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Related Concept Videos

Unusual Results01:16

Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value = μ + 2σ
Minimum unusual value...
P-value01:10

P-value

P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value.  P-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
A large P-value calculated from the data indicates to  not reject the null hypothesis. But a higher P-value does not mean that the null hypothesis is true. The smaller the P-value, the more unlikely...
Types of Limits I01:23

Types of Limits I

Limits are a key mathematical concept for understanding how functions behave as their input approaches specific values, particularly when the function is undefined. They help reveal trends and discontinuities by examining the values a function approaches rather than its actual value.One-sided limits focus on the direction from which a value is approached. When a function behaves differently depending on whether the input approaches from the left or the right, the two one-sided limits may not...
Decision Making: P-value Method01:09

Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim  is also stated. These statements can act as null and alternative hypotheses:  a null hypothesis would be a neutral statement while the alternative hypothesis can have a...
Critical Values01:31

Critical Values

A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

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Updated: Jun 21, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Plausible values: how to deal with their limitations.

Christian Monseur1, Raymond Adams

  • 1Université de Liège, FAPSE, Department Education, Bld. du Rectorat, 5 (B32) 4000 Liège, Belgium. cmonseur@ulg.ac.be

Journal of Applied Measurement
|August 13, 2009
PubMed
Summary

This study examines the use of plausible values in the Programme for International Student Achievement (PISA) assessments. It explores potential biases and the adequacy of variance component estimation in hierarchical data structures.

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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
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Setting Limits on Supersymmetry Using Simplified Models
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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

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

Published on: September 19, 2012

Area of Science:

  • Educational Measurement
  • Psychometrics
  • Large-Scale Assessment

Background:

  • The Programme for International Student Achievement (PISA) utilizes Rasch modeling and plausible values for scaling and reporting results.
  • Plausible values, a multiple imputation technique, are integral to modern large-scale assessments.

Purpose of the Study:

  • To detail the scaling methodology employed in PISA.
  • To critically evaluate the implications of using plausible values generated via a flat linear regression model.
  • To assess the suitability of PISA procedures for hierarchical data analysis.

Main Methods:

  • Rasch modeling for data scaling.
  • Multiple imputation using plausible values.
  • Flat linear regression with student background variables as regressors.
  • Analysis of secondary data analyses and variance component estimation.

Main Results:

  • The study identifies conditions under which secondary analyses may be biased when using variables not included in the plausible value generation model.
  • It explores the adequacy of PISA's procedures for estimating variance components in hierarchically structured data, as plausible values were not derived from a multi-level model.

Conclusions:

  • The approach to generating plausible values in PISA has implications for the validity of secondary analyses and the estimation of variance components.
  • Further investigation is needed to ensure robust statistical inferences from PISA data, particularly concerning nested structures.