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Related Concept Videos

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...
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...
Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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 + error bound)
The...
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
Variability: Analysis01:11

Variability: Analysis

Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...

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Related Experiment Video

Updated: May 24, 2026

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index
06:55

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index

Published on: January 8, 2020

Variance estimation for stratified propensity score estimators.

E J Williamson1, R Morley, A Lucas

  • 1Centre for MEGA Epidemiology, School of Population Health, University of Melbourne, Melbourne, Australia. ewi@unimelb.edu.au

Statistics in Medicine
|February 25, 2012
PubMed
Summary
This summary is machine-generated.

Propensity score methods like stratification and inverse-probability weighting are common in non-randomized studies. Standard variance estimators for these methods can yield overly conservative confidence intervals, suggesting bootstrap variance estimation for more accurate results.

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Last Updated: May 24, 2026

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Statistical Modeling

Background:

  • Propensity score methods are vital for estimating treatment effects in observational studies.
  • Common methods include stratification and inverse-probability weighting (IPW).
  • Accurate variance estimation is crucial for reliable confidence intervals.

Purpose of the Study:

  • To evaluate the accuracy of standard variance estimators used with propensity score stratification and IPW.
  • To derive correct asymptotic marginal variances for these methods.
  • To provide practical recommendations for variance estimation in propensity score analysis.

Main Methods:

  • Derivation of asymptotic marginal variance for propensity score stratification.
  • Comparison with the asymptotic marginal variance for IPW.
  • Analysis of routinely used variance estimators in practice.

Main Results:

  • Routinely used variance estimators for propensity score stratification can be overly conservative, especially when outcome predictors weakly influence treatment.
  • Variance estimators for IPW are consistently too conservative.
  • Accurate calculation of asymptotic marginal variance can be complex.

Conclusions:

  • Standard variance estimators in propensity score analysis may lead to misleadingly wide confidence intervals.
  • Bootstrap variance estimation is recommended for practical application due to complexity and potential inaccuracy of analytical methods.
  • Improved variance estimation enhances the reliability of treatment effect estimates from observational studies.