حجم الأثر البنائي في شبكات القياس النفسي: إطار تحليلي تقاربي للتحيز واستعادة البنية لاشتقاق قانون تصميم حجم العينة

نسرين محمد سعيد زارع

doi:10.55074/hesj.vi55.1890

Authors

Nisreen Mohamed Saeed Zarea Associate Professor of Psychology Psychology Department - College of Languages and Human Sciences Qassim University - KSA

DOI:

https://doi.org/10.55074/hesj.vi55.1890

Keywords:

Structural effect size, Psychometric networks, Small-sample bias, Network recovery, Sample size design

Abstract

The present study aimed to develop a quantitative analytical framework for defining Structural Effect Size in psychometric networks and examining its statistical properties under limited sample conditions, with the goal of deriving a quantitative design rule for determining sample size in network studies. The proposed framework measures the structural difference between the true network and the estimated network using the normalized Frobenius distance between their adjacency matrices, which is then transformed into a structural similarity index bounded between zero and one. Structural effect size is defined as the degree of deviation from perfect structural similarity, reflecting the structural recovery error of the network system. To examine the statistical behavior of this indicator, a large-scale simulation study was conducted on psychometric networks with different numbers of nodes (pⓜ=10"،" 20"،" 40) and varying network densities (dⓜ=0.2"،" 0.5"،" 0.8), while varying sample size. The results showed that structural recovery error, which represents the structural effect size resulting from network estimation error, increases with the structural complexity of the network and decreases inversely with the square root of the sample size. The analyses also revealed a regular asymptotic relationship that can be expressed as: y≈C√((d" " p)/N) Where y represents the structural effect size of the recovery error, p denotes the number of nodes, d the network density, and N the sample size. The findings indicate that the accuracy of network recovery depends more strongly on the ratio of sample size to structural network complexity than on the absolute sample size alone. Based on this relationship, a quantitative design rule was derived to estimate the sample size required to achieve a targeted level of structural similarity. The study thus provides a theoretical contribution by introducing the concept of structural effect size into psychometric network analysis and a methodological contribution by offering a priori design guidance for planning sample size in psychological network research.

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