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Related Concept Videos

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 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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Sample Size Calculation01:19

Sample Size Calculation

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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
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Estimating Population Standard Deviation01:26

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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

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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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Estimating the sample mean and standard deviation from order statistics and sample size in meta-analysis.

Siyu Cai1, Jie Zhou1,2, Jianxin Pan3

  • 1College of Mathematics, 12530Sichuan University, Chengdu, Sichuan, China.

Statistical Methods in Medical Research
|October 20, 2021
PubMed
Summary

Researchers developed new meta-analysis methods to accurately estimate treatment effects using medians and quartiles when standard deviations are unavailable. These novel techniques improve estimation accuracy for skewed data in medical studies.

Keywords:
Meta-analysismaximum likelihood estimationorder statisticsample meansample standard deviation

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Area of Science:

  • Medical Statistics
  • Biostatistics
  • Quantitative Research Methods

Background:

  • Meta-analysis is crucial for synthesizing evidence but often lacks necessary data like means and standard deviations.
  • Skewed outcomes in medical studies frequently result in reporting medians, quartiles, and extrema instead of means and standard deviations.
  • Existing meta-analytic methods struggle with non-normally distributed data, limiting the synthesis of results.

Purpose of the Study:

  • To propose novel statistical methods for meta-analysis that can utilize reported order statistics (median, quartiles, extrema).
  • To enable consistent estimation of overall treatment effects even when standard deviations are not available.
  • To enhance the accuracy and applicability of meta-analysis for skewed continuous outcomes.

Main Methods:

  • Developed maximum likelihood estimation (MLE) methods for known distributions with unknown parameters.
  • Applied the Box-Cox transformation to convert reported order statistics for unknown underlying distributions.
  • Proposed two distinct approaches for estimating the power parameter within the Box-Cox transformation.

Main Results:

  • Simulation studies demonstrated superior estimation accuracy of the proposed methods compared to existing techniques.
  • Real data analysis confirmed the practical effectiveness and improved accuracy of the new methods.
  • The methods successfully convert order statistics, allowing for the use of standard meta-analytic techniques.

Conclusions:

  • The proposed MLE and Box-Cox transformation-based methods offer a robust solution for meta-analysis with skewed data.
  • These techniques significantly improve estimation accuracy, overcoming limitations of traditional meta-analytic approaches.
  • The findings enhance the ability to conduct comprehensive and accurate medical research synthesis.