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Variance

Variance

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.

Variability: Analysis

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Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
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Relative Risk

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Mean Absolute Deviation

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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...

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Related Experiment Video

Updated: Jun 1, 2026

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Variance computations for functional of absolute risk estimates.

R M Pfeiffer¹, E Petracci

¹Biostatistics Branch, DCEG, National Cancer Institute, 6120 Executive Blvd, EPS/8030, Bethesda, MD 20892-7244, USA.

Statistics & Probability Letters

|June 7, 2011

Summary

This summary is machine-generated.

We developed a new method using influence functions to calculate the uncertainty of absolute risk estimates. This approach helps assess how changes in risk factors affect breast cancer risk for individuals and populations.

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Area of Science:

Biostatistics
Epidemiology
Risk Prediction Modeling

Background:

Estimating absolute risk is crucial for personalized medicine and public health interventions.
Assessing the impact of risk factor changes on absolute risk requires robust statistical methods.
Current methods for variance estimation can be computationally intensive or lack theoretical grounding.

Purpose of the Study:

To introduce a novel, simple influence function-based approach for computing variances of absolute risk estimates.
To apply this method to evaluate the impact of risk factor distribution changes on absolute risk.
To compare the proposed variance estimates with bootstrap methods.

Main Methods:

Developed an influence function-based methodology for variance estimation of absolute risk.
Applied the method to assess the effects of risk factor modifications on individual and population-level absolute risk.
Utilized a breast cancer absolute risk prediction model incorporating modifiable and standard risk factors for illustration.

Main Results:

Influence function-based variance estimates were successfully computed for absolute risk and related criteria.
The approach provided a computationally efficient alternative to bootstrap variance estimation.
Demonstrated the utility of the method in a practical breast cancer risk prediction scenario.

Conclusions:

The influence function-based approach offers a simple and effective method for variance estimation in absolute risk prediction.
This method facilitates the assessment of risk factor impacts on absolute risk at both individual and population levels.
The findings support the use of influence functions for robust uncertainty quantification in risk prediction models.