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A non-parametric effect-size measure capturing changes in central tendency and data distribution shape.

Jörn Lötsch1,2, Alfred Ultsch3

  • 1Institute of Clinical Pharmacology, Goethe-University, Frankfurt am Main, Germany.

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|September 24, 2020
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Summary
This summary is machine-generated.

A new non-parametric effect size measure, "Impact," is introduced to detect treatment effects missed by traditional methods like Cohen's d. This novel measure enhances quantitative science by capturing changes in data distribution beyond central tendency.

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Area of Science:

  • Quantitative science
  • Data science
  • Artificial intelligence

Background:

  • Standard effect size measures, such as Cohen's d, primarily focus on central tendency.
  • These measures can fail to detect treatment effects if changes are not reflected in the mean or median.
  • Limitations exist in numerical stability and capturing distribution shape alterations.

Purpose of the Study:

  • To develop a non-parametric effect size measure as an alternative to Cohen's d.
  • To create a measure that overcomes numerical limitations of existing methods.
  • To identify effects not captured by central tendency-based measures, particularly changes in data distribution.

Main Methods:

  • A novel non-parametric effect size measure named "Impact" was developed.
  • "Impact" combines a difference-based component (change in central tendency) and a distribution shape-based component (difference in probability density).
  • The measure is normalized to pooled variability and is invariant to data scaling.

Main Results:

  • "Impact" demonstrated superiority over Cohen's d in detecting effects not evident in central tendencies.
  • The measure effectively captures changes in data distribution shape as significant effects.
  • It exhibits numerical stability, even with zero variances in datasets or subgroups.

Conclusions:

  • "Impact" offers a more comprehensive assessment of effect sizes, complementing traditional measures.
  • Its ability to detect distribution changes aligns with machine learning capabilities for knowledge discovery.
  • The measure is highly suitable for big and heterogeneous data analysis in data science and AI.