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Related Concept Videos

Distributions to Estimate Population Parameter01:26

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...
Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Contaminants and Errors01:16

Contaminants and Errors

Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
Another key consideration is determining the appropriate number of samples required to...
Sampling Distribution01:12

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
Sampling Plans01:23

Sampling Plans

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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Related Experiment Video

Updated: May 18, 2026

Using Single-Worm Data to Quantify Heterogeneity in Caenorhabditis elegans-Bacterial Interactions
09:54

Using Single-Worm Data to Quantify Heterogeneity in Caenorhabditis elegans-Bacterial Interactions

Published on: July 22, 2022

Fitting distributions to microbial contamination data collected with an unequal probability sampling design.

M S Williams1, E D Ebel, Y Cao

  • 1Risk Assessment Division, Office of Public Health Science, Food Safety Inspection Service, USDA, Fort Collins, CO 80526, USA. mike.williams@fsis.usda.gov

Journal of Applied Microbiology
|September 19, 2012
PubMed
Summary
This summary is machine-generated.

Statistical fitting of microbial data often assumes simple random sampling, but this study introduces a weighted maximum likelihood estimation to correct for unequal sampling probabilities, reducing bias in risk assessments.

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Microbiota Analysis Using Two-step PCR and Next-generation 16S rRNA Gene Sequencing
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Microbiota Analysis Using Two-step PCR and Next-generation 16S rRNA Gene Sequencing

Published on: October 15, 2019

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Last Updated: May 18, 2026

Using Single-Worm Data to Quantify Heterogeneity in Caenorhabditis elegans-Bacterial Interactions
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Microbiota Analysis Using Two-step PCR and Next-generation 16S rRNA Gene Sequencing
11:22

Microbiota Analysis Using Two-step PCR and Next-generation 16S rRNA Gene Sequencing

Published on: October 15, 2019

Area of Science:

  • Quantitative microbiology
  • Statistical modeling
  • Food safety analysis

Background:

  • Microbial sampling data analysis commonly uses statistical distribution fitting.
  • A key assumption is simple random sampling, which is frequently violated in practice.
  • This violation can lead to biased results in quantitative microbiology and risk assessments.

Purpose of the Study:

  • To develop a statistical framework for microbial data analysis that accounts for unequal sampling probabilities.
  • To address biases introduced by the assumption of simple random sampling in microbial data.
  • To improve the reliability of inferences drawn from microbial sampling data.

Main Methods:

  • Development of a weighted maximum likelihood estimation (WMLE) framework.
  • Application of WMLE to microbiological samples collected with unequal selection probabilities.
  • Demonstration using two case studies involving food sample collection during processing.

Main Results:

  • The proposed weighted maximum likelihood estimation framework is suitable for microbiological samples with unequal selection probabilities.
  • Biases resulting from the assumption of simple random sampling were quantified in the provided examples.
  • The study highlights the significant impact of ignoring unequal sampling probabilities on statistical inferences.

Conclusions:

  • Failure to account for unequal sample weighting can introduce substantial bias into data analysis.
  • The proposed methodology mitigates bias in microbial data analysis, enhancing the reliability of risk assessments.
  • This approach facilitates more accurate comparisons and data integration across different studies.