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Related Concept Videos

Sample Size Calculation01:19

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...
Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
Decision Making: Traditional Method01:14

Decision Making: Traditional Method

The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
Types of Hypothesis Testing01:11

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p ≠ 0.5.

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Related Experiment Video

Updated: Jun 5, 2026

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

Bayesian sample size determination under hypothesis tests.

Xiao Zhang1, Gary Cutter, Thomas Belin

  • 1Department of Biostatistics, School of Public Health, University of Alabama at Birmingham, Birmingham, AL 35294, USA. xzhang@ms.soph.uab.edu

Contemporary Clinical Trials
|January 5, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian method for determining clinical trial sample sizes using hypothesis testing. It incorporates prior information and uses Bayes factors for robust sample size calculation in medical research.

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Bayesian Inference

Background:

  • Traditional sample size calculations often lack flexibility in incorporating prior knowledge.
  • Existing methods may not adequately address uncertainty in treatment effects and variance.
  • Bayesian approaches offer a framework for integrating prior information into statistical decision-making.

Purpose of the Study:

  • To develop a Bayesian approach for calculating sample sizes in clinical trials.
  • To extend existing methods by including composite distributions for treatment effects and data variance.
  • To utilize Bayes factors and averaged error rates for sample size determination.

Main Methods:

  • Developed a Bayesian framework for sample size calculation based on hypothesis testing.
  • Extended Weiss's methodology to incorporate composite distributions for null and alternative hypotheses.
  • Employed Bayes factors and averaged type I and type II errors for sample size selection.

Main Results:

  • The proposed Bayesian method allows for the incorporation of uncertainty in prior information.
  • It permits informative prior distributions for unknown quantities within hypothesis specifications.
  • Demonstrated the method's utility with real-world examples from multiple sclerosis and preterm birth prevention trials.

Conclusions:

  • The Bayesian approach provides a flexible and robust method for clinical trial sample size calculation.
  • This framework effectively handles uncertainty and prior information, enhancing trial design.
  • The method is applicable to various clinical settings, improving statistical rigor.