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Related Concept Videos

Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Cluster Sampling Method01:20

Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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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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What are Estimates?01:06

What are Estimates?

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such...
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One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

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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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Small area mean estimation after effect clustering.

Zhihuang Yang1, Jiahua Chen1,2

  • 1School of Mathematics and Statistics, Yunnan University, Kunming, People's Republic of China.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces advanced small area estimation methods using a novel nested error regression model with multiple centers. These new techniques improve parameter estimation accuracy and confidence interval coverage for policymakers.

Keywords:
62D05Nested error regression modelseparation penaltysmall area clustersmall area estimation

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Area of Science:

  • Statistics
  • Econometrics
  • Survey Methodology

Background:

  • Reliable subpopulation/area parameter estimation is crucial for policymaking.
  • Traditional indirect small area estimation methods often assume a single model structure for all areas.
  • Existing methods may not adequately capture heterogeneity in auxiliary variable effects across different small areas.

Purpose of the Study:

  • To extend the nested error regression model to accommodate auxiliary variables with multiple centers.
  • To develop new small area mean estimators and their mean square error estimators.
  • To evaluate the efficiency and accuracy of the proposed methods.

Main Methods:

  • An extended nested error regression model with mixed effects and multiple centers was examined.
  • A penalty approach was utilized for simultaneous identification of centers and parameter estimation.
  • Two novel small area mean estimators and their mean square error estimators were constructed.

Main Results:

  • Simulations demonstrated that the new estimators are efficient for both artificial and realistic populations.
  • The proposed methods yield confidence intervals with accurate coverage probabilities.
  • The methods were successfully applied to the Survey of Labour and Income Dynamics in Canada.

Conclusions:

  • The extended nested error regression model with multiple centers offers a more flexible and accurate approach to small area estimation.
  • The developed estimators provide reliable estimates and accurate confidence intervals, outperforming existing methods in certain scenarios.
  • The practical application highlights the utility of these methods for real-world data analysis and policy support.