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Three Statistical Methods for the Social Sciences

  • Author(s): Miratrix, Luke Weisman
  • Advisor(s): Yu, Bin
  • Sekhon, Jasjeet S
  • et al.
Abstract

Social sciences offer particular challenges to statistics due to difficulties such as conducting randomized experiments in this domain, the large variation in humans, the difficulty in collecting complete datasets, and the typically unstructured nature of data at the human scale. New technology allows for increased computation and data recording, which has in turn brought forth new innovations for analysis.

Because of these challenges and innovations, statistics in the social sciences is currently thriving and vibrant.

This dissertation is an argument for evaluating statistical methodology in the social sciences along four major axes: \emph{validity}, \emph{interpretability}, \emph{transparency}, and \emph{employability}. We illustrate how one might develop methods that achieve these four goals with three case studies.

The first is an analysis of post-stratification, a form of covariate adjustment to evaluate treatment effect. In contrast to recent results showing that regression adjustment can be problematic under the Neyman-Rubin model, we show post-stratification, something that can easily done in, e.g., natural experiments, has a similar precision to a randomized block trail as long as there are not too many strata. The difference is $O(1/n^2)$. Post-stratification thus potentially allows for transparently exploiting predictive covariates and random mechanisms in observational data. This case study illustrates the value of analyzing a simple estimator under weak assumptions, and of finding similarities between different methodological approaches so as to leverage earlier findings to a new domain.

We then present a framework for building statistical tools to extract topic-specific key-phrase summaries of large text corpora (e.g., the New York Times) and a human validation experiment to determine best practices for this approach. These tools, built from high-dimensional, sparse classifiers such as L1-logistic regression and the Lasso, can be used to, for example, translate essential concepts across languages, investigate massive databases of aviation reports, or understand how different topics of interest are covered by various media outlets. This case study demonstrates how more modern methods can be evaluated using external validation in order to demonstrate that they produce meaningful and comprehendible results that can be broadly used.

The third chapter presents the trinomial bound, a new auditing technique for elections rooted in very minimal assumptions. We demonstrated the usability of this technique by, in November 2008, auditing contests in Santa Cruz and Marin counties, California.

The audits were risk-limiting, meaning they had a pre-specified minimum chance of requiring a full hand count if the outcomes were wrong. The trinomial bound gave better results than the Stringer bound, a tool common in accounting for analyzing financial audit samples drawn with probability proportional to an error bound. This case study focuses on generating methods that are employable and transparent so as to serve a public need.

Throughout, we argue that, especially in the difficult domain of the social sciences, we must spend extra attention on the first axis of validity. This motivates our using the Neyman-Rubin model for the analysis of post-stratification, our developing an approach for external, model-independent validation for the key-phrase extraction tools, and our minimal assumptions for election auditing.

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