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Estimating Population Standard Deviation

Estimating Population Standard Deviation

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...

Estimating Population Mean with Known Standard Deviation

Estimating Population Mean with Known Standard Deviation

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 + error bound)
The...

Estimating Population Mean with Unknown Standard Deviation

Estimating Population Mean with Unknown Standard Deviation

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 Guinness...

Margin of Error

Margin of Error

The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.

Confidence Interval for Estimating Population Mean

Confidence Interval for Estimating Population Mean

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.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...

Distributions to Estimate Population Parameter

Distributions to Estimate Population Parameter

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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Related Experiment Video

Updated: Jul 11, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Estimating regression standard errors with data from the Current Population Survey's public use file.

Michael Davern¹, Arthur Jones, James Lepkowski

¹School of Public Health, University of Minnesota, Minneapolis, MN 55414, USA. daver004@umn.edu

Inquiry : a Journal of Medical Care Organization, Provision and Financing

|September 14, 2007

Summary

Calculating standard errors for multivariate models using the public Current Population Survey Annual Social and Economic Supplement (CPS ASEC) file is feasible. While estimates generally align with internal data, method selection is crucial for accurate complex survey analysis.

Related Experiment Videos

Last Updated: Jul 11, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

Economics
Statistics
Survey Methodology

Background:

The Current Population Survey Annual Social and Economic Supplement (CPS ASEC) is a key data source for socioeconomic research.
Accurate standard error estimation is vital for valid statistical inference from complex survey designs.

Purpose of the Study:

To assess the reliability of standard error calculations for multivariate models using the public CPS ASEC data.
To compare these estimates with those derived from restricted Census Bureau internal data.

Main Methods:

Analysis of the 2003 CPS ASEC public use file.
Modeling individual-level dependent variables: income, poverty, and health insurance coverage.
Comparison of standard error estimates between public and internal Census Bureau datasets.

Main Results:

Multivariate standard error estimates from the public CPS ASEC file generally perform well against internal data.
Significant discrepancies were observed among different methods for adjusting complex sample designs.

Conclusions:

The public CPS ASEC file can yield reasonable standard errors for multivariate analyses.
Users must exercise caution and select appropriate methods for complex survey data analysis to avoid biased estimates.