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Quantifying error in effect size estimates in attention, executive function, and implicit learning.

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Small sample sizes in psychological research lead to inaccurate effect size estimates, potentially doubling information loss. Basing power calculations on prior studies with small N is unreliable, highlighting the need for larger samples.

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Area of Science:

  • Cognitive psychology
  • Psychological research methodology

Background:

  • Accurate effect size quantification is crucial for scientific progress and efficient resource allocation.
  • Publication bias and small sample sizes (N≈25) compromise the reliability of current effect size estimates.

Purpose of the Study:

  • To assess how sample size impacts effect size estimation errors in attention, executive function, and implicit learning paradigms.
  • To evaluate the reliability of power calculations based on existing effect size estimates.

Main Methods:

  • A large dataset was combined with bootstrapping to simulate 1,000 experiments across a range of sample sizes (N=13-313).
  • Analysis focused on quantifying effect size, statistical power, and information loss.
  • The study examined the precision of power calculations and identified predictors of erroneous estimates.

Main Results:

  • Experiments with smaller sample sizes (lower N) can result in doubled or tripled information loss.
  • Power calculations based on effect sizes from similar studies were imprecise 40%-67% of the time with common sample sizes.
  • Skewness in intersubject behavioral effects emerged as a predictor of erroneous effect size estimates.

Conclusions:

  • Small sample sizes significantly increase the risk of inaccurate effect size estimates and unreliable power calculations.
  • Researchers are advised to consider larger sample sizes and the potential impact of effect size estimate variability.
  • The simulation approach offers valuable theoretical insights, including the information gained from null hypothesis rejection and the role of individual variation in estimation error.