Beta (Type II Error) Calculator
Here’s a comprehensive table summarizing all you need to know about Beta (Type II Error):
| Aspect | Description |
|---|---|
| Definition | The probability of failing to reject a false null hypothesis in a statistical test |
| Also known as | False negative, Type II error |
| Symbol | β (beta) |
| Formula | β = P(fail to reject H₀ |
| Relationship with Power | Power = 1 – β |
| When it occurs | When the test fails to detect a real effect or difference in the population |
| Consequences | Missing important effects, leading to incorrect conclusions |
| Factors affecting β | Sample size, effect size, significance level (α), variability in data |
| How to reduce β | Increase sample size, choose a larger significance level, reduce variability |
| Trade-off | Reducing β often increases the risk of Type I error (α) |
| Calculation method | Using power analysis or statistical software |
| Importance | Critical in experimental design and interpreting test results |
| Relationship with α | As α decreases, β tends to increase (and vice versa) |
| In hypothesis testing | Represents the probability of a “false negative” result |
| Example | Concluding a drug is ineffective when it actually works |
| Ideal value | As low as possible, typically aimed for β ≤ 0.2 (power ≥ 0.8) |
| Difference from Type I error | Type I error (α) is rejecting a true null hypothesis |
| Use in study design | Helps determine required sample size for desired statistical power |
This table provides a comprehensive overview of Beta (Type II Error), covering its definition, relationships with other statistical concepts, factors affecting it, and its importance in statistical analysis and study design.