Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take as our starting point traditional nonparametric tests, which require no distributional assumption (e.g., normality) about the data distribution. We present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test. These tests use novel test statistics developed specifically for the private setting. We compare our tests to prior work, both on parametric and nonparametric tests. We find that in all cases our new nonparametric tests achieve large improvements in statistical power, even when the assumptions of parametric tests are met.

infer implements an expressive grammar to perform statistical inference that adheres to the tidyverse design framework (Wickham et al., 2019). Rather than providing methods for specific statistical tests, this package consolidates the principles that are shared among common hypothesis tests and confidence intervals into a set of four main verbs (functions), supplemented with many utilities to visualize and extract value from their outputs.

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1. Neighborhood competition models are powerful tools to measure the effect of interspecific competition. Statistical methods to ease the application of these models are currently lacking. 2. We present the forestecology package providing methods to i) specify neighborhood competition models, ii) evaluate the effect of competitor species identity using permutation tests, and iii) measure model performance using spatial cross-validation. Following Allen (2020), we implement a Bayesian linear regression neighborhood competition model. 3. We demonstrate the package’s functionality using data from the Smithsonian Conservation Biology Institute’s large forest dynamics plot, part of the ForestGEO global network of research sites. Given ForestGEO’s data collection protocols and data formatting standards, the package was designed with cross-site compatibility in mind. We highlight the importance of spatial cross-validation when interpreting model results. 4. The package features i) tidyverse-like structure whereby verb-named functions can be modularly “piped” in sequence, ii) functions with standardized inputs/outputs of simple features ‘sf‘ package class, and iii) an S3 object-oriented implementation of the Bayesian linear regression model. These three facts allow for clear articulation of all the steps in the sequence of analysis and easy wrangling and visualization of the geospatial data. Furthermore, while the package only has Bayesian linear regression implemented, the package was designed with extensibility to other methods in mind.