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Revisiting the Relationship Between Correlation Coefficient, Confidence Level, and Sample Size.

Qifan Yang1,2, Minyi Su1,2, Yan Li1,2,3

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Summary
This summary is machine-generated.

Determining the minimum sample size for comparing computational chemistry models is crucial. This study introduces a more accurate method, suggesting a few hundred samples suffice for reliable comparisons.

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Area of Science:

  • Computational chemistry
  • Statistical modeling
  • Theoretical model validation

Background:

  • Comparing theoretical model predictive power using Pearson correlation coefficients is common in computational chemistry.
  • Existing methods for determining minimum sample size for model comparison are limited and may overestimate requirements.

Purpose of the Study:

  • To develop a more accurate method for estimating the minimum sample size needed to compare two computational chemistry models.
  • To address limitations in previous methods, specifically the neglect of intercorrelation between models and the use of two-sided tests.

Main Methods:

  • Proposed a novel method based on Dunn and Clark's test statistic for minimum sample size estimation.
  • Conducted extensive numerical tests to validate the proposed method under various conditions.
  • Considered intercorrelation between models and utilized one-sided tests for more realistic comparisons.

Main Results:

  • The new method provides a more accurate estimation of minimum sample size compared to previous approaches.
  • Minimum sample size is influenced by confidence level, statistical power, correlation coefficients, and intercorrelation between models.
  • A rule of thumb indicates that a few hundred samples are adequate for comparisons with 90% confidence or higher.

Conclusions:

  • The developed method offers a more appropriate approach to sample size determination for comparing computational chemistry models.
  • Accurate sample size estimation is vital for robust and reliable benchmark comparisons of theoretical models.
  • The findings provide practical guidance for researchers in computational chemistry regarding sample size requirements.