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Related Concept Videos

Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

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A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
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One-Way ANOVA: Equal Sample Sizes01:15

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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.
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Sample Proportion and Population Proportion01:20

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Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the...
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What are Estimates?01:06

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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One-Way ANOVA: Unequal Sample Sizes01:15

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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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Confidence Intervals

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
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Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
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Inferences on Small Area Proportions.

Shijie Chen1, P Lahiri2

  • 1Bristol-Myers Squibb, 311 Pennington-Rocky Hill Road, Pennington, NJ 08534, USA.

Journal of the Indian Society of Agricultural Statistics. Indian Society of Agricultural Statistics
|January 24, 2014
PubMed
Summary
This summary is machine-generated.

Hierarchical Bayes methods offer an efficient alternative to traditional design-based approaches for estimating rare event proportions in small areas. This study presents a novel hierarchical model and methodology, ensuring reliable parameter estimations.

Keywords:
Credible intervalMCMCRare event

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Area of Science:

  • Statistics
  • Small Area Estimation
  • Bayesian Inference

Background:

  • Traditional design-based methods struggle with efficiency for small area proportion estimation, especially for rare events.
  • Accurate statistical inference in small areas with limited data is a persistent challenge.

Purpose of the Study:

  • To introduce an alternative hierarchical model and hierarchical Bayes methodology for small area proportion estimation.
  • To address the inefficiencies of design-based methods in scenarios involving rare events.

Main Methods:

  • Development of a hierarchical model tailored for small area statistics.
  • Application of hierarchical Bayes methodology for parameter inference.
  • Presentation of sufficient conditions for the propriety of posterior distributions.

Main Results:

  • The proposed hierarchical Bayes approach demonstrates improved efficiency for small area proportion estimation of rare events.
  • The methodology provides a robust framework for statistical inference in challenging small area contexts.

Conclusions:

  • Hierarchical Bayes methodology offers a powerful and efficient alternative for small area estimation of rare events.
  • The presented model and conditions for posterior propriety contribute to advancing statistical inference techniques.