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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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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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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.
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Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible

Shi-Fang Qiu1, Xiao-Song Zeng1, Man-Lai Tang2

  • 11 Department of Statistics, Chongqing University of Technology, Chongqing, China.

Statistical Methods in Medical Research
|December 14, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces new statistical methods for situations where no perfect classifier exists. It offers recommended procedures and sample size formulas for accurate population proportion estimation with two fallible classifiers.

Keywords:
Approximate unconditional methoddouble-sampling schemeimperfect gold standardsample size determinationscore test

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiological Methods

Background:

  • Double sampling typically relies on an infallible classifier for validation.
  • Existing inference procedures are based on partially validated data.
  • A practical challenge arises when a gold standard or infallible classifier is unavailable.

Purpose of the Study:

  • To develop statistical inference procedures for situations with two fallible classifiers.
  • To propose asymptotic and approximate unconditional test procedures for population proportion.
  • To derive approximate sample size formulas for practical applications.

Main Methods:

  • Proposed asymptotic and approximate unconditional test procedures.
  • Utilized six test statistics for population proportion estimation.
  • Developed five approximate sample size formulas under two models.
  • Evaluated performance across various sample sizes and models.

Main Results:

  • Score statistic-based procedures (asymptotic and approximate) perform well across all sample sizes.
  • Wald, likelihood rate, log-, and logit-transformation statistics perform well for moderate to large sample sizes.
  • Specific approximate procedures are recommended for small sample sizes under different models.
  • Sample size formulas based on Wald, likelihood rate, and score statistics are generally recommended.

Conclusions:

  • The proposed methods provide robust statistical inference when infallible classifiers are absent.
  • The score statistic offers reliable performance for population proportion estimation.
  • Recommended procedures and sample size formulas enhance practical applicability in research settings.