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Related Concept Videos

Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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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:
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Estimating Population Standard Deviation01:26

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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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Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
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Estimating Population Mean with Unknown Standard Deviation01:22

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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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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Inference about age-standardized rates with sampling errors in the denominators.

Jiming Jiang1, Eric J Feuer2, Yuanyuan Li1

  • 1Department of Statistics, University of California, Davis, Davis, CA, USA.

Statistical Methods in Medical Research
|October 16, 2020
PubMed
Summary

This study introduces a new method to accurately estimate cancer rates when denominator data has sampling errors. This improves cancer disparity analysis and statistical accuracy.

Keywords:
ApproximationPoissonbias correctioncancer ratesmortality ratessampling errorvariance estimation

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Area of Science:

  • Epidemiology
  • Biostatistics

Background:

  • Cancer incidence and mortality rates commonly use age-standardization.
  • Inference is challenging when denominators have sampling errors.

Purpose of the Study:

  • To propose a bias-corrected rate estimator and variance estimator accounting for denominator sampling errors.
  • To develop confidence intervals based on these new estimators.
  • To address limitations in current cancer rate calculations.

Main Methods:

  • Developed a bias-corrected rate estimator and its variance estimator.
  • Incorporated sampling error corrections for denominators.
  • Empirically evaluated performance via simulation studies.
  • Applied methods to a real-world cancer mortality disparity study.

Main Results:

  • The proposed estimators effectively account for sampling errors in denominators.
  • Demonstrated advantage in analyzing cancer mortality disparities.
  • A user-friendly computational tool is under development.

Conclusions:

  • The novel estimators enhance accuracy in calculating cancer rates, especially with sampling errors.
  • The methods have significant implications for cancer surveillance and disparity research.
  • Potential applications include addressing errors from differential privacy in census data.