Type II Error Calculator – Beta and Statistical Power
Calculate Type II error probability and statistical power for hypothesis testing
How to Use
- Enter your sample size (number of observations)
- Enter the significance level (alpha, typically 0.05)
- Enter the effect size you want to detect
- Enter the standard deviation of your population
- Select the type of alternative hypothesis
- Click calculate to see your Type II error and power
What is Type II Error?
Type II error (β) is the probability of failing to reject a false null hypothesis. In other words, it's the probability of concluding there is no effect when in reality there is an effect. This is also known as a 'false negative' in hypothesis testing.
Statistical power (1-β) is the complement of Type II error and represents the probability of correctly rejecting a false null hypothesis. Higher power means a better ability to detect true effects.
Type I vs Type II Error
| Decision | H₀ is True | H₀ is False |
|---|---|---|
| Fail to reject H₀ | Correct decision (1-α) | Type II error (β) |
| Reject H₀ | Type I error (α) | Correct decision (1-β = Power) |
Type I error (α) is the probability of rejecting a true null hypothesis (false positive), while Type II error (β) is the probability of failing to reject a false null hypothesis (false negative).
Factors Affecting Statistical Power
Several factors influence statistical power and Type II error probability:
- Sample size: Larger samples increase power and reduce Type II error
- Effect size: Larger effects are easier to detect, increasing power
- Significance level (α): Lower α increases β (decreases power)
- Standard deviation: Lower variability increases power
- Test type: One-tailed tests have more power than two-tailed tests for directional hypotheses
Power Analysis and Sample Size Planning
Power analysis is typically conducted before a study to determine the required sample size. A conventional target for statistical power is 0.80 (80%), meaning there's an 80% chance of detecting an effect if it truly exists, with a 20% chance of Type II error.
To increase power, you can: increase sample size, use more reliable measurement instruments (reduce σ), use one-tailed tests when appropriate, or increase the significance level (though this increases Type I error risk).
Interpreting Power and Beta
- Power < 0.50 (50%): Low power - high risk of missing real effects
- Power 0.50-0.79: Moderate power - may miss some effects
- Power ≥ 0.80 (80%): High power - generally considered adequate
- Power ≥ 0.95 (95%): Very high power - excellent detection capability
- β = 1 - Power: The probability of Type II error
Frequently Asked Questions
- What is the difference between Type I and Type II error?
- Type I error (α) is rejecting a true null hypothesis (false positive), while Type II error (β) is failing to reject a false null hypothesis (false negative). Type I error is the significance level you set, while Type II error depends on sample size, effect size, and other factors.
- What is considered adequate statistical power?
- A statistical power of 0.80 (80%) is conventionally considered adequate for most research. This means there's an 80% chance of detecting an effect if it exists, with a 20% chance of Type II error.
- How can I increase the power of my study?
- You can increase power by: increasing sample size, using more reliable measurements (reducing variability), detecting larger effect sizes, increasing the significance level (though this increases Type I error), or using one-tailed tests when directional hypotheses are appropriate.
- What is effect size and how does it relate to power?
- Effect size measures the magnitude of the difference or relationship you're studying. Larger effect sizes are easier to detect and result in higher statistical power. Common effect size measures include Cohen's d for mean differences and correlation coefficients for relationships.
- Can Type I and Type II errors both be minimized simultaneously?
- Not without increasing sample size. For a fixed sample size, decreasing Type I error (α) increases Type II error (β), and vice versa. The best way to reduce both errors is to increase sample size.