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Related Concept Videos

Cluster Sampling Method01:20

Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
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Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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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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Variance01:15

Variance

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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the data....
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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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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.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
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On use of adaptive cluster sampling for variance estimation.

Shameem Alam1, Javid Shabbir2, Malaika Nadeem1

  • 1Department of Mathematics & Statistics, International Islamic University, Islamabad, Pakistan.

Journal of Applied Statistics
|September 10, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new adaptive cluster sampling method for estimating finite population variance. The proposed ratio-product-logarithmic estimator proved more effective than existing methods in simulations and real-world data analysis.

Keywords:
Adaptive cluster samplingauxiliary informationbiasmean square error

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Adaptive cluster sampling is effective for populations that are unevenly distributed or hard to locate.
  • Accurate estimation of finite population variance is crucial in various statistical applications.

Purpose of the Study:

  • To propose a novel ratio-product-logarithmic type estimator for finite population variance.
  • To evaluate the performance of the proposed estimator using adaptive cluster sampling.

Main Methods:

  • Developed a new estimator using a single auxiliary variable under an adaptive cluster sampling framework.
  • Assessed the bias and mean square error through simulation studies.
  • Validated the estimator's performance with real-world datasets.

Main Results:

  • The proposed ratio-product-logarithmic estimator demonstrated superior performance in estimating finite population variance.
  • The estimator's effectiveness was confirmed through both simulated and empirical data analysis.
  • Outperformed traditional competing estimators in accuracy and efficiency.

Conclusions:

  • The developed adaptive cluster sampling approach offers a more accurate method for estimating finite population variance.
  • The proposed estimator is a valuable tool for statistical inference in challenging population scenarios.
  • This research contributes to the advancement of survey sampling techniques for variance estimation.