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Stratified Sampling Method01:16

Stratified Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures 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 stratified sample, divide the population into groups called strata and then take a...
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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

One-Way ANOVA: Equal Sample Sizes

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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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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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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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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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One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

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One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
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Related Experiment Video

Updated: Aug 19, 2025

Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index
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A simulation study: Using dual ancillary variable to estimate population mean under stratified random sampling.

Sohaib Ahmad1, Sardar Hussain2, Uzma Yasmeen3

  • 1Department of Statistics Abdul Wali Khan University Mardan Pakistan.

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|November 28, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces an improved estimator for finite population mean using stratified random sampling. The new method enhances estimation precision by incorporating an ancillary variable and its rank, outperforming existing techniques.

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Accurate estimation of finite population parameters is crucial in statistical surveys.
  • Stratified random sampling is a common technique to improve precision.
  • Existing estimators may not fully leverage available ancillary information.

Purpose of the Study:

  • To propose an improved ratio-in-regression type estimator for the finite population mean.
  • To enhance estimation precision in stratified random sampling by utilizing ancillary variables and their ranks.
  • To provide a theoretical and numerical comparison with existing estimators.

Main Methods:

  • Development of a novel ratio-in-regression type estimator.
  • Derivation of bias and mean square error expressions up to the first order of approximation.
  • Empirical evaluation using two real data sets and a simulation study.

Main Results:

  • The proposed estimator demonstrates improved performance compared to existing methods.
  • The use of ancillary variables and their ranks significantly enhances estimation precision.
  • Theoretical derivations and numerical results confirm the superiority of the new estimator.

Conclusions:

  • The proposed estimator offers a more precise estimation of the finite population mean.
  • Effective utilization of ancillary information is key to improving survey estimates.
  • This work contributes a valuable tool for survey statisticians.