Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Introduction to z Scores01:05

Introduction to z Scores

1.5K
A z score (or standardized value) is measured in units of the standard deviation. It indicates how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
z scores...
1.5K
Introduction to z Scores01:06

Introduction to z Scores

8.5K
A z score (or standardized value) is measured in units of the standard deviation. It tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
z scores...
8.5K
z Scores and Unusual Values01:07

z Scores and Unusual Values

8.2K
The z score is one of the three measures of relative standing. It describes the location of a value in a dataset relative to the mean. z scores are obtained after the standardization of the values in a dataset. The z score for the mean is 0.
 This score indicates how far a value is from the mean in terms of standard deviation. For example, if a data value has a z score of +1, the researcher can infer that the particular data value is one standard deviation above the mean. If another data...
8.2K
z Scores and Area Under the Curve01:17

z Scores and Area Under the Curve

14.9K
z scores are the standardized values obtained after converting a normal distribution into a standard normal distribution. A z score is measured in units of the standard deviation. The z score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a z score of...
14.9K
Standard Deviation01:10

Standard Deviation

17.8K
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more...
17.8K
Coefficient of Correlation01:12

Coefficient of Correlation

7.8K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
7.8K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

High-temperature-resistant fiber-based aerogel composites for dynamic capture of low-concentration radioactive iodine vapor: Theoretical calculations and experimental validation.

Journal of hazardous materials·2026
Same author

Nitrogen-rich three-dimensional porous crosslinked polymers for efficient capture of iodine vapor and methyl iodide under complex conditions.

Environmental research·2026
Same author

A Dimer for Dinner: The Impact of GHS-R1a Heterodimerization on Feeding Circuits.

Biomolecules·2026
Same author

Multiple Reaction Monitoring (MRM)-Based Targeted Kidney Metabolite Profiling of a Mouse Model of Hyperuricemia.

Metabolites·2026
Same author

High-salt diet promotes atopic dermatitis by partially enhancing intestinal SGK1/ENaC signaling and destroying gut <i>Lactobacillus</i>-maintained systemic type 1 interferon.

Frontiers in cellular and infection microbiology·2026
Same author

A Comparative Analysis of Muscle Nutritional Composition, Texture, Microstructure, and Metabolomics: Hybrid Sturgeon (<i>Acipenser baerii</i> Brandt ♀ × <i>Acipenser schrenckii</i> Brandt ♂) Versus Its Parent Varieties.

Foods (Basel, Switzerland)·2026

Related Experiment Video

Updated: May 6, 2026

Objectively Assessing Sports Concussion Utilizing Visual Evoked Potentials
12:11

Objectively Assessing Sports Concussion Utilizing Visual Evoked Potentials

Published on: April 27, 2021

3.5K

U-Scores for Multivariate Data in Sports.

Knut M Wittkowski1, Tingting Song, Kent Anderson

  • 1The Rockefeller University.

Journal of Quantitative Analysis in Sports
|October 29, 2013
PubMed
Summary

Multivariate data analysis using mu-scores offers a flexible approach to evaluating performance when variables have different scales and unknown interactions. This method provides situation-independent ability measures, applicable beyond sports to fields like medicine and finance.

Keywords:
OlympicsTour-de-Franceabilitybaseballmultivariateperformancerankingsoccerstatisticstriathlonvoting

More Related Videos

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.6K
Qualitative and Quantitative Validation of Tools with Rating Scales Aimed at Assessing the Quality of University Service-Learning
10:39

Qualitative and Quantitative Validation of Tools with Rating Scales Aimed at Assessing the Quality of University Service-Learning

Published on: August 29, 2025

1.3K

Related Experiment Videos

Last Updated: May 6, 2026

Objectively Assessing Sports Concussion Utilizing Visual Evoked Potentials
12:11

Objectively Assessing Sports Concussion Utilizing Visual Evoked Potentials

Published on: April 27, 2021

3.5K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.6K
Qualitative and Quantitative Validation of Tools with Rating Scales Aimed at Assessing the Quality of University Service-Learning
10:39

Qualitative and Quantitative Validation of Tools with Rating Scales Aimed at Assessing the Quality of University Service-Learning

Published on: August 29, 2025

1.3K

Area of Science:

  • Multivariate statistical analysis
  • Sports analytics
  • Performance and ability measurement

Background:

  • Traditional linear weight scoring systems in competitions rely on strong assumptions about variable importance, interactions, and transformations, which are often difficult to justify theoretically or validate empirically.
  • Existing performance measures can be situation-dependent, lacking a robust method for assessing inherent ability.
  • A need exists for a scoring system that can integrate diverse variables with different scales and unknown interactions.

Purpose of the Study:

  • To introduce and extend the application of mu-scores (multivariate scores) for integrating diverse variables in performance evaluation.
  • To develop situation-independent measures of 'ability' that complement existing situation-dependent 'performance' measures.
  • To demonstrate the versatility of mu-scores by extending them to censored, penalized, and hierarchically structured variables.

Main Methods:

  • Utilized mu-scores, a method for integrating multivariate data with varying scales and unknown interactions, provided variables have a defined orientation.
  • Extended mu-score methodology to accommodate censored variables (e.g., lifetime achievements), penalty systems (e.g., win vs. tie weighting), and hierarchically structured data (e.g., Olympic event categories).
  • Applied the methodology using baseball performance as a primary example, with extensions to Olympic medals and cycling jerseys.

Main Results:

  • Mu-scores provide a robust framework for creating multivariate measures of 'ability' that are independent of situational factors.
  • The extended mu-score methods successfully handle complex data structures including censored, penalized, and hierarchical variables.
  • Demonstrated the practical application and flexibility of mu-scores in sports analytics, with potential for broader applicability.

Conclusions:

  • Mu-scores offer a powerful and flexible alternative to traditional scoring systems, particularly when dealing with complex, multi-variable data.
  • The developed extensions enable the quantification of latent 'ability' in various contexts, moving beyond simple performance metrics.
  • The mu-score methodology has wide-ranging applicability in diverse fields such as medicine, finance, social choice theory, and economics.