Type I and Type II errors

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Type I & II Errors - False Alarms & Missed Clues

  • Hypothesis Testing Goal: Determine if there's enough evidence to reject the null hypothesis ($H_0$), which presumes no effect or difference exists.
Error TypeDescriptionAnalogyProbability
Type IRejecting a true $H_0$False Alarm$α$ (alpha)
Type IIFailing to reject a false $H_0$Missed Clue$β$ (beta)
- Probability of a Type I error. You conclude there IS an effect, when there ISN'T.
- Conventionally set at **0.05**.
  • β (Beta):
    • Probability of a Type II error. You conclude there is NO effect, when there IS.
  • Power:
    • The probability of correctly detecting a true effect (correctly rejecting a false $H_0$).
    • Power = $1 - β$. Desired power is typically >80%.

📌 Mnemonic: The boy who cried wolf was making a Type I error (false positive). The villagers made a Type II error when they ignored the real wolf (false negative).

Type I and Type II Errors vs. Null Hypothesis Reality

⭐ Increasing sample size is the most common way to increase the power of a study. A larger sample provides a more precise estimate of the effect, reducing the probability of a Type II error (↓β).

Power & Sample Size - Finding a Real Difference

  • Power is the probability of finding a true difference when one exists. It is the ability to avoid a Type II error.
    • Power = $1 - β$
    • Standard is 80% power.
Error TypeReality: No Difference (H₀ True)Reality: Difference Exists (H₀ False)
Test Says: DifferenceType I Error (α)
False Positive
Correct (Power)
True Positive
Test Says: No DifferenceCorrect
True Negative
Type II Error (β)
False Negative
  • β (beta): Probability of a Type II error.

📌 Mnemonic: You can remember the two types of errors as:

  • Type A (I) error is α (alpha) or accusing an innocent person.
  • Type B (II) error is β (beta) or blinding yourself to a guilty person.

⭐ Decreasing the risk of a Type I error (↓ α) directly increases the risk of a Type II error (↑ β), and vice-versa.

Type I and Type II Errors in Hypothesis Testing

Error & Power Interplay - The Statistical Balancing Act

Hypothesis testing involves a trade-off between two key errors. Adjusting one directly impacts the other, as well as the study's power to detect a true effect.

  • Inverse Relationship: For a fixed sample size (N), decreasing α (risk of Type I error) inevitably increases β (risk of Type II error).
  • Power (1-β): The probability of correctly rejecting a false null hypothesis (H₀). The accepted standard for study power is ≥80%.
  • Increasing Power: The most effective methods are:
    • ↑ Sample size (N): The most common approach.
    • ↑ Effect size: Larger differences are easier to detect.
    • ↑ α level: Increases power but also the risk of a false positive.

⭐ Decreasing α (e.g., from 0.05 to 0.01) to be more confident in a positive result (reduce Type I error) makes the study more stringent. This increases the chance of missing a true effect (↑β) and thus reduces power.

Alpha, Beta, Power, and Effect Size in Hypothesis Testing

High‑Yield Points - ⚡ Biggest Takeaways

  • Type I error (α) is a false positive-incorrectly rejecting a true null hypothesis (H₀). The p-value represents the probability of committing this error.
  • Type II error (β) is a false negative-failing to reject a false null hypothesis when an effect is present.
  • Power (1 - β) is the probability of detecting a true effect; it is the ability to correctly reject a false null hypothesis.
  • α and β are inversely related; decreasing the risk of one error type increases the risk of the other.
  • Power is increased by ↑ sample size, ↑ effect size, or a higher α level.

Practice Questions: Type I and Type II errors

Test your understanding with these related questions

A researcher is trying to determine whether a newly discovered substance X can be useful in promoting wound healing after surgery. She conducts this study by enrolling the next 100 patients that will be undergoing this surgery and separating them into 2 groups. She decides which patient will be in which group by using a random number generator. Subsequently, she prepares 1 set of syringes with the novel substance X and 1 set of syringes with a saline control. Both of these sets of syringes are unlabeled and the substances inside cannot be distinguished. She gives the surgeon performing the surgery 1 of the syringes and does not inform him nor the patient which syringe was used. After the study is complete, she analyzes all the data that was collected and performs statistical analysis. This study most likely provides which level of evidence for use of substance X?

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Flashcards: Type I and Type II errors

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The probability of making a type 2 error is represented by _____

TAP TO REVEAL ANSWER

The probability of making a type 2 error is represented by _____

beta

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