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Related Concept Videos

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...
Factorial Design02:01

Factorial Design

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...
One-Way ANOVA01:18

One-Way ANOVA

One-way ANOVA analyzes more than three samples categorized by one factor. For example, it can compare the average mileage of sports bikes. Here, the data is categorized by one factor - the company. However, one-way ANOVA cannot be used to simultaneously compare the sample mean of three or more samples categorized by two factors. An example of two factors would be sports bikes from different companies driven in different terrains, such as a desert or snowy landscape. Here, two-way ANOVA is used...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Uncertainty: Overview00:59

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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...

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Related Experiment Video

Updated: Jun 27, 2026

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
08:27

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Published on: September 27, 2019

Entropy-Based Uncertainty-Aware Exploratory Factor Analysis for Ordinal Data: Application to Tramway Cultural Tourism

Jiaozi Pu1, Yaxin Shi1

  • 1School of Smart Culture and Tourism, Chengdu University of Information Technology, Chengdu 610103, China.

Entropy (Basel, Switzerland)
|June 26, 2026
PubMed
Summary

This study introduces fuzzy-entropy exploratory factor analysis (FE-EFA) to better analyze Likert-scale data in tourism research. The new method handles uncertainty in perception data, revealing a more nuanced factor structure and indicator importance.

Keywords:
Jensen–Shannon divergenceLikert-scale analysisShannon entropyfuzzy exploratory factor analysis (FE-EFA)ordinal dataperception-based evaluationtramway tourismuncertainty-aware representation

Related Experiment Videos

Last Updated: Jun 27, 2026

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
08:27

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Published on: September 27, 2019

Area of Science:

  • Social Sciences
  • Data Analysis
  • Tourism Research

Background:

  • Likert-scale surveys are common in tourism and transport research.
  • Conventional analysis methods impose artificial precision on ordinal data, ignoring ambiguity.
  • Subjective judgments in experiential contexts often involve transitional evaluations, highlighting the need for uncertainty-aware methods.

Purpose of the Study:

  • To develop a parameterized fuzzy-entropy exploratory factor analysis (FE-EFA) framework.
  • To enable uncertainty-aware analysis of ordinal perception data from Likert-scale surveys.
  • To address limitations of conventional point-valued encoding in capturing subjective judgments.

Main Methods:

  • Developed a parameterized fuzzy-entropy exploratory factor analysis (FE-EFA) framework.
  • Transformed ordinal responses into parameterized fuzzy membership distributions.
  • Incorporated Shannon entropy and Jensen-Shannon divergence for distributional analysis.
  • Applied the framework to survey data from Chengdu Tramway Line 2 (N = 1242; 32 indicators).

Main Results:

  • FE-EFA identified an additional factor compared to conventional EFA.
  • FE-EFA demonstrated fewer cross-loadings and a more differentiated loading pattern.
  • Information-theoretic measures showed higher entropy (0.8688) and low Jensen-Shannon divergence (0.0133).
  • Entropy-adjusted weighting revealed systematic shifts in indicator importance.

Conclusions:

  • The FE-EFA framework enhances Likert-scale analysis with an uncertainty-aware layer.
  • It preserves structural stability while suggesting a more differentiated latent construct organization.
  • The approach offers an exploratory extension for perception-based evaluation and decision support in tourism contexts.