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Random and Systematic Errors

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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

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In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
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Random Error

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...

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Adventitious Error and Its Implications for Testing Relations Between Variables and for Composite Measurement

Paul De Boeck¹, Michael L DeKay¹, Jolynn Pek¹

¹The Ohio State University.

|February 25, 2026

Summary

This summary is machine-generated.

Adventitious error accounts for approximate model fit by acknowledging random distortions in observed data. This concept impacts statistical power and measurement uncertainty, offering a framework for understanding research variability.

Keywords:

adventitious error covariance matrices heterogeneity of effects inferential uncertainty measurement uncertainty power

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Area of Science:

Statistics
Psychometrics
Data Analysis

Background:

Introduced by Wu & Browne (2015), adventitious error addresses approximate fit in covariance structure models (CSMs).
It posits that observed data matrices are randomly distorted from theoretical matrices due to implementation differences.
This distortion affects the accuracy of statistical inferences.

Purpose of the Study:

To generalize the concept of adventitious error beyond CSMs.
To illustrate its consequences on standard errors, effect sizes, statistical power, and measurement uncertainty.
To provide a statistical framework for understanding research variability.

Main Methods:

Simulations were used to demonstrate the impact of adventitious error on standard errors in pairwise relationships.
Derivations were employed to explore the link between adventitious error, effect size heterogeneity, and statistical power overestimation.
Further simulations assessed the effect of adventitious error on composite scores like factor and summed scores.

Main Results:

The impact of adventitious error on standard errors extends to pairwise variable relationships outside of CSMs.
Adventitious error may explain heterogeneity in effect sizes across studies and overestimation of statistical power.
The effect on measurement uncertainty of composite scores was found to be small, but larger for factor scores than summed scores.

Conclusions:

Adventitious error provides a statistical framework for understanding approximate fit, research finding variability, and power overestimation.
It highlights the importance of considering data generation mechanisms in statistical modeling.
The findings have implications for interpreting research results and designing future studies.