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Related Concept Videos

Stratified Sampling Method01:16

Stratified Sampling Method

Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures 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 stratified sample, divide the population into groups called strata and then take a...
Average Value on a Rectangle01:27

Average Value on a Rectangle

A snowfall map can represent how snow depth varies across a region, such as Colorado, over a fixed time period. Since different locations may receive different amounts of snow, the snowfall depth is described by a function of two variables. If f(x,y) represents the snow depth at a point in a rectangular region, then the average snowfall over the entire region is found by comparing the total accumulated snowfall with the area being measured.Total Snowfall over a RegionThe total snowfall over a...
Weighted Mean00:57

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
What are Estimates?01:06

What are Estimates?

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 as the mean,...
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...
Sampling Plans01:23

Sampling Plans

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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Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
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Estimating a weighted average of stratum-specific parameters.

Babette A Brumback1, Larry H Winner, George Casella

  • 1Department of Epidemiology and Biostatistics, University of Florida, Gainesville, FL 32611, USA. bbrumback@phhp.ufl.edu

Statistics in Medicine
|June 24, 2008
PubMed
Summary

This study introduces new adaptive estimators for weighted averages of survey data, outperforming standard methods by minimizing mean-squared error (MSE). The research focuses on Florida Medicaid beneficiaries, improving estimates for health plan satisfaction.

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Area of Science:

  • Statistics
  • Survey Methodology
  • Health Services Research

Background:

  • Estimating population parameters from stratified survey samples is crucial for policy-relevant research.
  • Florida Medicaid beneficiaries data provides a real-world context for evaluating statistical methods.
  • Weighted averages are essential for combining stratum-specific estimates in complex surveys.

Purpose of the Study:

  • To investigate and compare estimators for a weighted average of stratum-specific parameters using design-based mean-squared error (MSE).
  • To propose adaptive estimators motivated by random effects models and evaluate their performance.
  • To apply these methods to estimate satisfaction among Florida Medicaid beneficiaries.

Main Methods:

  • Comparison of estimators based on design-based MSE.
  • Development of adaptive estimators using random effects models.
  • Selection of tuning parameters to minimize design-based MSE, differing from model-based approaches.
  • Comparison of standard random effects models with a novel model where parameter variances are inversely proportional to weights.

Main Results:

  • The proposed design-based approach downweights strata with small weights, potentially reducing MSE.
  • A novel random effects model demonstrated effectiveness.
  • Theoretical and computational details for a general class of random effects models were provided.

Conclusions:

  • The study offers improved methods for estimating weighted averages in stratified surveys.
  • The findings are applicable to understanding beneficiary satisfaction in healthcare systems.
  • The design-based MSE minimization offers a practical advantage for real-world survey applications.