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Mean Absolute Deviation

Mean Absolute Deviation

The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to...

Absolute Motion Analysis- General Plane Motion

Absolute Motion Analysis- General Plane Motion

Visualize a drone, with its propellers spinning rapidly, hovering mid-air. The fascinating movements and operations of this drone can be comprehended by applying the principle of general plane motion.
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the drone...

Relative Motion Analysis using Rotating Axes

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it instrumental in...

Geometric Mean

Geometric Mean

The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...

Root Mean Square

Root Mean Square

If in an experiment, data values have a probability of being both positive and negative, neither the arithmetic mean, the geometric mean, nor the harmonic mean can be used to calculate the central tendency of the data set. In particular, if the positive and negative values are equally likely, the arithmetic mean is close to zero.
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...

Curvilinear Motion: Rectangular Components

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...

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Related Experiment Video

Updated: May 10, 2026

Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking

Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking

Published on: February 12, 2011

Spatial moving average risk smoothing.

P Botella-Rocamora¹, A López-Quílez, M A Martinez-Beneito

¹Universidad CEU-Cardenal Herrera, Valencia, Spain.

Statistics in Medicine

|June 12, 2013

Summary

This summary is machine-generated.

Spatial Moving Average Risk Smoothing (SMARS) offers a novel approach to disease mapping by adapting time series methods to spatial data. This method effectively models spatial disease risk patterns, proving competitive with existing techniques.

Related Experiment Videos

Last Updated: May 10, 2026

Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking

Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking

Published on: February 12, 2011

Area of Science:

Epidemiology
Biostatistics
Spatial Analysis

Background:

Traditional disease mapping models often struggle to capture complex spatial dependencies.
Existing methods may not adequately represent the range of spatial correlation structures observed in disease risk data.

Purpose of the Study:

Introduce Spatial Moving Average Risk Smoothing (SMARS) as an innovative disease mapping technique.
Develop a flexible model capable of reproducing diverse spatial correlation functions.
Evaluate SMARS performance against established disease mapping models.

Main Methods:

Applied time series moving average concepts to the spatial domain.
Utilized a spatial moving average process of unknown order to define disease risk dependence.
Theoretically analyzed the induced correlation structure and fitted neighborhood distances for zero correlation.

Main Results:

SMARS can reproduce a rich class of spatial correlation functions, from independent to long-range dependent.
Demonstrated SMARS's competitiveness through applications on simulated and real disease data.
Identified qualitative differences in mortality patterns for 21 causes of death in the Comunitat Valenciana.

Conclusions:

SMARS provides a flexible and competitive new tool for disease mapping.
The model effectively captures a wide spectrum of spatial disease risk dependencies.
SMARS applications can reveal nuanced patterns in epidemiological data.