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Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...

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Related Experiment Video

Updated: Jun 2, 2026

Sampling Soils in a Heterogeneous Research Plot
07:11

Sampling Soils in a Heterogeneous Research Plot

Published on: January 7, 2019

Variance estimation for systematic designs in spatial surveys.

R M Fewster1

  • 1Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand. r.fewster@auckland.ac.nz

Biometrics
|May 4, 2011
PubMed
Summary
This summary is machine-generated.

A new "striplet" estimator accurately quantifies variance in spatial surveys, improving density estimations. This method overcomes overestimation issues with systematic designs, offering more reliable ecological data.

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Last Updated: Jun 2, 2026

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Area of Science:

  • Ecology
  • Spatial Statistics
  • Wildlife Biology

Background:

  • Systematic designs in spatial surveys offer lower variance for density estimation compared to random designs.
  • Estimating variance for systematic designs is challenging, often leading to overestimation and loss of efficiency gains.
  • Current methods approximate systematic designs with random or stratified designs, but these can be biased.

Purpose of the Study:

  • To develop a novel, unbiased estimator for variance in systematic spatial surveys.
  • To improve the precision of density estimates in ecological studies.
  • To address limitations of existing variance estimation methods.

Main Methods:

  • Developed a new "striplet" estimator based on modeling the spatial encounter process.
  • Simulated various survey scenarios including strip-sampling, distance-sampling, and quadrat-sampling.
  • Applied the estimator to spotted hyena density data in Serengeti National Park.

Main Results:

  • The striplet estimator demonstrated negligible bias and excellent precision across diverse simulation scenarios.
  • Compared to existing methods, the striplet estimator significantly reduced the reported coefficient of variation for spotted hyena density (11% vs. 20% and 17%).
  • Simulations verified the substantial reduction in reported variance achieved by the new estimator.

Conclusions:

  • The striplet estimator provides a significant advancement for variance estimation in systematic spatial surveys.
  • This method enables more accurate reporting of precision for density estimates, particularly in complex ecological populations.
  • The findings support the use of the striplet estimator for more reliable wildlife density assessments.