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Statistical considerations regarding the use of ratios to adjust data
D B Allison1, F Paultre, M I Goran
1Obesity Research Center, St Luke's/Roosevelt Hospital Center, Columbia University College of Physicians and Surgeons, New York, NY 10025, USA.
Summary
Using ratios to adjust data in obesity research is common but problematic. This study highlights statistical issues with ratios, suggesting regression-based methods as a better alternative for data analysis.
Area of Science:
- Biostatistics
- Obesity Research
- Data Analysis
Background:
- Ratios are frequently used in obesity research to adjust data, often to control for the denominator's influence.
- The statistical assumptions and interpretational consequences of using ratios are not always fully appreciated.
Purpose of the Study:
- To critically evaluate the statistical assumptions underlying the use of ratios for data adjustment.
- To assess the impact of ratio usage on data interpretation in scientific research.
Main Methods:
- The study demonstrates the limitations of using ratios through theoretical explanations and examples.
- It analyzes the conditions under which ratios can appropriately control for denominator effects.
- The impact on data distribution and error structure is examined.
Main Results:
- Ratios can fail to control for confounding variables, especially with non-zero intercepts.
- The ratio of normally distributed variables is not normally distributed, violating parametric test assumptions.
- Ratios can introduce spurious correlations and complicate data interpretation.
- The mean of ratios is distinct from the ratio of means.
Conclusions:
- The indiscriminate use of ratios in data analysis is discouraged due to significant statistical limitations.
- Regression-based approaches are proposed as a more robust alternative for data adjustment and analysis.