An official website of the United States government
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.
more »
« less
On the relative efficiency of the intent-to-treat Wilcoxon–Mann–Whitney test in the presence of noncompliance
Summary A general framework is set up to study the asymptotic properties of the intent-to-treat Wilcoxon–Mann–Whitney test in randomized experiments with nonignorable noncompliance. Under location-shift alternatives, the Pitman efficiencies of the intent-to-treat Wilcoxon–Mann–Whitney and t tests are both derived. It is shown that the former is superior if the compliers are more likely to be found in high-density regions of the outcome distribution, or in other words, if the noncompliers tend to reside in the tails. By logical extension, the relative efficiency of the two tests is sharply bounded by a least and most favourable scenario where the compliers are segregated in regions of lowest or highest density, respectively. Such bounds can be derived analytically as a function of the compliance rate for common location families such as Gaussian, Laplace, logistic, and t distributions. These results help empirical researchers pick the more efficient test for existing data and calculate sample size for future trials in anticipation of noncompliance. Results for nonadditive alternatives and other tests follow along similar lines.
more »
« less
- Award ID(s):
- 2015526
- PAR ID:
- 10337136
- Date Published:
- Journal Name:
- Biometrika
- ISSN:
- 0006-3444
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Two-sample tests are widely used in hydrologic and climate studies to investigate whether two samples of a variable of interest could be considered drawn from different populations. Despite this, the information on the power (i.e., the probability of correctly rejecting the null hypothesis) of these tests applied to hydroclimatic variables is limited. Here, this need is addressed considering four popular two-sample tests applied to daily and extreme precipitation, and annual peak flow series. The chosen tests assess differences in location (t-Student and Wilcoxon) and distribution (Kolmogorov–Smirnov and likelihood-ratio). The power was quantified through Monte Carlo simulations relying on pairs of realistic samples of the three variables with equal size, generated with a procedure based on suitable parametric distributions and copulas. After showing that differences in sample skewness are monotonically related to differences in spread, power surfaces were built as a function of the relative changes in location and spread of the samples and utilized to interpret three case studies comparing samples of observed precipitation and discharge series in the U.S. It was found that (1) the t-Student applied to the log-transformed samples has the same power as the Wilcoxon test; (2) location (distribution) tests perform better than distribution (location) tests for small (moderate-to-large) differences in spread and skewness; (3) the power is relatively lower (higher) if the differences in location and spread or skewness have concordant (discordant) sign; and (4) the power increases with the sample size but could be quite low for tests applied to extreme precipitation and discharge records that are commonly short. This work provides useful recommendations for selecting and interpreting two-sample tests in a broad range of hydroclimatic applications.more » « less
-
null (Ed.)Food, energy and water (FEW) systems are critically stressed worldwide. These challenges require transformative science, engineering and policy solutions. However, cross-cutting solutions can only arise through transdisciplinary training of our future science and policy leaders. The University of Maryland Global STEWARDS National Science Foundation Research Traineeship seeks to meet these needs. This study assessed a foundational component of the program: a novel, experiential course focused on transdisciplinary training and communication skills. We drew on data from the first two offerings of the course and utilized a mixed-method, multi-informant evaluation that included validated pre–post surveys, individual interviews and focus groups. Paired Mann–Whitney–Wilcoxon tests were used to compare pre- and post-means. After the course, students reported improvements in their ability to identify strengths and weaknesses of multiple FEW nexus disciplines; articulate interplays between FEW systems at multiple scales; explain to peers the most important aspects of their research; and collaborate with scientists outside their field. Students also reported improvements in their oral and written communication skills, along with their ability to critically review others’ work. Our findings demonstrate that this graduate course can serve as an effective model to develop transdisciplinary researchers and communicators through cutting edge, experiential curricular approaches.more » « less
-
Lack of racial diversity has been an ongoing issue in higher education. Recently, the Theory of Racialized Organizations has been used to help explain why, despite many calls for diversity, the demographics of higher education have not changed. Considering this framework, we seek to understand what aspects of the graduate school application process are viewed as barriers by minoritized students for applying. As part of a larger study of undergraduate student knowledge of the graduate school application process, we analyze 515 responses from undergraduate math majors using Mann-Whitney U tests to identify differences in what participants view as a barrier to apply to graduate school by race/ethnicity. We discuss two main results and recommend changes to graduate programs wishing to recruit more minoritized students.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1093/biomet/asab053
