1. What is Bias in Statistics?

Bias refers to the systematic error in an estimator that causes it to consistently overestimate or underestimate the true parameter value. It represents the expected deviation between the estimator's average value and the true parameter.

2. How Does the Bias Formula Work?

The bias formula is defined as:

Where:

• \( E[\text{Estimator}] \) — Expected value of the estimator
• \( \text{True Parameter} \) — Actual population parameter value
• \( \text{Bias} \) — Systematic error in estimation

Explanation: A bias of zero indicates an unbiased estimator. Positive bias means overestimation, negative bias means underestimation.

3. Importance of Bias Calculation

Details: Understanding bias is crucial for statistical inference, model evaluation, and ensuring the reliability of estimators in research and data analysis.

4. Using the Calculator

Tips: Enter the expected value of your estimator and the true parameter value. Both values should be in the same units for accurate bias calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between bias and variance?
A: Bias measures systematic error (accuracy), while variance measures random error (precision) in estimation.

Q2: Can bias be eliminated completely?
A: While some bias can be reduced through better methods, complete elimination may not always be possible in practice.

Q3: What is an unbiased estimator?
A: An estimator with zero bias, meaning its expected value equals the true parameter value.

Q4: How does sample size affect bias?
A: Bias is primarily related to the estimation method, not sample size. Larger samples reduce variance but not necessarily bias.

Q5: What are common sources of bias?
A: Selection bias, measurement bias, specification bias in models, and sampling bias are common sources.