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Standard Error of the Mean01:13

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The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.
The standard error of the mean is an example of a standard error. It is a unique standard deviation known as the standard deviation of the sampling distribution of the mean. The standard error of the mean is a statistic that calculates how correctly a sample distribution represents a...
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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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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
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Estimating Population Mean with Unknown Standard Deviation01:22

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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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A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
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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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Methods for estimating the sampling variance of the standardized mean difference.

Manuel Suero1, Juan Botella1, Juan I Durán2

  • 1Facultad de Psicologia, Department of Social Psychology and Methodology, Universidad Autonoma de Madrid.

Psychological Methods
|December 16, 2021
PubMed
Summary
This summary is machine-generated.

Estimating sampling variances for standardized mean difference (SMD) in meta-analysis significantly impacts results. Different methods yield varied outcomes, particularly in random-effects models, necessitating careful selection for accurate synthesis.

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Area of Science:

  • Psychology
  • Statistical Methods

Background:

  • Standardized mean difference (SMD) is a key effect size in psychological meta-analysis.
  • Synthesizing SMD estimates typically involves inverse variance weighting.
  • Accurate estimation of sampling variances is crucial for reliable meta-analysis.

Purpose of the Study:

  • To compare the bias and efficiency of five different methods for estimating sampling variances of SMD.
  • To assess the sensitivity of meta-analysis results to the chosen variance estimation method.
  • To provide practical recommendations for method selection in meta-analysis software.

Main Methods:

  • Comparison of five distinct methods for estimating sampling variances of SMD.
  • Reanalysis of data from published meta-analyses using these five methods.
  • Assessment of combined estimates, confidence intervals, and between-studies variance.

Main Results:

  • Meta-analysis outcomes, especially under random-effects models, are sensitive to the method used for estimating sampling variances of SMD.
  • Different methods can lead to noticeable changes in combined estimates and confidence intervals.
  • The choice of method impacts the estimation of between-studies variance.

Conclusions:

  • The method for estimating sampling variances of SMD is a critical decision in meta-analysis.
  • Results can vary significantly based on the chosen estimation technique.
  • Recommendations are provided for selecting and implementing appropriate methods in statistical software.