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A note on Type S/M errors in hypothesis testing.

Jiannan Lu1, Yixuan Qiu2, Alex Deng1

  • 1Microsoft Corporation, Redmond, Washington, USA.

The British Journal of Mathematical and Statistical Psychology
|March 24, 2018
PubMed
Summary
This summary is machine-generated.

This study addresses the replication crisis by proposing new methods to control for Type S and Type M errors in hypothesis testing, offering theoretical advancements and practical demonstrations.

Keywords:
design calculationmonotonicityp-valuepower calculationreplicationreproducibilitystatistical significance

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Area of Science:

  • Statistics
  • Psychological Science

Background:

  • The replication and reproducibility crisis in science necessitates new statistical approaches.
  • Gelman and Carlin (2014) proposed controlling for Type S/M errors over Type I/II errors in hypothesis testing.

Purpose of the Study:

  • To address theoretical gaps in the methodology for controlling Type S/M errors.
  • To provide a closed-form expression for expected Type M error.
  • To analyze the mathematical properties of Type S and Type M errors.

Main Methods:

  • Derivation of a closed-form expression for expected Type M error.
  • Mathematical analysis of the properties of Type S error probability and expected Type M error.
  • Numerical and empirical examples to demonstrate the utility of the derived results.

Main Results:

  • A closed-form expression for expected Type M error has been derived.
  • Mathematical properties, including monotonicity, of Type S and Type M errors have been studied.
  • The proposed methods offer advantages demonstrated through simulations and real-world data.

Conclusions:

  • The study provides theoretical advancements for controlling Type S/M errors in hypothesis testing.
  • The derived results offer practical tools for researchers to improve the reliability of their findings.
  • This work contributes to addressing the replication crisis by enhancing statistical rigor.