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Related Concept Videos

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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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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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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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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What are Estimates?01:06

What are Estimates?

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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. 
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...
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Testing a Claim about Mean: Unknown Population SD01:21

Testing a Claim about Mean: Unknown Population SD

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A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used;...
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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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Simulation-based estimation of mean and standard deviation for meta-analysis via Approximate Bayesian Computation

Deukwoo Kwon1, Isildinha M Reis2,3

  • 1Sylvester Comprehensive Cancer Center, University of Miami, Miami, FL, 33136, USA. DKwon@med.miami.edu.

BMC Medical Research Methodology
|August 13, 2015
PubMed
Summary

Approximate Bayesian Computation (ABC) offers a flexible method for estimating means and standard deviations in meta-analysis when data are skewed or heavy-tailed. This simulation-based approach improves accuracy for continuous outcomes, especially when direct statistics are unavailable.

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Area of Science:

  • Statistical methods
  • Biostatistics
  • Meta-analysis

Background:

  • Meta-analysis of continuous outcomes requires study-specific means and standard deviations.
  • These statistics are often not directly reported, necessitating estimation from other summary statistics like medians, minimums, maximums, and quartiles.

Purpose of the Study:

  • To propose and evaluate a simulation-based estimation approach using Approximate Bayesian Computation (ABC) for mean and standard deviation.
  • To compare the performance of the ABC method against existing estimation techniques (Hozo et al., Bland, Wan et al.).

Main Methods:

  • Utilized Approximate Bayesian Computation (ABC) for estimating mean and standard deviation from various summary statistics.
  • Conducted a simulation study to compare ABC with Hozo et al. (2005), Bland (2015), and Wan et al. (2014) methods.

Main Results:

  • The ABC method demonstrated superior performance in estimating standard deviation for skewed or heavy-tailed distributions, with error decreasing as sample size increased.
  • For normally distributed data, the Wan et al. method was optimal for standard deviation estimation, while ABC excelled in mean estimation across all distributions.

Conclusions:

  • Approximate Bayesian Computation (ABC) is a versatile method for estimating essential meta-analysis parameters, particularly effective for skewed or heavy-tailed data.
  • The ABC method's applicability extends to Bayesian analyses, utilizing summary statistics like posterior means and credible intervals.