Equal Likelihood
Equal Likelihood - Related Videos
01:15
One-Way ANOVA: Equal Sample Sizes
0 Views •
2023
One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean. Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
01:30
Electric Field of Two Equal and Opposite Charges
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2023
Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero. A separation of the positive and negative charges can lead to a weak, remnant effect of the positive and negative charges. The expectation is that the more the distance between the positive and...
09:33
Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
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Cited by 12 •
2019
A protocol for the fabrication and optical characterization of dielectric metasurfaces is presented. This method can be applied to the fabrication of not only beam splitters, but also of general dielectric metasurfaces, such as lenses, holograms, and optical cloaks.
07:15
Determining the Likelihood of Variant Pathogenicity Using Amino Acid-level Signal-to-Noise Analysis of Genetic Variation
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Cited by 6 •
2019
Amino acid-level signal-to-noise analysis determines the prevalence of genetic variation at a given amino acid position normalized to background genetic variation of a given population. This allows for identification of variant "hotspots" within a protein sequence (signal) that rises above the frequency of rare variants found in a population (noise).
04:01
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
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2020
Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws. According to kinetic molecular theory, particles of an ideal gas do not exhibit...
FAQs
They make the outcome categories nonoverlapping and complete, so each possible result is counted once and no result is omitted. Under that structure, assigning the same probability to every outcome produces probabilities that sum to one. If outcomes overlap or leave gaps, comparing favorable outcomes with the total can give a misleading result.
Symmetry provides a reason to treat outcomes alike, as in idealized coins, dice, or cards where no listed result is given an advantage. The assumption is not automatic: the experiment must support the relevant symmetry or use randomization that creates comparable chances. Without that justification, the resulting probability calculation may describe an ideal model rather than the experiment.
It fails when the possible outcomes do not have comparable chances, even if they are listed clearly and counted correctly. Real-world data may contain unequal selection probabilities or other features that break the assumed symmetry. In that situation, the equal-likelihood calculation should not be treated as an accurate representation of uncertainty; the probability model requires reconsideration.
Once the possible outcomes are specified, identify the outcomes that satisfy the event of interest and compare their number with the total number of outcomes. This counting approach works because each outcome contributes the same probability. It is useful for finite models such as coin, die, or card experiments, provided the stated outcomes are mutually exclusive and exhaustive.
First specify the sample space and confirm that its outcomes represent all relevant results without overlap. Then ask whether the randomization or experimental design gives those outcomes the same chance, rather than assuming equality from the notation alone. These checks connect the mathematical calculation to the actual experiment and help reveal when a classical model is inappropriate.
In randomized sampling, the principle helps frame uncertainty by treating the specified sampling outcomes as having comparable chances when the design justifies that assumption. Researchers can then use the sample space to evaluate possible results and compare favorable outcomes with all outcomes. Its value depends on the randomization being genuine and on the defined outcomes matching the sampling question.
It helps distinguish uncertainty produced by a justified probability model from uncertainty that has merely been assumed. When symmetry or randomization supports equal chances, the resulting calculation can organize the sample space and quantify the event under study. When that support is absent, recognizing the limitation prevents an idealized result from being mistaken for a description of real-world data.