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A complete procedure to test a claim about population standard deviation or population variance is explained here.
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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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Are Experts Well-Calibrated? An Equivalence-Based Hypothesis Test.

Gayan Dharmarathne1, Anca M Hanea2, Andrew Robinson2

  • 1Department of Statistics, University of Colombo, Colombo 00700, Sri Lanka.

Entropy (Basel, Switzerland)
|June 24, 2022
PubMed
Summary
This summary is machine-generated.

Assessing expert calibration using direct coverage comparisons is statistically flawed. A new equivalence testing framework offers better insights but may require more calibration questions, increasing costs.

Keywords:
credible intervalsequivalence testexperts’ calibrationexperts’ hit rates

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Area of Science:

  • Decision Analysis
  • Expert Elicitation
  • Statistical Inference

Background:

  • Expert judgment estimates supplement or replace measurements when data is scarce or costly.
  • Credible intervals quantify uncertainty in expert estimates, aiming for accurate coverage of true values.
  • Expert calibration assesses if stated confidence intervals match actual observed coverage.

Purpose of the Study:

  • To evaluate the statistical validity of directly comparing stated versus actual coverage for expert calibration.
  • To propose and analyze an alternative equivalence testing framework for assessing expert calibration.
  • To investigate the power and cost-effectiveness of formal expert calibration testing.

Main Methods:

  • Statistical hypothesis testing framework applied to expert calibration.
  • Generalization of existing methods to an equivalence testing framework.
  • Power analysis of calibration tests with varying numbers of calibration questions.

Main Results:

  • Direct comparison of coverage percentages has statistical drawbacks in hypothesis testing.
  • The proposed equivalence testing framework offers improved properties for calibration assessment.
  • Formal testing of expert calibration using a modest number of questions demonstrates poor statistical power.

Conclusions:

  • Traditional methods for assessing expert calibration are statistically suboptimal.
  • Equivalence testing provides a more rigorous approach but may necessitate more calibration questions.
  • The high cost and low power suggest limitations for formal experimental assessment of expert calibration.