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Accuracy when inferential statistics are used as measurement tools.

Michael T Bradley1, Andrew Brand2

  • 1Department of Psychology, University of New Brunswick, 100 Tucker Park Road, PO Box 5050, Saint John, NB, E2L 4L5, Canada. Bradley@unb.ca.

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|April 27, 2016
PubMed
Summary
This summary is machine-generated.

Acceptance procedures, used in inferential statistics, can approximate measurement. This study found these procedures yield values slightly larger than actual effect sizes, with the degree of approximation depending on the chosen error rates.

Keywords:
AccuracyMeasurementNeyman and PearsonProbabilitiesType 1 errorsType 2 errors

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Area of Science:

  • Statistical Methods
  • Biostatistics
  • Health Sciences

Background:

  • Inferential statistical tests, known as acceptance procedures, are used to approximate measurement.
  • These procedures involve managing type 1 errors (falsely rejecting the null hypothesis) and type 2 errors (failing to reject the null hypothesis when the alternative is true).
  • The accuracy of these procedures in approximating measurement depends on controlling error probabilities through repeated sampling.

Purpose of the Study:

  • To examine how closely acceptance procedures approximate actual measurement values.
  • To evaluate the impact of type 1 and type 2 error rates on the approximation accuracy.

Main Methods:

  • A Monte Carlo simulation was employed to assess acceptance procedures.
  • Type 1 error was fixed at p = 0.05, with type 2 errors set at p = 0.20 or p = 0.10.
  • Effect sizes (d) of 0.2, 0.5, and 0.8 were analyzed.

Main Results:

  • Acceptance procedures resulted in approximated values that were approximately 15% larger than the entered effect sizes when the type 2 error rate was p < 0.20.
  • With a type 2 error rate of p < 0.10, the approximated values were about 6.25% larger than the entered effect sizes.
  • The study quantified the degree to which these statistical procedures approximate measurement under different error conditions.

Conclusions:

  • Acceptance procedures provide approximate values suitable for decision-making, potentially indicating health changes in a district.
  • While approximations can be reasonable, achieving higher accuracy requires adjusting for statistical power, which may increase type 1 errors and decrease type 2 errors.
  • The trade-offs between error rates and accuracy in acceptance procedures are crucial for their application in health-related contexts.