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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...

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...

Statistical Analysis: Overview

Statistical Analysis: Overview

When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...

Accuracy and Errors in Hypothesis Testing

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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...

Sensitivity, Specificity, and Predicted Value

Sensitivity, Specificity, and Predicted Value

In healthcare diagnostics, laboratory tests play a crucial role in identifying and diagnosing a wide range of medical conditions. However, interpreting test results is not always straightforward. An abnormal test result does not always confirm the presence of a disease, just as a normal result does not guarantee its absence. To assess the reliability of these diagnostic tools, healthcare practitioners rely on two key statistical indicators: sensitivity and specificity.
Sensitivity is the...

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Related Experiment Video

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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

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Sensitivity analysis and the expected value of perfect information

J C Felli¹, G B Hazen

¹Defense Resources Management Institute, Naval Postgraduate School, Monterey, California 93943-5201, USA.

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

|February 10, 1998

Summary

This study evaluates decision sensitivity measures in medical problems. Expected Value of Perfect Information (EVPI) offers a superior approach by considering both decision change probability and payoff impact.

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Area of Science:

Decision Analysis
Medical Informatics
Health Economics

Background:

Medical decision-making relies on sensitivity analyses to assess the robustness of conclusions.
Existing methods like threshold proximity, probabilistic sensitivity analysis, and entropy-based measures have limitations.

Purpose of the Study:

To critically examine current decision sensitivity measures in medical contexts.
To introduce and advocate for the Expected Value of Perfect Information (EVPI) as a superior sensitivity analysis method.

Main Methods:

Review and comparison of traditional sensitivity analysis techniques.
Introduction of a novel EVPI-based sensitivity measure.
Revisiting three case studies to compare probabilistic, entropy-based, and EVPI-based measures.

Main Results:

Traditional and some novel measures may overstate problem sensitivity by focusing solely on the likelihood of decision change.
EVPI integrates both the probability of decision change and the marginal benefit of that change.
EVPI provides a more comprehensive and accurate assessment of decision problem sensitivity.

Conclusions:

The Expected Value of Perfect Information (EVPI) offers a methodologically and pragmatically superior approach to sensitivity analysis in medical decision problems.
EVPI's consideration of payoff changes alongside decision change probability enhances its utility.
This measure provides a more realistic evaluation of problem sensitivity compared to existing methods.