Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Multiple Regression

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...

Coefficient of Correlation

Coefficient of Correlation

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 strength of the linear...

Calculating and Interpreting the Linear Correlation Coefficient

Calculating and Interpreting the Linear Correlation Coefficient

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. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:

Correlation and Regression

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...

Calibration Curves: Correlation Coefficient

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...

Friedman Two-way Analysis of Variance by Ranks

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...

You might also read

Related Articles

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

Sort by

Same author

Guidance for the Methodological Challenges of Polytobacco Use in Tobacco Regulatory Science.

Public health reports (Washington, D.C. : 1974)·2025

Same author

Apolipoprotein E, Executive Function, and Falls across Cognitive Status: A Cross-Sectional Study.

Dementia and geriatric cognitive disorders·2025

Same author

Qualitative Mediation Analysis: an Important Method for Exploring Mediating Mechanisms in Prevention Science.

Prevention science : the official journal of the Society for Prevention Research·2025

Same author

Three Approaches to Testing for Statistical Suppression.

Multivariate behavioral research·2025

Same author

Comparison of two-bag and three-bag acetylcysteine regimens in the treatment of paracetamol poisoning: a systematic review and meta-analysis.

Clinical toxicology (Philadelphia, Pa.)·2025

Same author

Adherence to a digital therapeutic mediates the relationship between momentary self-regulation and health risk behaviors.

Frontiers in digital health·2025

Search research articles

Related Experiment Videos

Covariances between regression coefficient estimates in a single mediator model.

Davood Tofighi¹, David P Mackinnon, Myeongsun Yoon

¹Department of Psychology, Arizona State University, Tempe, AZ 85287-1104, USA. dtofighi@asu.edu

The British Journal of Mathematical and Statistical Psychology

|July 26, 2008

Summary

This study provides formulas for parameter estimate covariances in single mediator models, enabling accurate confidence intervals (CI) for mediation effect sizes. A simulation study validated the method

Related Experiment Videos

Area of Science:

Statistics
Psychometrics
Biostatistics

Background:

Mediation analysis is crucial for understanding indirect effects in various scientific fields.
Accurate confidence intervals (CI) for effect sizes are essential for interpreting mediation results.
Existing methods for CI construction in mediation analysis may lack precision.

Purpose of the Study:

To derive and present formulae for covariances between parameter estimates in a single mediator model.
To utilize these covariances for calculating multivariate-delta standard errors and constructing 95% CIs for mediation effect sizes.
To evaluate the performance of the proposed CI method through a simulation study.

Main Methods:

Analytical derivation of covariances between parameter estimates in a single mediator model.
Computation of multivariate-delta standard errors using the derived covariances.
Construction of 95% confidence intervals for effect size measures.
A simulation study assessing standard error accuracy, Type I error rate, statistical power, and CI coverage.

Main Results:

Formulae for parameter estimate covariances in single mediator models were analytically derived.
The derived covariances enabled the computation of standard errors and the construction of 95% CIs for effect sizes.
The simulation study demonstrated the accuracy of the standard errors and the desirable properties (Type I error, power, coverage) of the proposed CIs across various conditions.
A practical SAS macro was developed for calculating these confidence intervals.

Conclusions:

The presented formulae and methods provide a statistically sound approach for constructing confidence intervals for effect sizes in single mediator models.
The developed method enhances the reliability of effect size interpretation in mediation analysis.
The availability of a SAS macro facilitates the application of these methods in research practice.