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Related Concept Videos

Expected Value01:15

Expected Value

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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...
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Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

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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).
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Determination of Expected Frequency01:08

Determination of Expected Frequency

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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...
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Uncertainty: Overview00:59

Uncertainty: Overview

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Probability in Statistics01:14

Probability in Statistics

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Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Related Experiment Video

Updated: Apr 23, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
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Quantifiers induced by subjective expected value of sample information.

Kaihong Guo

    IEEE Transactions on Cybernetics
    |September 16, 2014
    PubMed
    Summary

    This study introduces a new method for decision making under uncertainty using ordered weighted averaging (OWA) operators. It develops personalized quantifiers based on decision maker behavior for more accurate aggregation.

    Area of Science:

    • Decision Sciences
    • Operations Research
    • Artificial Intelligence

    Background:

    • The ordered weighted averaging (OWA) operator is a key framework for multiattribute decision making (MADM) under uncertainty.
    • Existing quantifier-guided aggregation methods using OWA operators face limitations in personalization.

    Purpose of the Study:

    • To address limitations in quantifier-guided OWA aggregation by developing personalized quantifiers.
    • To generate quantifiers tailored to individual decision makers (DMs) using sample information and preferences.

    Main Methods:

    • Developed a repeatable interactive procedure to extract DM decision attitudes.
    • Built nonlinear optimal models to derive OWA weighting vectors from DM preferences and sample values.
    • Utilized piecewise linear interpolations to create DM-specific quantifiers, termed subjective expected value of sample information-induced quantifiers.

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    Main Results:

    • Successfully generated personalized quantifiers reflecting individual DM decision attitudes.
    • Demonstrated properties of the developed subjective expected value of sample information-induced quantifiers.
    • Proved the consistency of OWA aggregation guided by these personalized quantifiers.

    Conclusions:

    • The developed subjective quantifiers offer a more intuitive and convincing approach to OWA aggregation compared to parameterized quantifiers.
    • This method enhances MADM by incorporating specific DM behavior and attitudinal characteristics.
    • Personalized OWA aggregation leads to more accurate and appealing decision outcomes.