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Two-tailed significance tests for 2 × 2 contingency tables: What is the alternative?
1Centre for Population Health Studies, Usher Institute of Population Health Sciences and Informatics, University of Edinburgh, Edinburgh, Scotland, UK.
Statistics in Medicine
|July 3, 2019
Summary
Statistical testing for 2x2 contingency tables is controversial. This study recommends doubling Fisher's exact test one-tailed probability for medical research, offering a more appropriate significance testing method.
Area of Science:
- Biostatistics
- Medical Statistics
- Epidemiological Methods
Background:
- The use of two-tailed significance testing for 2x2 contingency tables is a persistent source of controversy in medical literature.
- Inconsistent application of statistical tests can lead to differing conclusions regarding the significance of findings.
- This variability in test selection is problematic for reproducible and reliable medical research.
Purpose of the Study:
- To address the controversy surrounding significance testing for 2x2 contingency tables.
- To clarify the role of alternative hypotheses in statistical testing.
- To recommend a standardized and appropriate testing method for medical research.
Main Methods:
- The study analyzes the theoretical underpinnings of significance testing for 2x2 tables.
- It differentiates between two possible alternative hypotheses to the Null hypothesis.
- The paper evaluates the applicability of different tests within the context of medical research.
Main Results:
- A key finding is that the controversy stems partly from overlooking two distinct alternative hypotheses.
- One alternative hypothesis allows for more powerful tests, while the other is more suitable for medical contexts.
- The recommended approach involves doubling the one-tailed exact probability from Fisher's exact test.
Conclusions:
- For medical research, 2x2 contingency tables should be tested by doubling the one-tailed exact probability from Fisher's exact test.
- As an approximation, the chi-squared test with Yates' correction for continuity is also recommended.
- Adopting this standardized approach will improve consistency and reduce ambiguity in medical research findings.
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