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Related Concept Videos

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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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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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:
(point estimate - error bound, point estimate +...
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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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Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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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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One-Way ANOVA01:18

One-Way ANOVA

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One-way ANOVA analyzes more than three samples categorized by one factor. For example, it can compare the average mileage of sports bikes. Here, the data is categorized by one factor - the company. However, one-way ANOVA cannot be used to simultaneously compare the sample mean of three or more samples categorized by two factors. An example of two factors would be sports bikes from different companies driven in different terrains, such as a desert or snowy landscape. Here, two-way ANOVA is used...
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Updated: Sep 1, 2025

Meta-analysis of Voxel-Based Neuroimaging Studies using Seed-based d Mapping with Permutation of Subject Images SDM-PSI
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Meta-analysis with sample-standardization in multi-site studies.

Di Shu1,2,3, Michael Webster-Clark4, Robert W Platt4,5

  • 1Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania Perelman School of Medicine, Philadelphia, Pennsylvania, USA.

Pharmacoepidemiology and Drug Safety
|August 17, 2022
PubMed
Summary
This summary is machine-generated.

Sample-standardization offers a valid method for causal inference in multi-site studies, ensuring consistent results even with varying treatment effects across sites. This approach is reliable when the target population includes all individuals within the network.

Keywords:
distributed data networkmeta-analysismulti-site studystandardizationtarget population

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Area of Science:

  • Pharmacoepidemiology
  • Biostatistics
  • Causal Inference

Background:

  • Multi-site pharmacoepidemiologic studies require robust methods for analyzing data across diverse networks.
  • Standard meta-analytic techniques may yield inconsistent results when treatment effects vary by site.

Approach:

  • This study conceptualizes a target population and estimand for multi-site studies.
  • Sample-standardization is proposed as a meta-analytic method, estimating network-wide causal effects.
  • The sample-standardization estimator is analytically compared with inverse-variance weighted meta-analyses.

Key Points:

  • Sample-standardization provides a consistent estimator for network-wide causal treatment effects.
  • Consistency is maintained even with heterogeneity of treatment effects across sites.
  • Inverse-variance weighted meta-analyses can produce inconsistent estimators in the presence of such heterogeneity.

Conclusions:

  • Sample-standardization is a valid approach for causal inference in multi-site studies, encompassing the entire network population.
  • Clear specification of target population and estimand is crucial for selecting appropriate meta-analytic methods.