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Related Concept Videos

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The Arrhenius equation relates the activation energy and the rate constant, k, for chemical reactions. In the Arrhenius equation, k = Ae−Ea/RT, R is the ideal gas constant, which has a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is a constant called the frequency factor, which is related to the frequency of collisions and the orientation of the reacting molecules.
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A residual plot is a statistical representation of data used to analyze correlation and regression results. It helps verify the requirements for drawing specific conclusions about correlation and regression. To obtain the residual plot, first, the residual for each data value is calculated, which is simply the vertical distance between the observed and the predicted value obtained from the regression equation.
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In Microsoft Excel, plotting the mean along with standard deviation (SD) and standard error (SE) helps visualize data variability and reliability. To plot these values, follow these steps:
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Updated: Jan 30, 2026

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Graphical augmentations to sample-size-based funnel plot in meta-analysis.

Lifeng Lin1

  • 1Department of Statistics, Florida State University, Tallahassee, Florida.

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|January 22, 2019
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Summary
This summary is machine-generated.

Publication bias in meta-analyses can be misleadingly assessed using standard-error funnel plots. This study introduces new contours for sample-size funnel plots to improve accuracy in detecting publication bias.

Keywords:
funnel plotmeta-analysispublication biassample sizestandard error

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Area of Science:

  • Biostatistics
  • Medical Research Methodology

Background:

  • Assessing publication bias is crucial for evaluating meta-analysis evidence.
  • Traditional funnel plots (effect size vs. standard error) can yield false positives due to inherent associations between variables.
  • Existing methods for interpreting funnel plot asymmetry are limited.

Purpose of the Study:

  • To introduce novel contours for sample-size-based funnel plots.
  • To provide meta-analysts with a tool for more accurate interpretation of publication bias.
  • To address limitations of standard-error-based funnel plots.

Main Methods:

  • Development of contours for sample-size-based funnel plots across various effect sizes.
  • Comparison with standard-error-based funnel plot interpretation.
  • Illustration using five practical examples.

Main Results:

  • Standard-error-based funnel plots may incorrectly suggest publication bias.
  • Sample-size-based funnel plots offer a more reliable alternative for bias assessment.
  • Proposed contours aid in distinguishing true publication bias from other sources of asymmetry.

Conclusions:

  • Sample-size-based funnel plots with new contours enhance the accuracy of publication bias assessment in meta-analyses.
  • This method helps mitigate false positive conclusions often seen with standard-error-based plots.
  • The findings support more robust evidence synthesis in medical research.