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When performing multiple statistical tests, the significance level (α) requires adjustment to prevent inflated Type I errors. This study uses probability theory, analogous to rolling a 20-sided die twice, to calculate the risk of a Type I error occurring at least once.

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Area of Science:

  • Statistics
  • Probability Theory
  • Statistical Significance

Background:

  • * Standard statistical analyses often use a significance level (α) of 0.05.
  • * Conducting multiple tests without adjustment inflates the Type I error rate.
  • * This issue is analogous to scenarios in probability where outcomes are repeatedly observed.

Purpose of the Study:

  • * To determine the probability of a Type I error occurring at least once across repeated, independent statistical tests.
  • * To provide a method for adjusting significance levels when multiple tests are performed.
  • * To illustrate the concept using the probability of outcomes from a 20-sided die (d20).

Main Methods:

  • * Application of probability theory to independent events.
  • * Calculation of the probability of a specific outcome (Type I error) in repeated trials.
  • * Analogous modeling using the outcomes of a 20-sided die (d20).

Main Results:

  • * The probability of a Type I error increases significantly with the number of statistical tests conducted.
  • * A formula is derived to quantify this inflated error probability.
  • * The d20 analogy demonstrates how common practices can lead to higher error rates than intended.

Conclusions:

  • * Standard α=0.05 significance levels are insufficient when multiple statistical tests are performed.
  • * Adjustments are necessary to control the overall Type I error rate.
  • * Understanding probability is crucial for accurate interpretation of multiple statistical tests.