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Characterizing nonconstant instrumental variance in emerging miniaturized analytical techniques.

Scott D Noblitt1, Kathleen E Berg1, David M Cate2

  • 1Department of Chemistry, Colorado State University, Fort Collins, CO 80523, USA.

Analytica Chimica Acta
|March 21, 2016
PubMed
Summary

Measurement variance is critical in quantitative chemical analysis. This study confirms heteroskedasticity (non-constant variance) in paper-based analytical devices, cathodic stripping voltammetry, and microchip electrophoresis, recommending weighted regression for improved accuracy.

Keywords:
CalibrationCathodic stripping voltammetryMicrochip electrophoresisPaper-based analytical devicePrecisionWeighted regression

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Area of Science:

  • Analytical Chemistry
  • Metrology
  • Instrument Science

Background:

  • Measurement variance significantly impacts analytical figures of merit like detection limits and confidence intervals.
  • Many emerging analytical techniques implicitly assume constant variance (homoskedasticity) using unweighted regression, despite known instrument heteroskedasticity (variance changing with signal intensity).
  • Ignoring heteroskedasticity leads to suboptimal calibrations, inaccurate uncertainty estimates, and unreliable detection limits.

Purpose of the Study:

  • To evaluate the quantitative impact of heteroskedasticity on emerging analytical techniques.
  • To assess the effectiveness of weighted regression compared to unweighted regression when dealing with non-constant variance.
  • To provide recommendations for accounting for heteroskedasticity in quantitative chemical analysis.

Main Methods:

  • Investigated heteroskedasticity in naked-eye detection with paper-based analytical devices (PADs), cathodic stripping voltammetry (CSV), and microchip electrophoresis (MCE).
  • Analyzed general variance forms and performed Monte Carlo simulations of instrument responses.
  • Quantified the benefits of weighted regression and tested sensitivity to uncertainty in the variance function.

Main Results:

  • Heteroskedastic behavior was confirmed across all three diverse techniques (PADs, CSV, MCE).
  • Weighted regression consistently outperformed unweighted regression, even with moderate uncertainty (30%) in the variance function.
  • The power model of variance was identified as a practical and effective approach.

Conclusions:

  • Heteroskedasticity must be considered during the development of new analytical techniques.
  • Utilizing weighted regression, particularly with the power model of variance, enhances precision and reliability of uncertainty estimates.
  • Adopting methods that account for non-constant variance is crucial for robust quantitative chemical analysis.