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Related Concept Videos

Skewness

Skewness

The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency...

Types of Skewness

Types of Skewness

If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...

Regression Toward the Mean

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...

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Related Experiment Video

Updated: May 24, 2025

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

Smooth Normative Brain Mapping of Three-Dimensional Morphometry Imaging Data Using Skew-Normal Regression.

Marco Palma¹, Shahin Tavakoli², Julia Brettschneider^3,4

¹MRC Biostatistics Unit, University of Cambridge, Cambridge, UK.

Human Brain Mapping

|March 3, 2025

Summary

This summary is machine-generated.

This study introduces a novel statistical model for brain imaging analysis, improving the detection of subtle volume changes in conditions like Alzheimer's disease. The method enhances diagnostic accuracy by creating personalized risk assessments for neurodegeneration.

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Last Updated: May 24, 2025

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

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Published on: November 14, 2019

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Published on: June 26, 2013

Area of Science:

Neuroimaging
Biostatistics
Medical Image Analysis

Background:

Tensor-based morphometry (TBM) analyzes local brain volume differences relative to a template.
TBM data can exhibit complex distributions, including mean-variance relationships and spatial skewness, particularly in diseased brain regions like lateral ventricles.
Existing methods may not fully capture these complex distributional characteristics.

Purpose of the Study:

To develop a statistical model for 3D neuroimaging data that accounts for smooth variations in mean, variance, and skewness across brain locations.
To model voxelwise distributions using the skew-normal distribution.
To create subject-specific normative maps for assessing individual risk of pathological degeneration.

Main Methods:

Proposed a statistical model for 3D imaging data with spatially varying mean, variance, and skewness functions.
Modeled voxelwise distributions as skew-normal.
Employed an interpolation-based approach to derive smooth parameter functions from a subset of voxels, using Alzheimer's Disease Neuroimaging Initiative (ADNI) data to estimate age and sex effects.

Main Results:

Demonstrated a method to obtain smooth parameter functions for mean, variance, and skewness.
Generated normative maps by transforming TBM images based on Gaussian distributions using the derived parameter functions.
Showcased the utility of subject-specific normative maps for deriving deviation indices from healthy conditions.

Conclusions:

The proposed skew-normal model effectively captures complex distributional properties in TBM data, including mean-variance relationships and spatial skewness.
The developed method allows for the creation of subject-specific normative maps, enhancing the assessment of individual neurodegenerative risk.
This approach offers a more refined tool for analyzing brain morphometry and identifying early signs of pathology.