1. What is Type II Error?

Type II error (β) occurs when a statistical test fails to reject a false null hypothesis. It represents the probability of accepting the null hypothesis when the alternative hypothesis is actually true.

2. How Does the Calculator Work?

The calculator uses the Type II error formula:

Where:

• \( \beta \) — Type II error probability
• \( \text{Power} \) — Statistical power of the test

Explanation: Statistical power is the probability of correctly rejecting a false null hypothesis. Type II error is the complement of power.

3. Importance of Type II Error Calculation

Details: Understanding Type II error is crucial for study design, sample size determination, and interpreting statistical results. It helps researchers assess the risk of missing true effects.

4. Using the Calculator

Tips: Enter the statistical power value between 0 and 1. The calculator will compute the corresponding Type II error probability.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between Type I and Type II errors?
A: Type I error (α) is rejecting a true null hypothesis, while Type II error (β) is failing to reject a false null hypothesis. They have an inverse relationship.

Q2: What is considered an acceptable Type II error rate?
A: Typically, β ≤ 0.2 is acceptable, corresponding to power ≥ 0.8. However, this depends on the study context and consequences of missing an effect.

Q3: How can Type II error be reduced?
A: Increase sample size, use more sensitive measures, increase effect size, or use more powerful statistical tests.

Q4: What factors affect Type II error?
A: Sample size, effect size, variability in data, significance level (α), and test sensitivity all influence Type II error.

Q5: Is Type II error the same as false negative?
A: Yes, in medical testing, Type II error corresponds to a false negative result - failing to detect a condition that is actually present.