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Related Concept Videos

Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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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...
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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.
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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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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...
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Small population sizes put a species at extreme risk of extinction due to a lack of variation, and a consequent decrease in adaptability. This weakens the chances of survival under pressures such as climate change, competition from other species, or new diseases. Large populations are more likely to survive pressures such as these, as such populations are more likely to harbor individuals that have genetic variants that are adaptive under new stresses. Small populations are much less...
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Topographical Estimation of Visual Population Receptive Fields by fMRI
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Simplified procedure for efficient and unbiased population size estimation.

Marcos Cruz1, Javier González-Villa1

  • 1Department of Mathematics, Statistics and Computer Science, Univ. of Cantabria, Av. Los Castros 48, E-39005 Santander, Spain.

Plos One
|October 30, 2018
PubMed
Summary

This study introduces a simpler way to use the CountEm method for population size estimation. It refines grid parameters for faster, unbiased counting in ecological and social science applications.

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Area of Science:

  • Ecological sciences
  • Social sciences
  • Computational biology

Background:

  • Accurate population size estimation is crucial for ecological and social sciences.
  • Existing methods like manual counting, density estimation, and computer vision often lack speed, efficiency, or unbiasedness.
  • The CountEm method offers an unbiased approach using systematic sampling but requires complex parameter selection.

Purpose of the Study:

  • To simplify parameter selection for the CountEm population estimation method.
  • To analyze the impact of grid parameter choices on estimation error.
  • To provide a user-friendly procedure for selecting optimal parameters.

Main Methods:

  • Developed an intuitive grid parametrization for CountEm using initial quadrats and sampling fraction.
  • Utilized a crowd counting dataset with 51 images and annotated point patterns.
  • Performed Monte Carlo resampling to assess error variation with different parameter choices.

Main Results:

  • Estimation error is influenced by sample size and the number of occupied quadrats, not population size.
  • The refined parametrization provides a more intuitive approach to grid selection.
  • Specific parameter choices can achieve low coefficients of error (e.g., <10% with ~100 particles in 30 quadrats).

Conclusions:

  • The simplified CountEm parametrization enhances usability for population size estimation.
  • The method offers a fast, efficient, and unbiased estimation applicable across various populations.
  • Provides guidance for selecting parameters to achieve desired accuracy in ecological and social studies.