Statistics & Probability

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Statistics & Probability

Bias Calculator.

Calculates the statistical bias of an estimator by comparing its expected value to the true population parameter.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the true population value.

  2. 2

    Enter the expected value of your estimator.

  3. 3

    The bias is the difference: expected value minus true value.

  4. 4

    A positive bias means overestimation; negative means underestimation.

expected_value - true_value

Frequently asked questions

What does a positive bias indicate?

A positive bias means the estimator tends to overestimate the true value on average.

What is relative bias?

Relative bias expresses the bias as a percentage of the true value, making it easier to compare across different scales.

Is zero bias always ideal?

Zero bias means the estimator is unbiased on average, but it doesn't guarantee accuracy for a single sample; variance also matters.

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Bias

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Relative bias (%)0%
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How it works

Calculates the statistical bias of an estimator by comparing its expected value to the true population parameter.

  1. Enter the true population value.
  2. Enter the expected value of your estimator.
  3. The bias is the difference: expected value minus true value.
  4. A positive bias means overestimation; negative means underestimation.

Formulas

The math behind this calculator, written out so you can verify the result.

Bias

Bias = E[θ̂] - θ

The difference between the expected value of the estimator and the true parameter.

Example:

Input: E[θ̂] = 105, θ = 100

Calculation: 105 - 100

Result: 5

Relative Bias

Relative Bias = (Bias / θ) × 100%

Bias expressed as a percentage of the true value.

Example:

Input: Bias = 5, θ = 100

Calculation: (5 / 100) × 100

Result: 5%

Real-world use cases

Where this calculation shows up in everyday life.

Evaluating estimators

Compare different estimators to see which one is less biased.

Example: Comparing sample mean vs. sample median for skewed data.

Survey sampling

Assess if a survey method systematically over- or under-reports a population characteristic.

Example: Checking if a poll's average response matches known census data.

Machine learning models

Measure bias in predictions to identify systematic errors.

Example: Comparing average predicted house price to actual market average.

Tips and common mistakes

Tips

  • Use relative bias when comparing across different scales.
  • Bias is a property of the estimator, not a single estimate.
  • Combine bias with variance to assess overall accuracy (MSE).
  • A small bias may be acceptable if variance is low.

Common Mistakes to Avoid

  • Confusing bias with error: error includes random variation, bias is systematic.
  • Using a single sample's difference as bias; bias is the average over many samples.
  • Ignoring the sign of bias; direction matters.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.