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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

7.9K
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...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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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.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
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Margin of Error01:27

Margin of Error

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The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Combined Immunofluorescence and DNA FISH on 3D-preserved Interphase Nuclei to Study Changes in 3D Nuclear Organization
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Approximate confidence intervals for the difference in proportions for partially observed binary data.

Ujjwal Das1, Ranojoy Basu2

  • 1OM, QM & IS Area, 308663IIM Udaipur, Rajasthan- 313001, India.

Statistical Methods in Medical Research
|November 29, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces an EM-algorithm for analyzing incomplete binary matched-pair data, offering improved interval estimation for proportion differences. Simulations guide method selection for reliable statistical inference in real-world applications.

Keywords:
EM algorithmPaired binary datadifference of proportionincomplete datainterval estimatormissing at random

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Partially observed binary matched-pair data presents analytical challenges.
  • Missing data is often assumed to be missing at random (MAR).

Purpose of the Study:

  • To develop an EM-algorithm based approach for interval estimation of proportion differences in MAR data.
  • To propose and evaluate methods for improving interval estimators using correction factors.
  • To provide recommendations for statistical methods based on simulation studies.

Main Methods:

  • An Expectation-Maximization (EM) algorithm was developed for interval estimation.
  • Two correction factors were introduced to enhance the proposed interval estimator.
  • Extensive simulations were conducted to evaluate method performance.
  • An R-function was created for practical implementation.

Main Results:

  • The study evaluated three competing methods through simulations.
  • Method performance was assessed based on the preservation of Type-I error rates across various sample sizes.
  • The developed methods were illustrated using two real-world datasets.

Conclusions:

  • The EM-algorithm approach effectively incorporates all subjects for proportion difference estimation.
  • Simulation results guide the selection of the most appropriate method for preserving Type-I error.
  • The R-package provides a practical tool for applying these statistical methods.