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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:
(point estimate - error bound, point estimate +...
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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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Standard Error of the Mean01:13

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The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.
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Regression Toward the Mean01:52

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Testing a Claim about Mean: Unknown Population SD01:21

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A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used;...
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Testing a Claim about Standard Deviation01:19

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A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
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Estimating the standardized mean difference with minimum risk: Maximizing accuracy and minimizing cost with

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Summary

This study introduces a purely sequential sampling procedure to accurately estimate the standardized mean difference while minimizing sampling costs. This method optimizes sample size estimation for research efficiency.

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • The standardized mean difference is a crucial effect size measure in statistical analysis.
  • Fixed sample size methods often fail to balance estimator accuracy and sampling costs effectively.

Purpose of the Study:

  • To develop a general theory for estimating population standardized mean difference.
  • To minimize both mean square error and total sampling cost simultaneously.
  • To introduce a purely sequential sampling procedure for optimal sample size estimation.

Main Methods:

  • Development of a general theory for standardized mean difference estimation.
  • Introduction of a purely sequential sampling procedure.
  • Validation through a simulation study and provision of R functions.

Main Results:

  • The purely sequential procedure effectively estimates sample size for accurate results with minimal cost.
  • Analytic developments demonstrate high accuracy in performance.
  • Freely available R functions facilitate the implementation of the proposed algorithm.

Conclusions:

  • The purely sequential sampling procedure offers a superior alternative to fixed sample size methods.
  • This approach enhances research efficiency by optimizing sample size and cost.
  • The provided R functions will aid researchers in applying this advanced statistical technique.