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Statistical Power Calculator

Probability of correctly rejecting a false null hypothesis.

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Power

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Overview

Statistical power represents the probability that a study will correctly reject a null hypothesis when a true effect actually exists. It is mathematically defined as the complement of the Type II error rate, reflecting the sensitivity of a research design to detect differences or relationships within a population.

Symbols

Variables

1-\beta = Power, \beta = Beta (Type II Error)

Power
Beta (Type II Error)

Apply it well

When To Use

When to use: Researchers use this calculation during the planning phase to determine the necessary sample size for detecting an effect of a specific magnitude. It is also utilized in sensitivity analyses to evaluate whether a non-significant result was likely due to a lack of effect or insufficient detection capability.

Why it matters: High power reduces the risk of false negatives, ensuring that valuable psychological interventions or cognitive phenomena are not overlooked. In clinical research, maintaining sufficient power protects against wasting resources on underpowered studies that cannot yield conclusive evidence.

Avoid these traps

Common Mistakes

  • Thinking a non-significant result means no effect exists (it might just be low power).

One free problem

Practice Problem

A clinical psychologist is designing a study on CBT for anxiety. If the probability of committing a Type II error (b) is set at 0.20, what is the statistical power (p) of the study?

Beta (Type II Error)0.2

Solve for:

Hint: Power is the probability of not making a Type II error.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Statistical power
  2. Wikipedia: Type II error
  3. Gravetter, F. J., Wallnau, L. B., Forzano, L. B., & Witnauer, J. E. (2021). Essentials of statistics for the behavioral sciences.
  4. American Psychological Association (APA) Publication Manual, 7th Edition
  5. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.
  6. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
  7. American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.).
  8. AQA Psychology A-level Specification or similar A-level Psychology textbook