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Ordinal Level of Measurement00:55

Ordinal Level of Measurement

The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using an ordinal scale are similar to nominal scale data, but there is one major difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the...
Outliers and Influential Points01:08

Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...
Ranks01:02

Ranks

Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
Drug Concentration Versus Time Correlation01:15

Drug Concentration Versus Time Correlation

The plasma drug concentration-time curve is a crucial tool in pharmacokinetics, representing the drug's concentration in plasma at different time intervals post-administration. This curve illustrates the drug's journey from absorption into the systemic circulation, distribution to body tissues, and eventual elimination through excretion or biotransformation.
Two pivotal parameters are the minimum effective concentration (MEC) and the minimum toxic concentration (MTC). The MEC is the lowest drug...
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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...
Derivatives: Problem Solving01:26

Derivatives: Problem Solving

Temperature-Dependent Growth of Brook TroutThe growth of brook trout is closely influenced by water temperature. Experimental data demonstrate how trout weight changes over a 24-day period in response to varying water temperatures. At lower temperatures, such as 15.5 degrees Celsius, brook trout show significant weight gain. However, as the temperature increases, the amount of weight gained steadily decreases. At the highest temperature measured, 24.4 degrees Celsius, trout experience a net...

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Related Experiment Video

Updated: Jun 12, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Evaluating Methods for Detrending Time Series Using Ordinal Patterns, with an Application to Air Transport Delays.

Felipe Olivares1, F Javier Marín-Rodríguez1, Kishor Acharya1

  • 1Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus UIB, 07122 Palma, Spain.

Entropy (Basel, Switzerland)
|March 28, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces ordinal patterns to verify if detrending methods effectively remove spurious connections in time series data. The findings offer practical insights into managing functional network analysis for complex systems like airport delay propagation.

Keywords:
causalityfunctional complex networksordinal patternsstationaritytime series

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Area of Science:

  • Complex Systems Analysis
  • Network Science
  • Time Series Analysis

Background:

  • Functional networks are crucial for understanding complex system connectivity through observed dynamics.
  • A key assumption for reliable functional network analysis is the stationarity of time series data.
  • Non-stationarity can introduce spurious functional connections, complicating analysis.

Purpose of the Study:

  • To introduce and validate ordinal patterns as a method for assessing the effectiveness of detrending techniques.
  • To evaluate detrending methods on real-world airport delay data and synthetic datasets.
  • To provide operational conclusions on managing time series stationarity in functional network analysis.

Main Methods:

  • Utilized ordinal patterns and derived metrics to quantify time series properties.
  • Applied detrending methods to time series data.
  • Assessed the impact of detrending on functional connectivity using ordinal pattern analysis.

Main Results:

  • Demonstrated that ordinal patterns can effectively detect residual non-stationarity after detrending.
  • Showcased the application of this method to airport delay data from European and US systems.
  • Provided evidence of how non-stationarity and its correction affect the observed functional connections.

Conclusions:

  • Ordinal pattern analysis offers a robust tool for validating detrending effectiveness in complex systems.
  • Proper detrending is essential to avoid spurious connections in functional network analysis.
  • The findings have implications for understanding propagation dynamics in real-world systems like air traffic.