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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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Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
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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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Polygenic Traits01:18

Polygenic Traits

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When more than one gene is responsible for a given phenotype, the trait is considered polygenic. Human height is a polygenic trait. Studies have uncovered hundreds of loci that influence height, and there are believed to be many more. Due to the high number of genes involved, as well as environmental and nutritional factors, height varies significantly within a given population. The distribution of height forms a bell-shaped curve, with relatively few individuals in the population at the...
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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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Estimating Population Mean with Known Standard Deviation01:16

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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:
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Updated: Jul 9, 2025

Infinium Assay for Large-scale SNP Genotyping Applications
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统计推论与大规模的特征归因.

Jingchen Ren1,2, Wei Pan2

  • 1School of Statistics, University of Minnesota, Minneapolis, Minnesota, USA.

Statistics in medicine
|December 1, 2023
PubMed
概括
此摘要是机器生成的。

一种新的方法通过计算归算值之间的相关性来改善大规模的特征归算,放松了以前的错误假设. 虽然原来的方法表现良好,但新的方法在遗传分析中提供了潜在的改进.

关键词:
在GWAS中,GWAS就是GWAS.这就是LS-imputation.在SNP中,SNP是SNP.最小平方的最小平方.线性模型是一种线性模型.

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Large-Scale Multi-Omics Genome-Wide Association Studies Mo-GWAS: Guidelines for Sample Preparation and Normalization
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科学领域:

  • 遗传学 是一个遗传学.
  • 统计遗传学 统计遗传学
  • 生物信息学是一种生物信息学.

背景情况:

  • 使用全基因组协会研究 (GWAS) 总结数据和基因型个体的大规模特征归因对于下游遗传分析至关重要.
  • 现有的LS归算方法假定特征值是独立的,这是可能影响准确性的简化.
  • 由于数据集庞大,计算归算特征值的完整共变矩阵在计算上具有挑战性.

研究的目的:

  • 开发一种在大规模遗传分析中计算特征值的协差矩阵的方法.
  • 放松假定属性值之间的独立性假设,从而提高下游分析的准确性.
  • 增强GWAS总结数据对个体级遗传研究的有用性.

主要方法:

  • 提出了一种"划分和征服/结合"的策略,以估计和纳入指定的特征值的协变矩阵.
  • 实现批处理,以管理共变矩阵估计的计算复杂性.
  • 将修订后的归算方法应用于英国生物银行数据进行边际关联分析.

主要成果:

  • 这种新方法在边际关联分析中显示了一些改进,与最初的LS-归算方法相比,在特定情况下.
  • 原始的LS归算方法表现出强的性能,归因于测试数据集中归算值之间的近常差和弱相关性.
  • 这些发现表明,虽然独立性假设在技术上是不正确的,但其影响可能在具有特定协差结构的数据集中是有限的.

结论:

  • 拟议的"分裂与征服/结合"策略提供了一种解释归算特征值共变量的方法,解决了以前方法的局限性.
  • 新方法的实际好处可能因特征和数据集的特征而异.
  • 进一步的研究是有必要的,以探索在不同的遗传数据集和特征中改进的归算方法的性能.