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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...
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...
Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
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 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 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...

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Related Experiment Video

Updated: Jun 3, 2026

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

Calculation of prediction error variances using sparse matrix methods.

R Thompson1, N R Wray, R E Crump

  • 1AFRC Roslin Institute (Edinburgh), Roslin, Scotland Scottish Agricultural College, Genetics and Behavioural Science, Bush Estate, Penicuik, Scotland Victorian Institute of Animal Science, Australia.

Journal of Animal Breeding and Genetics = Zeitschrift Fur Tierzuchtung Und Zuchtungsbiologie
|March 15, 2011
PubMed
Summary
This summary is machine-generated.

This study demonstrates algorithms for calculating prediction error variances in animal breeding, including maternal effects. An approximation significantly speeds up computation while maintaining reliable results for national beef evaluations.

Related Experiment Videos

Last Updated: Jun 3, 2026

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

Area of Science:

  • Animal breeding and genetics
  • Quantitative genetics
  • Statistical genetics

Background:

  • Accurate prediction of genetic merit is crucial for animal breeding programs.
  • Calculating prediction error variances (PEVs) is computationally intensive.
  • Sparse matrix methods offer efficient solutions for large-scale genetic evaluations.

Purpose of the Study:

  • To demonstrate exact and approximate algorithms for calculating PEVs using sparse matrix methods.
  • To evaluate the computational efficiency and reliability of different algorithms.
  • To assess the applicability of these methods in national genetic evaluation systems.

Main Methods:

  • Implementation of exact algorithms for PEV calculation.
  • Development and testing of an approximate algorithm based on the best exact method.
  • Utilizing sparse matrix techniques for computational efficiency.
  • Comparison of computational speed and reliability across algorithms.

Main Results:

  • One exact algorithm significantly outperformed two others in speed.
  • An approximation of the best exact method reduced computation by approximately 50-fold.
  • The approximate method provided acceptable reliability for genetic evaluations.
  • The approximate method is currently used in British national beef evaluations.

Conclusions:

  • Efficient algorithms for PEV calculation are essential for large-scale genetic evaluations.
  • Approximate algorithms can substantially reduce computational burden without compromising reliability.
  • The demonstrated approximate method is a practical tool for national beef genetic evaluation.