Explained Variance Threshold
Explained Variance Threshold - Related Videos
01:25
Variance
0 Views •
2024
Variance is a statistical measure that quantifies the degree of risk associated with an investment's returns by indicating how much the returns deviate from their expected value over time. It provides essential insights into the stability and predictability of an investment's performance. The variance calculation involves determining the mean return, which is the average return over a specified period, and then calculating the deviations of each return from this mean. These deviations are...
01:15
Variance
0 Views •
2023
The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
06:48
The Staircase Procedure for Finding a Perceptual Threshold
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2023
Source: Laboratory of Jonathan Flombaum—Johns Hopkins University Psychophysics is the name for a set of methods in perceptual psychology designed in order to relate the actual intensity of stimuli to their perceptual intensity. One important aspect of psychophysics involves the measurement of perceptual thresholds: How bright does a light need to be for a person to be able to detect it? How little pressure applied to the skin is detectable? How soft can a sound be and still be heard? Put...
01:21
Friedman Two-way Analysis of Variance by Ranks
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2025
Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
05:45
Rapid Determination of the Thermal Nociceptive Threshold in Diabetic Rats
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Cited by 10 •
2012
Here, we describe a rapid reliable and simple procedure to determine the lowest temperature at which rats or mice show nocifensive behavior, i.e. the thermal nociceptive threshold (TNT). This method applies a slowly increasing thermal stimulus allowing precise and reproducible estimation of TNTs with minimum, if any, stress to the animals.
FAQs
The threshold is applied to the cumulative explained variance, which adds the variance accounted for by successive principal components in ranked order. Researchers identify the first point at which this cumulative value reaches the selected criterion, then retain that smallest number of components. This links dimensionality reduction directly to a measurable level of preserved variation in the behavioral dataset.
Orthogonal components represent independent directions in the transformed measurement space, while the original behavioral variables may be correlated. Because PCA ranks these components by the variation they explain, researchers can examine dominant patterns without carrying the original correlated measurements into every analysis. The resulting component structure supports simpler interpretation of relationships among behavioral observations or traits.
Individual explained variance describes how much variation is associated with one principal component, whereas cumulative explained variance combines the contributions of multiple components in sequence. The threshold uses the cumulative quantity, not the value for a single component. This distinction allows researchers to determine whether the retained set, considered together, captures the desired proportion of variation in the behavioral data.
A higher threshold generally requires retaining more ranked components before the cumulative explained variance reaches the criterion, while a lower threshold permits a smaller representation. Thus, the selected value controls the balance between simplification and preservation of variation. Researchers can choose a criterion such as 90% or 95% according to how much of the dataset’s dominant behavioral pattern they intend to retain.
Researchers first organize the behavioral measurements into a dataset and apply PCA to transform correlated variables into ranked, orthogonal components. They then calculate the cumulative explained variance across those components, compare it with the chosen threshold, and retain the smallest qualifying set. That reduced representation can subsequently support visualization, statistical modeling, clustering, or interpretation of behavioral relationships.
This approach is useful when behavioral data contain multiple measurements whose dominant patterns need to be summarized in fewer dimensions. The retained components can make complex observations easier to visualize, provide inputs for statistical modeling, or support clustering. They also offer a structured way to examine relationships among behavioral traits while preserving the selected level of overall variation.
After PCA, the retained components provide a reduced coordinate system for examining the dominant variation shared across the original behavioral measurements. Researchers can use this representation to compare observations or explore how traits relate within the simplified dataset. Applying the chosen threshold clarifies how much of the original variation contributes to that interpretation, rather than relying on an arbitrary number of components.