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Expected Value

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:In the equation, x is an event, and P(x) is the probability of the event occurring.The expected value has practical applications in decision theory.This text is adapted from Openstax, Introductory Statistics, Section 4.2 Mean or Expected Value and...

Sampling Distribution

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...

Binomial Probability Distribution

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...

Expected Frequencies in Goodness-of-Fit Tests

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).

Determination of Expected Frequency

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...

Randomized Experiments

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...

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Related Experiment Video

Updated: May 7, 2026

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Expected value of sample information for multi-arm cluster randomized trials with binary outcomes.

Nicky J Welton¹, Jason J Madan¹, Deborah M Caldwell¹

¹School of Social and Community Medicine, University of Bristol, Bristol, UK (NJW, JJM, DMC, AEA).

Medical Decision Making : an International Journal of the Society for Medical Decision Making

|October 3, 2013

Summary

This summary is machine-generated.

Expected value of sample information (EVSI) can now be efficiently calculated for cluster randomized trials. This new method simplifies complex calculations for research design and reimbursement decisions.

Keywords:

Bayesian inference heterogeneity optimal trial design sample size determination value of information

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Last Updated: May 7, 2026

An R-Based Landscape Validation of a Competing Risk Model

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Published on: September 16, 2022

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index

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Published on: January 8, 2020

Area of Science:

Health economics
Biostatistics
Clinical trial design

Background:

Expected value of sample information (EVSI) guides research funding by quantifying the value of new evidence.
Cluster randomized trials (CRTs) present unique challenges for EVSI due to hierarchical data and heterogeneity.
Multi-arm trials and nonlinear net benefit functions further complicate EVSI computations.

Purpose of the Study:

To develop a computationally efficient method for calculating EVSI in cluster randomized multi-arm trials.
To address the challenges of hierarchical models, between-cluster variability, and correlated parameter estimates in EVSI.
To simplify EVSI calculations by avoiding the computationally intensive inner-simulation step.

Main Methods:

Developed a novel method for EVSI computation in cluster randomized multi-arm trials with binary outcomes.
The method is applicable when the net benefit function is linear in event probability but nonlinear in log-odds ratio parameters.
Illustrated the method using a UK-based cluster randomized 2x2 factorial trial for breast screening attendance.

Main Results:

The proposed method avoids the need for an inner-simulation step, significantly reducing computational intensity.
Demonstrated the practical application of the EVSI method in a real-world trial design scenario.
Highlighted the computational efficiency and applicability of the EVSI approach for CRTs.

Conclusions:

The developed EVSI computation method is practical and appropriate for designing cluster randomized trials.
This approach facilitates better decision-making in research design and resource allocation.
Further developments can extend the method to individually randomized trials and incorporate covariates.