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

Paul De Boeck¹, Michael L DeKay², Jolynn Pek²

¹Department of Psychology, The Ohio State University, 1827 Neil Avenue, Columbus, OH, 43210, USA. deboeck.2@osu.edu.

|July 4, 2024

Summary

This summary is machine-generated.

Adventitious error accounts for approximate model fit by acknowledging random distortions in observed data. This phenomenon impacts statistical power and parameter estimates, offering a framework for understanding varied research findings.

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 deviate from theoretical ones due to implementation variations.
This concept links to Root Mean Square Error of Approximation (RMSEA) and augmented standard errors (SEs).

Purpose of the Study:

To generalize the concept of adventitious error beyond CSMs.
To illustrate its consequences on statistical estimates and measurement uncertainty.
To provide a statistical framework for diverse research phenomena.

Main Methods:

Utilized simulations to demonstrate the impact of adventitious error on SEs in broader contexts.
Employed derivations to explore connections between adventitious error, effect size heterogeneity, and statistical power.
Conducted simulation studies to assess adventitious error's effect on composite scores (factor and summed scores).

Main Results:

The impact of adventitious error on SEs extends to pairwise variable relationships outside CSMs.
Heterogeneity of effect sizes and overestimated statistical power are conjectured to stem from adventitious error.
Adventitious error has a minor impact on measurement uncertainty, greater for factor scores than summed scores.

Conclusions:

Adventitious error provides a statistical framework for understanding approximate fit, varying findings, and power overestimation.
It is an assumption about the data-generating mechanism with broad implications.
The study highlights the generalizability and consequences of adventitious error in statistical modeling.