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Related Concept Videos

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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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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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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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:
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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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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Estimating Population Standard Deviation01:26

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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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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Robust estimation of marginal regression parameters in clustered data.

Somnath Datta1, James D Beck2

  • 1University of Louisville, Louisville, KY 40202, USA.

Statistical Modelling
|April 8, 2015
PubMed
Summary

We developed new methods for analyzing clustered data, improving regression parameter estimation by accounting for cluster size. This approach enhances statistical accuracy for complex datasets.

Keywords:
Informative cluster sizeR estimatordental datarandom cluster size

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Analyzing clustered data presents challenges, particularly when cluster size influences outcomes.
  • Accurate estimation of marginal regression parameters is crucial in many scientific fields.

Purpose of the Study:

  • To develop robust statistical methods for analyzing clustered data.
  • To address the issue of informative cluster sizes in regression analysis.
  • To provide reliable inference and variance estimation for clustered data.

Main Methods:

  • Incorporation of inverse cluster size reweighting into the objective function.
  • Development of estimators robust to informative cluster sizes.
  • Simulation studies to evaluate estimator performance.
  • Large sample inference and variance estimation techniques.

Main Results:

  • The proposed methods demonstrate robustness in analyzing clustered data.
  • Inverse cluster size reweighting effectively handles informative cluster sizes.
  • Simulation results validate the performance of the developed estimators.

Conclusions:

  • The developed methodology offers a robust approach for marginal regression analysis with clustered data.
  • The methods are applicable to various fields, including public health and epidemiology.
  • The study provides a practical illustration using a periodontal disease dataset.