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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.
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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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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. 
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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.
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Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis.

Sean McGrath1, XiaoFei Zhao1, Russell Steele2

  • 1Respiratory Epidemiology and Clinical Research Unit (RECRU), McGill University Health Centre, Montreal, Quebec, Canada.

Statistical Methods in Medical Research
|April 16, 2020
PubMed
Summary
This summary is machine-generated.

New methods improve meta-analysis for skewed data by estimating the mean and standard deviation from medians. These novel approaches enhance data synthesis when standard assumptions are unmet.

Keywords:
Meta-analysisfirst quartilemaximum valuemedianminimum valuethird quartile

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Area of Science:

  • Biostatistics
  • Medical Research Methodology

Background:

  • Meta-analysis synthesizes study results to estimate common effects.
  • Standard meta-analysis assumes normally distributed continuous outcomes with reported means and standard deviations.
  • Studies with skewed data may report medians and quartiles/ranges instead of means, hindering meta-analysis inclusion.

Purpose of the Study:

  • To develop and evaluate novel methods for estimating sample mean and standard deviation from summary data in skewed distributions.
  • To improve the inclusion of studies with non-normally distributed outcomes in meta-analyses.

Main Methods:

  • Proposed two novel statistical approaches to estimate mean and standard deviation from medians, quartiles, and ranges.
  • Conducted simulation studies and empirical assessments to compare proposed methods with existing ones.

Main Results:

  • Existing methods for estimating mean and standard deviation from summary data often assume normal distributions.
  • The proposed methods demonstrated superior performance compared to existing methods when applied to non-normal data.
  • Simulation and empirical results support the utility of the novel approaches for skewed outcome variables.

Conclusions:

  • The developed methods offer a valuable alternative for meta-analysis when dealing with skewed continuous outcomes.
  • These novel approaches enhance the ability to synthesize evidence from studies reporting medians, improving research synthesis.
  • Researchers can more effectively include studies with non-normally distributed data in their meta-analyses.