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相关概念视频

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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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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Sample Size Calculation01:19

Sample Size Calculation

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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
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Bonferroni Test01:10

Bonferroni Test

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The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
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Introduction to Test of Independence01:21

Introduction to Test of Independence

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In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
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Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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在贝叶斯信息标准中的有效样本大小,用于在两级嵌套模型中对特定水平的固定和随机效应的选择.

Sun-Joo Cho1, Hao Wu1, Matthew Naveiras2

  • 1Vanderbilt University, Nashville, Tennessee, USA.

The British journal of mathematical and statistical psychology
|April 9, 2024
PubMed
概括

新贝叶斯信息标准 (BIC) 公式用于多层模型,解决现有方法的差异. 这些增强的BIC标准为复杂的层次数据结构提供了优越的模型选择.

关键词:
贝叶斯信息标准是贝叶斯信息标准.特定水平的固定效应.线性混合模型 线性混合模型这是一个混合模型混合模型.模型选择,模型选择.多层次模型的多层次模型.随机效应是一种随机效应.

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科学领域:

  • 统计 统计 统计 统计
  • 多层次建模多层次建模
  • 计量经济学 计量经济学

背景情况:

  • 现有的贝叶斯信息标准 (BIC) 在多层模型的统计软件中的实现不一致.
  • 差异源于多级模型的BIC惩罚术语中样本大小规范的变化.
  • 对于正确应用BIC来选择具有特定水平固定和随机效应的模型存在不确定性.

研究的目的:

  • 在双层嵌套多层模型中选择固定和随机效应的准确BIC惩罚条款.
  • 提出新的BIC版本,标记为BIC_A和BIC_B,分别解决全等级和冗余随机效应.
  • 评估新的BIC标准的性能与现有的多层次模型选择方法相比.

主要方法:

  • 在两级嵌套设计中,针对特定级别的固定和随机效应的BIC惩罚条款的导出.
  • 对BIC_A.的惩罚项分解为集群级和参数级组件.
  • 对于具有冗余随机效应的场景,BIC_B的导出.
  • 数字和模拟研究以验证衍生式和比较性能.

主要成果:

  • 对BIC_A和BIC_B的公式被推导出,并根据经验值进行验证.
  • BIC_A将罚款分解为每个集群的平均样本大小和总参数乘以集群的数量.
  • 模拟研究表明,新的BIC标准 (BIC_A或BIC_B) 优于使用总样本大小或集群数量的标准BIC版本.
  • 拟议的BIC标准在各种多层次条件下至少与现有方法一样有效.

结论:

  • 衍生的BIC公式 (BIC_A和BIC_B) 为多级模型选择提供了更准确和可靠的方法.
  • 新的BIC标准被推为复杂的层次数据的优越全球选择标准.
  • 使用教科书中的示例数据集来说明新的BIC的实际应用.