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Related Concept Videos

Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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 + error bound)
The...
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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 Guinness...
Variation01:19

Variation

An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...
Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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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Related Experiment Video

Updated: Jun 26, 2026

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
06:33

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

Published on: October 11, 2018

Reliable computing in estimation of variance components.

I Misztal1

  • 1University of Georgia, Athens, GA 30602, USA. ignacy@uga.edu

Journal of Animal Breeding and Genetics = Zeitschrift Fur Tierzuchtung Und Zuchtungsbiologie
|January 13, 2009
PubMed
Summary
This summary is machine-generated.

Selecting statistical algorithms for variance components estimation requires careful consideration. Residual maximal likelihood (REML) and Bayesian methods via Gibbs sampling offer different strengths and weaknesses depending on model complexity and data size.

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Area of Science:

  • Quantitative genetics
  • Statistical genetics
  • Computational biology

Background:

  • Variance components estimation is crucial for genetic analyses.
  • Software packages are widely used for these computations.
  • Algorithm selection impacts accuracy and efficiency.

Purpose of the Study:

  • Provide guidelines for choosing statistical and computing algorithms for variance components estimation.
  • Compare Residual Maximal Likelihood (REML) and Bayesian via Gibbs sampling methods.
  • Illustrate method selection with real-world research examples.

Main Methods:

  • Expectation-Maximization (EM) REML: stable but slow, potential convergence issues.
  • Average Information (AI) REML: faster but relies on heuristics, can diverge.
  • Bayesian via Gibbs sampling: easier programming for complex models, large datasets; termination criteria can be challenging.

Main Results:

  • REML algorithms can be unstable with multiple traits; canonical transformation REML offers stability for limited models.
  • Bayesian methods are more scalable for large datasets and complex models.
  • No single algorithm is universally optimal; method choice is problem-dependent.

Conclusions:

  • The optimal algorithm for variance components estimation depends on specific research needs, model complexity, and dataset size.
  • Understanding the trade-offs between REML and Bayesian approaches is essential for accurate genetic parameter estimation.
  • Careful algorithm selection ensures robust and reliable results in quantitative genetic studies.