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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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Estimating Population Mean with Known Standard Deviation01:16

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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.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Estimating Population Mean with Unknown Standard Deviation01:22

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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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Distributions to Estimate Population Parameter01:26

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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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Testing a Claim about Population Proportion01:24

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A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
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Confidence Interval for Estimating Population Mean01:25

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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.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Validating Population Estimates for Harmonized Census Tract Data, 2000-2010.

John R Logan1, Brian D Stults2, Zengwang Xu3

  • 1Brown University.

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|June 20, 2017
PubMed
Summary
This summary is machine-generated.

Comparing population estimates for U.S. census tracts reveals that simple areal weighting has significant errors. More advanced methods like the Longitudinal Tract Data Base (LTDB) and NHGIS offer better accuracy for tracking small area changes over time.

Keywords:
boundariescensus datacensus tractsinterpolation

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Area of Science:

  • Demography
  • Geographic Information Science
  • Social Sciences

Background:

  • Social scientists utilize population estimates for small area analysis over time.
  • U.S. census tract boundaries change significantly between decades, complicating longitudinal studies.
  • Accurate population data is crucial for understanding demographic shifts and their impacts.

Purpose of the Study:

  • To compare alternative population estimation methods for U.S. census tracts.
  • To quantify the error associated with different interpolation techniques for census tract data.
  • To evaluate the accuracy of population estimates within harmonized tract datasets.

Main Methods:

  • Comparison of areal weighting, Longitudinal Tract Data Base (LTDB), and NHGIS population estimates against Census Bureau re-tabulations.
  • Quantification of errors in population estimation methods for U.S. census tracts.
  • Evaluation of methods considering factors like water area, ancillary data, land cover, road networks, and block-level distributions.

Main Results:

  • Simple areal weighting exhibits substantial error, particularly for tracts with complex boundary changes.
  • The LTDB and NHGIS methods demonstrate significantly improved accuracy compared to basic areal weighting.
  • Errors persist in LTDB and NHGIS when both tract and block boundaries are redrawn.

Conclusions:

  • Users of harmonized census tract data must be aware of potential inaccuracies.
  • Advanced methods like LTDB and NHGIS provide more reliable population estimates for longitudinal studies.
  • Careful consideration of data sources and their limitations is essential for accurate small area demographic research.