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Examining the reliability of interval level data using root mean square differences and concordance correlation

Kimberly A Barchard¹

¹Department of Psychology, University of Nevada, Las Vegas, 4505 Maryland Parkway, P.O. Box 455030, Las Vegas, NV 89154-5030, USA. barchard@unlv.nevada.edu

Psychological Methods

|May 18, 2011

Summary

This study introduces new statistics, the root mean square difference (RMSD) and concordance correlation coefficient (CCC), for evaluating score consistency beyond simple linear relationships. These methods offer a more stringent assessment of agreement between measurements.

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Area of Science:

Measurement science
Statistical analysis
Biostatistics

Background:

Traditional correlation coefficients (e.g., Pearson's r) assess linear relationships but ignore score means and standard deviations.
Many scientific fields require stricter agreement criteria, focusing on the identical equality of scores.
Existing methods may not fully capture the nuances of score consistency.

Purpose of the Study:

Introduce novel statistics for evaluating score consistency.
Compare new metrics with established measures like intraclass correlation coefficients and standard error of measurement.
Adapt these statistics for various definitions of agreement (linear, consistency, absolute).

Main Methods:

Calculation of the difference between paired scores for each unit of measurement.
Utilizing the root mean square difference (RMSD) to quantify average change between score sets.
Employing the concordance correlation coefficient (CCC) to rescale RMSD, with a maximum value of 1.

Main Results:

Demonstrated the relationship between RMSD, CCC, and other common statistical measures (ICC, product-moment correlation, SEM).
Showcased the adaptability of RMSD and CCC for different agreement definitions.
Provided a more comprehensive approach to assessing score consistency.

Conclusions:

RMSD and CCC offer a more rigorous evaluation of score consistency compared to traditional correlation methods.
These new statistics are valuable for fields requiring precise agreement assessment.
The adaptability of RMSD and CCC enhances their utility across diverse measurement scenarios.