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M09.02.08 Types of error
When conducting hypothesis testing, even if we reject the null hypothesis, there is still some level of uncertainty. The results derived from a sample may not accurately represent the population, leading to potential errors. In hypothesis testing, two primary types of errors are identified:
1. Type I Error (α Error)
Definition: Type I error occurs when the null hypothesis is rejected when it is true. This type of error implies that we assume a statistically significant effect in the sample that does not exist in the population.
- Example: Concluding that a drug is effective based on sample data when, in reality, it does not affect the population.
- Probability: The chance of a Type I error is represented by the p-value (e.g., a p-value of 0.05 indicates a 5% chance of committing a Type I error if we reject the null hypothesis).
Characteristics of Type I Error
| Aspect | Description |
|---|---|
| Nature | False Positive (Error of Commission) |
| Representation | α (Alpha) |
| Example | Incorrectly concluding drug efficacy |
| Impact | Overestimating the effectiveness of treatments or interventions |
2. Type II Error (β Error)
Definition: Type II error occurs when the null hypothesis is not rejected even though it is false. This error suggests that we conclude no significant effect based on the sample data, despite an effect being present in the population.
- Example: Concluding that a drug has no effect when, in reality, it is effective.
- Probability: The probability of a Type II error is denoted by β, which is not directly related to the p-value and requires separate calculation.
Characteristics of Type II Error
| Aspect | Description |
|---|---|
| Nature | False Negative (Error of Omission) |
| Representation | β (Beta) |
| Example | Failing to identify a drug’s effectiveness |
| Impact | Underestimating potential treatments or interventions |
Role of the p-value in Hypothesis Testing
The p-value plays a critical role in decision-making in hypothesis testing. However, it is crucial to understand its limitations:
What the p-value Indicates:
- The criterion for rejecting or retaining the null hypothesis.
- Probability of committing a Type I error.
- Significance: Statistical significance, not clinical significance.
What the p-value Does Not Indicate:
- The probability that an individual patient will benefit.
- The proportion of the population that will benefit.
- Expected degree of benefit for any given individual.
Points to Remember
- Type I Error is generally considered more serious than Type II Error.
- Mutual Exclusivity:
- If the null hypothesis is rejected, Type II error is impossible.
- If the null hypothesis is retained, a Type I error is impossible.
Summary Table
| Type of Error | Definition | Symbol | Example | Probability | Impact |
|---|---|---|---|---|---|
| Type I (α) | Rejecting a true null hypothesis | α | Concluding drug works when it doesn’t | Represented by p-value | May lead to unnecessary treatments |
| Type II (β) | Failing to reject a false null hypothesis | β | Concluding drug doesn’t work when it does | Not represented by p-value | May prevent beneficial treatment |
Bibliography
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. SAGE Publications.
- Schervish, M. J. (1996). Theory of Statistics. Springer Science & Business Media.
- Goodman, S. N. (1999). “Toward Evidence-Based Medical Statistics. 2: The Bayes Factor.” Annals of Internal Medicine, 130(12):1005-1013.