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Related Concept Videos

Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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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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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:
(point estimate - error bound, point estimate +...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As 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 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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Observational Studies01:11

Observational Studies

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Observational studies are a type of analytical study where researchers observe events without any interventions. In other words, the researcher does not influence the response variable or the experiment's outcome.
There are three types of observational studies – Prospective, retrospective, and cross-sectional.
Prospective Study
Prospective studies, also known as longitudinal or cohort studies, are carried out by collecting future data from groups sharing similar characteristics. One...
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Estimating the Population Average Treatment Effect in Observational Studies with Choice-Based Sampling.

Zhiwei Zhang1, Zonghui Hu2, Chunling Liu3

  • 1Department of Statistics, University of California, Riverside, CA,USA.

The International Journal of Biostatistics
|April 17, 2019
PubMed
Summary

This study introduces novel methods for causal inference in observational studies using choice-based sampling, enhancing treatment effect estimation for uncommon therapies. The research offers practical guidance for study design, including sample size and treatment proportion selection.

Keywords:
causal inferencedouble robustnessefficient influence functionmachine learningsemiparametric theorysuper learner

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Econometrics

Background:

  • Observational studies often face challenges with treatment effect estimation, particularly when sampling is stratified by treatment choice.
  • Choice-based sampling, while common in econometrics, offers unique advantages for biomedical research, especially for rare treatments.

Purpose of the Study:

  • To develop and evaluate new methods for estimating population average treatment effects under choice-based sampling.
  • To provide robust statistical techniques applicable to biomedical and observational studies.

Main Methods:

  • Proposed doubly robust methods, grounded in semiparametric theory, for unbiased treatment effect estimation.
  • Utilized machine learning techniques to estimate nuisance functions, improving consistency and asymptotic efficiency.

Main Results:

  • Demonstrated the effectiveness of the proposed methods through simulation experiments.
  • Illustrated the practical application of these methods in a large obstetrics observational study.

Conclusions:

  • The developed methods offer a robust approach to causal inference in choice-based sampling settings.
  • Provided recommendations for optimizing the design of choice-based observational studies, including sample size and treatment allocation.