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Sample Size Calculation

Sample Size Calculation

Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...

Choosing Between z and t Distribution

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...

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...

Stratified Sampling Method

Stratified Sampling Method

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...

Sampling Plans

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...

One-Way ANOVA: Unequal Sample Sizes

One-Way ANOVA: Unequal Sample Sizes

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: Jun 25, 2026

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

Sample size determination for the non-randomised triangular model for sensitive questions in a survey.

Guo-Liang Tian¹, Man-Lai Tang, Zhenqiu Liu

¹Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, PR China. gltian@hku.hk

Statistical Methods in Medical Research

|February 18, 2009

Summary

New sample size formulas for non-randomized triangular designs are now available for public health surveys on sensitive topics. These formulas improve efficiency and cost-effectiveness compared to randomized response models.

Related Experiment Videos

Last Updated: Jun 25, 2026

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

Area of Science:

Biostatistics
Public Health Research Methodology
Survey Design

Background:

Accurate sample size determination is critical for public health surveys involving sensitive topics.
Non-randomized models offer efficiency and cost-effectiveness over randomized response models.
Existing sample size formulas are lacking for non-randomized designs.

Purpose of the Study:

To derive novel sample size formulas for the non-randomized triangular design using a power analysis approach.
To evaluate the performance and accuracy of the derived sample size formulas.
To compare sample size requirements across different survey designs.

Main Methods:

Derivation of power functions and sample size formulas for one- and two-sided tests using large-sample normal approximation.
Evaluation of formula performance via power accuracy and sample size ratios (non-randomized triangular design vs. direct questioning design).
Numerical comparison of sample sizes for Warner design, direct questioning design, and non-randomized triangular design.

Main Results:

Novel sample size formulas for the non-randomized triangular design have been successfully derived.
The performance of the derived formulas was validated through accuracy assessments and comparative analyses.
The study provides theoretical justification and extends the methodology to two-sample problems.

Conclusions:

The derived sample size formulas provide essential tools for designing public health surveys on sensitive topics.
The non-randomized triangular design offers a more efficient and cost-effective alternative.
The findings are illustrated with a practical example from an induced abortion study in Taiwan.