Boundary Estimation

TL;DR

• Uses sample data to produce an interval (confidence interval) that indicates where a population parameter likely falls.
• Commonly computed with a point estimate plus/minus a margin of error derived from sample variability and a critical value.
• Precision depends on sample size and chosen confidence level.

Definition

Boundary estimation is a statistical method that involves determining the range within which the true value of a population parameter is likely to lie. This range is determined by using sample data to calculate an interval estimate, which is a type of confidence interval.

Explanation

Boundary estimation uses sample statistics (for example, a sample mean or sample proportion) together with a measure of sampling variability and a chosen confidence level to construct an interval around the point estimate. The interval is interpreted as the range in which the true population parameter is likely to lie with the stated level of confidence. The accuracy and width of the boundary estimate depend on the sample size and the chosen level of confidence.

Examples

Estimating average height

A researcher samples 100 adult men and measures heights. The sample mean is 175cm with a standard deviation of 10cm. A 95% confidence interval is calculated as:

$$175\text{ cm} \pm 1.96\left(\frac{10\text{ cm}}{\sqrt{100}}\right)$$

This results in an interval estimate of 160.4cm to 189.6cm.

Predicting election support

A pollster surveys 1000 voters and finds 55% support for a candidate. A 95% confidence interval for the true percentage is calculated as:

$$55\% \pm 1.96\left(\sqrt{\frac{55\%(100\%-55\%)}{1000}}\right)$$

This results in an interval estimate of 50.3% to 59.7%.

Use cases

• Researchers estimating population means (for example, average height).
• Pollsters estimating population proportions (for example, percentage support in an election).

Notes or pitfalls

• The accuracy of boundary estimation depends on sample size and the level of confidence chosen. A larger sample size and a higher level of confidence will result in a more precise estimate, but it also means that the range of the estimated boundary will be wider.

Related terms

• Confidence interval