Point estimate and bias
A point estimate is a single number guessing a parameter, such as the sample mean for the population mean. An estimator is unbiased if its average over many samples equals the true parameter.
Last updated
Analogy
A dart thrower whose throws centre on the bullseye is unbiased, even if single throws miss.
Example
Sample: 12, 15, 9, 14, 10Mean = 60 / 5 = 12Gaps squared: 0,9,9,4,4 = 26s squared = 26 / 4 = 6.5s = 2.55
In practice
The sample mean and the sample variance with n minus 1 are unbiased estimators.
Practice
Flashcards
- What makes an estimator unbiased?Its average over many samples equals the true parameter.
Questions people ask
Is an unbiased estimator always the best?
Not always. It means the estimate is right on average, but any one estimate can still be far off. A slightly biased estimator with much smaller spread can have lower total error. Statisticians also look at variance, not only bias.
Why is a point estimate not enough?
A single number gives no sense of how far off it might be. A poll saying 54 percent backs a law is far less useful than 54 percent plus or minus 3. A confidence interval adds the missing information about precision.