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Related Concept Videos

F Distribution01:19

F Distribution

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The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of freedom; one for the numerator and one for the denominator. The F distribution is derived from the Student's t distribution. The values of the F distribution are squares of the corresponding values of the t distribution. One-Way ANOVA expands the t test for comparing more than two groups. The scope of that derivation is beyond the level of this...
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Test for Homogeneity01:23

Test for Homogeneity

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The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

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One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
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Identifying Statistically Significant Differences: The F-Test01:14

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The F-test is used to compare two sample variances to each other or compare the sample variance to the population variance. It is used to decide whether an indeterminate error can explain the difference in their values. The underlying assumptions that allow the use of the F-test include the data set or sets are normally distributed, and the data sets are independent of each other. The test statistic F is calculated by dividing one variance by another. In other words, the square of one standard...
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One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

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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.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
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Admixture, Population Structure, and F-Statistics.

Benjamin M Peter1

  • 1Department of Human Genetics, University of Chicago, Chicago, Illinois 60637 bpeter@uchicago.edu.

Genetics
|February 10, 2016
PubMed
Summary
This summary is machine-generated.

F-statistics offer insights into human genetic history by analyzing shared genetic variation. New interpretations using coalescent theory simplify estimators and improve population divergence analysis.

Keywords:
admixturegene flowphylogenetic networkphylogeneticspopulation genetics

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Area of Science:

  • Population Genetics
  • Human Evolutionary Studies
  • Bioinformatics

Background:

  • Examining shared genetic variation between populations is key to understanding human genetic history.
  • F-statistics provide a framework for measuring shared genetic drift and testing admixture hypotheses.

Purpose of the Study:

  • To provide theoretical context for F-statistics using phylogenetic and population genetic theory.
  • To derive new interpretations of F-statistics using coalescent theory and explore their application to phylogenies.
  • To investigate the impact of population substructure on F-statistic inference and develop simplified estimators.

Main Methods:

  • Reviewing F-statistics within phylogenetic and population genetic theory.
  • Applying coalescent theory to derive new interpretations of F-statistics as branch lengths or paths.
  • Analyzing the behavior of F-statistics under various population structure models.

Main Results:

  • F-statistics and admixture tests can be interpreted through general properties of phylogenetic trees.
  • Population substructure significantly complicates F-statistic inference.
  • Simplified estimators are proposed, recommending the average number of pairwise differences over F3 for population divergence.

Conclusions:

  • New theoretical interpretations enhance the utility of F-statistics in population genetics.
  • Understanding population substructure is crucial for accurate genetic history inference.
  • The average number of pairwise differences is a more robust estimator for population divergence than F3.