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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.
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Updated: Sep 8, 2025

Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index
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Simulating the Overall Hospital Quality Star Ratings With Random Measure Weights.

Benjamin D Pollock1, Daniel S Ubl2, Subashnie Devkaran2,3

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Summary
This summary is machine-generated.

Few US hospitals achieve consistently excellent care. A study of 2700 hospitals found only 9% were reliably excellent, highlighting the need for better quality measurement beyond current ratings.

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Area of Science:

  • Health Services Research
  • Quality Improvement
  • Hospital Performance Measurement

Background:

  • Existing hospital ratings like US News & World Report and Centers for Medicare & Medicaid Services (CMS) Overall Hospital Quality Star Ratings measure different outcomes and show weak correlation.
  • There is a need for methods to define and measure reliable excellence, defined as consistent high performance across all quality metrics.

Purpose of the Study:

  • To assess a novel measure of reliable excellence using the 45 quality measures from the CMS Overall Star Ratings.
  • To determine the proportion of US hospitals that demonstrate consistently great performance across all quality measures.

Main Methods:

  • A cross-sectional study analyzed 2023 and 2024 CMS Overall Star Rating data for all US hospitals.
  • 100,000 simulations were performed, randomly weighting the 45 quality measures to calculate each hospital's summary score.
  • Reliable excellence was defined as achieving a 90th percentile score in at least 50,000 simulations.

Main Results:

  • Out of 2700 hospitals, only 244 (9.0%) met the definition of reliable excellence.
  • Less than two-thirds of hospitals with a 5-star CMS rating achieved reliable excellence.
  • While 47.7% of hospitals achieved excellence in at least one simulation, consistent high performance was rare.

Conclusions:

  • A small proportion of US hospitals demonstrate reliably excellent performance across all quality measures.
  • Current hospital rating systems may not fully capture consistent high-quality care.
  • The findings underscore the need for improved methodologies to identify hospitals providing consistently excellent care.