Domain-Specific Gender Skew Index (DS-GSI)

• DS-GSI is a metric that quantifies deviations from gender parity in specific domains using statistical and computational analysis.
• It employs methodologies like LLM probing, corpus quantification, and embedding analysis to capture nuanced gender imbalances.
• The framework informs language model auditing and corpus curation by revealing subtle patterns of gender bias across disciplines and cultures.

The Domain-Specific Gender Skew Index (DS-GSI) is a quantitative metric and methodological framework designed to measure and analyze deviations from gender parity within specific domains, corpora, or LLM outputs. The DS-GSI extends general concepts of gender skew quantification by focusing on domain-specific, linguistically grounded, and computationally validated indicators, particularly in contexts where gender imbalances and stereotypes manifest subtly across semantic categories, disciplines, or languages.

1. Conceptual Definition and Key Principles

The DS-GSI is defined as a measure of gender imbalance that captures how much the representation or output distribution within a given system (such as a language corpus, academic discipline, or LLM) deviates from an ideal state of parity (usually defined as equal proportion of male and female, or more generally, of all genders, although most current implementations are binary due to limitations in detection and annotation tools). The core mathematical formulation for a category $i$ within domain $d$ is:

$$\text{DS-GSI}_d = \frac{1}{N} \sum_{i=1}^N |2p_i - 1|$$

where $N$ is the number of categories (e.g., professions, academic disciplines, sports), and $p_i$ is the observed proportion of female representations (or outputs identified as female) in category $i$. Values near 1 indicate a strong gender skew; values near 0 indicate balanced parity (Kalhor et al., 24 Sep 2025).

The DS-GSI is explicitly domain-adaptive: the relevant “domain” may be a semantic category (e.g., professions), a textual corpus (e.g., Wikipedia biographies, computer science publications, textbooks), or the set of outputs from a LLM under specific prompts.

2. Methodologies for DS-GSI Calculation

Calculation of DS-GSI is highly dependent on the data type and linguistic context. Core methodologies include:

• Template-Based Probing: Controllable prompts generate outputs from LLMs, with gender assignment of generated entities (e.g., names) inferred using tools such as Genderize.io or NamSor (Kalhor et al., 24 Sep 2025). The output gender distribution is then compared to parity.
• Corpus-Based Quantification: In textual corpora, all gender-relevant references are identified (using NLP pipelines, LLM-driven parsing, or lexicon-based approaches). Person-referring nouns and pronouns are extracted and classified by gender, often using part-of-speech tagging and named entity recognition, sometimes augmented with few-shot prompting of LLMs for higher accuracy in distinguishing between personal and nonpersonal, and masculine/feminine references (Derner et al., 19 Jun 2024).
• Index Construction by Ratios: Classic indices such as the Wikipedia Gender Index (WIGI) count the number of female (or nonbinary) entries over total entries per region or time period, e.g., $$\text{femaleratio} = N_{\text{female}} / N_{\text{total}}$$ (Klein et al., 2015). This ratio can be applied to any sufficiently annotated domain corpus; its adaptation as DS-GSI involves restricting the calculation to well-defined domain subsets.
• Probabilistic and Embedding Methods: When quantifying gender associations for words or entities, bias metrics may employ vector-space similarity measures (e.g., cosine similarity of embedding vectors to gender-defining clusters), topic or entropy measures (Shannon entropy to gauge diversity), or statistical classification (e.g., SVM-based direction removal in embeddings to disentangle grammatical from social gender bias) (Sabbaghi et al., 2022, Hajibabaei et al., 2021).
• Hybrid and Robust Estimation: In contexts where ground truth is unknown, global inference strategies leverage the joint distribution of all names in a data set, imposing self-consistency constraints for robust group-level gender estimation without sample bias under strong skew (Antonoyiannakis et al., 2023).

Table: Representative Calculation Approaches

Methodology	Input Type	Gender Assignment
Template-Based Probing	LLM Outputs	Automated tools + prompts
Corpus-Based Quantification	Text corpora	Lexicon/LLM/NER
Ratio Index (e.g., WIGI)	Structured metadata	Database-annotated
Embedding-Based	Word embeddings	Projection/classification
Global Inference (gGEM)	Name lists	Population-level stats

3. Domain and Cultural Adaptability

DS-GSI is explicitly designed for domain specificity and cultural adaptability:

• Semantic Domains: The metric can be applied separately to academic disciplines, professions, sports, or any defined set of semantic categories, revealing granular patterns (e.g., sports domains consistently display the most rigid gender skews in LLM outputs) (Kalhor et al., 24 Sep 2025).
• Language and Culture: In linguistically gendered languages (e.g., Persian, Spanish), the DS-GSI must account for grammatical gender and sociolinguistic usage. Studies have shown that low-resource languages can display stronger gender skews than high-resource ones, underscoring the need for language-specific probing and metric adaptation (Kalhor et al., 24 Sep 2025).
• Cross-Cultural Comparison: Aggregating and comparing DS-GSI across regions or cultural clusters enables analysis of heterogeneity, as seen in Wikipedia biography parity trends by Inglehart-Welzel clusters (Klein et al., 2015).
• Corpus and Output Contexts: DS-GSI can be used to compare the gender skew in source corpora (e.g., textbooks, academic databases) and resultant model outputs, revealing how upstream data biases propagate (Derner et al., 19 Jun 2024, Liu, 3 Jun 2025).

4. Empirical Results and Patterns

Empirical applications of DS-GSI and related indices have revealed several robust findings:

• Marked Gender Skew: All evaluated domains display strong gender skews, often far from parity, with ratios in some scenarios (e.g., Spanish parliamentary corpora) reaching as high as 6:1 male to female (Derner et al., 19 Jun 2024).
• Domain-Heterogeneous Patterns: DS-GSI surfaced pronounced gender imbalances in certain domains—sports and technical professions being the most polarized—while others may show partial mitigation due to domain characteristics or data curation strategies.
• Language and Cultural Effects: The metric often reveals greater skew in low-resource or highly gendered languages, and considerable variation between cultural-linguistic clusters in textbook analysis (Liu, 3 Jun 2025, Kalhor et al., 24 Sep 2025).
• Temporal Trends: Longitudinal monitoring, as in WIGI, demonstrates slow but steady improvements in many domains but persistent inequalities overall (Klein et al., 2015).

5. Limitations, Calibration, and Future Directions

Current implementations and empirical findings highlight several limitations and challenges for DS-GSI:

• Binary Gender Assumptions: Most metrics to date assume a male-female binary, due to detection and annotation limitations; expansion to nonbinary categories is a key avenue for future work (Antonoyiannakis et al., 2023).
• Bias in Underlying Tools: Gender detection methods themselves introduce bias, particularly around names that have shifted gender associations over time or are under-represented in reference databases. Empirical studies have shown overestimation or undercounting of female representation, dramatically affecting DS-GSI values (Misa, 2022, Karimi et al., 2016).
• Frequency Dependence in Embedding Metrics: Embedding-based DS-GSI calculations are sensitive to word frequency, potentially resulting in spurious male or female bias for high or low frequency words, suggesting Pointwise Mutual Information-based metrics as preferable alternatives (Valentini et al., 2023).
• Calibration to Established Indices: Cross-validation with established gender equality indices (e.g., GGGI, GEI, SIGI) is necessary to interpret DS-GSI outputs; calibration procedures ensure DS-GSI is not confounded by sampling artifacts or database coverage (Klein et al., 2015, Vela et al., 2021).
• Domain and Context Sensitivity: Adjusting for domain-specific notability criteria, reporting standards, and linguistic idiosyncrasies is essential for meaningful DS-GSI application.

Future work is anticipated in integrating richer gender annotations, context-aware and multilingual probing, dynamic weighting to handle underrepresented groups, and expansion of DS-GSI frameworks to encompass multi-dimensional or intersectional bias quantification.

6. Applications and Impact

DS-GSI serves a range of analytical and policy applications:

• LLM Auditing: Quantifies and tracks the degree to which LLM outputs for various prompts and tasks perpetuate gender bias, enabling targeted debiasing interventions (Kalhor et al., 24 Sep 2025, Zakizadeh et al., 2023).
• Corpus Curation: Reveals imbalances in training and evaluation datasets, guiding remediation strategies such as balanced augmentation (Muller et al., 2023, Derner et al., 19 Jun 2024).
• Cross-Domain and Cross-Linguistic Comparison: Facilitates benchmarking of academic disciplines, media, or educational materials for gender bias, controlling for local linguistic and cultural norms (Vela et al., 2021, Liu, 3 Jun 2025, Hajibabaei et al., 2021).
• Research Policy and Social Metrics: Informs science policy, diversity monitoring, and resource allocation for gender equity interventions based on empirical, quantitative indices.
• Temporal Monitoring: Enables longitudinal analysis of gender representation, assessing the efficacy of policies or social changes over time (Klein et al., 2015).

7. Summary Table of DS-GSI Attributes Across Key Studies

Study / Domain	Data Type	Key Metric	Main Findings
Wikipedia Biographies	Wikidata	Female ratio ($N_{\text{female}}/N_{\text{total}}$)	Exponential growth in parity
LLM Output (Persian)	Model generations	$\frac{1}{N} \sum |2p_i-1|$	High skew, esp. in sports/prof.
Textbooks (Global)	English textbooks	Male/female count, firstness, TF-IDF, embeddings	Universal male overrepresentation
Computer Science Papers	Authorship metadata	$(\# F - \# M + \# U) / \# \text{total}$	8.5x more all-male than all-female
AI Ecosystem	Publications/topics	Entropy, cosine similarity by gender	Homophily, lower diversity for females

References to Key Works

• “Probing Gender Bias in Multilingual LLMs: A Case Study of Stereotypes in Persian” (Kalhor et al., 24 Sep 2025)
• “Leveraging LLMs to Measure Gender Representation Bias in Gendered Language Corpora” (Derner et al., 19 Jun 2024)
• “Gender Gap Through Time and Space: A Journey Through Wikipedia Biographies and the 'WIGI' Index” (Klein et al., 2015)
• “A Geo-Gender Study of Indexed Computer Science Research Publications” (Vela et al., 2021)
• “Gender Inequality in English Textbooks Around the World: an NLP Approach” (Liu, 3 Jun 2025)
• “Measuring Gender Bias in Word Embeddings of Gendered Languages Requires Disentangling Grammatical Gender Signals” (Sabbaghi et al., 2022)
• “Global method for gender profile estimation from distribution of first names” (Antonoyiannakis et al., 2023)
• “Gender Bias in Big Data Analysis” (Misa, 2022)
• “The Undesirable Dependence on Frequency of Gender Bias Metrics Based on Word Embeddings” (Valentini et al., 2023)
• “Gender-Specific Patterns in the Artificial Intelligence Scientific Ecosystem” (Hajibabaei et al., 2021)
• “Inferring Gender from Names on the Web: A Comparative Evaluation of Gender Detection Methods” (Karimi et al., 2016)
• “DiFair: A Benchmark for Disentangled Assessment of Gender Knowledge and Bias” (Zakizadeh et al., 2023)
• “The Gender-GAP Pipeline: A Gender-Aware Polyglot Pipeline for Gender Characterisation in 55 Languages” (Muller et al., 2023)
• “Easy Adaptation to Mitigate Gender Bias in Multilingual Text Classification” (Huang, 2022)
• “Stereotype and Skew: Quantifying Gender Bias in Pre-trained and Fine-tuned LLMs” (Manela et al., 2021)

The DS-GSI provides a versatile, empirically grounded framework for rigorous gender bias assessment across domains, facilitating both analytic insight and policy response in computational and social science research.