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Related Concept Videos

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.
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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.
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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: 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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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.
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Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and...
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Improved exponential type mean estimators for non-response case using two concomitant variables in simple random

Mujeeb Hussain1, Qamruz Zaman1, Lakhkar Khan2

  • 1Department of Statistics, University of Peshawar, Peshawar, Pakistan.

Heliyon
|March 27, 2024
PubMed
Summary
This summary is machine-generated.

New exponential estimators improve population mean estimation when data is missing on study and concomitant variables. These novel estimators demonstrate superior efficiency compared to existing methods in statistical sampling.

Keywords:
Concomitant variableExponentialMean square errorNon-response

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Non-response is a common challenge in surveys, affecting both study variables and auxiliary information.
  • Accurate estimation of population mean is crucial for reliable statistical inference.

Purpose of the Study:

  • To develop and evaluate new exponential estimators for population mean in the presence of non-response.
  • To assess the efficiency of these new estimators against existing methods.

Main Methods:

  • Utilizing simple random sampling techniques.
  • Deriving theoretical bias and mean square error expressions for new estimators.
  • Performing numerical comparisons using real-life datasets.

Main Results:

  • The proposed exponential estimators show improved efficiency over classical unbiased estimators and other existing methods.
  • Numerical analyses confirm the superior performance based on bias, mean square error, and percent relative efficiency.

Conclusions:

  • The developed exponential estimators are effective in handling non-response in both study and concomitant variables.
  • These new estimators offer a more accurate and efficient approach to population mean estimation in complex survey situations.