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Randomization Tests for Weak Null Hypotheses in Randomized Experiments

The Fisher randomization test (FRT) is appropriate for any test statistic, under a sharp null hypothesis that can recover all missing potential outcomes. However, it is often sought after to test a weak null hypothesis that the treatment does not affect the units on average. To use the FRT for a weak null hypothesis, we must address two issues. First, we need to impute the missing potential outcomes although the weak null hypothesis cannot determine all of them. Second, we need to choose a proper test statistic. For a general weak null hypothesis, we propose an approach to imputing missing potential outcomes under a compatible sharp null hypothesis. Building on this imputation scheme, we advocate a studentized statistic. The resulting FRT has multiple desirable features. First, it is model-free. Second, it is finite-sample exact under the sharp null hypothesis that we use to impute the potential outcomes. Third, it conservatively controls large-sample Type I error under the weak null hypothesis of interest. Therefore, our FRT is agnostic to the treatment effect heterogeneity. We establish a unified theory for general factorial experiments and extend it to stratified and clustered experiments. Supplementary materials for this article are available online.

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Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (JASA); Vol.116 No.536 December 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1898-1913

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

CAUSAL INFERENCE
POTENTIAL OUTCOMES
RANDOMIZATION-BASED INFERENCE
STUDENTIZATION
SHARP NULL HYPOTHESIS
FINITE POPULATION ASYMPTOTICS

Info Detail Spesifik

https://doi.org/10.1080/01621459.2020.1750415

Pernyataan Tanggungjawab

Jason Wu, Peng Ding

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