Appendix B · Correlations

Appendix B: correlations

This section presents the complete matrix of Spearman correlations among the 13 composite variables of the instrument. The thematic chapters extract subsets of this matrix for their predictor rankings. Here we offer the integral view for consultation and further research.

Construction of the 13 variables

The correlations are computed among 13 composite variables, each representing a dimension of the instrument.

VariableSourceScale
InfrastructureMean of 5 Likert items Q12/Q171-5 (agreement)
Professional adaptationMean of 3 Likert items Q17/Q211-5 (agreement)
EfficiencyMean of 5 Likert items Q18/Q221-5 (agreement)
Client experienceMean of 5 Likert items Q21/Q251-5 (agreement)
AI impactMean of 5 Likert items Q26/Q301-5 (agreement)
Ethical practicesMean of 4 Likert items Q27/Q311-5 (frequency)
KPI maturitySingle item Q6/Q81-5 (maturity)
KnowledgeSingle item Q15/Q191-5 (level)
Digitalization (%)Single item Q13/Q160-4 (% range)
TrainingMean of 14 topics Q16/Q200-4 (frequency)
Tool usageMean of 15 tools Q11/Q130-5 (usage)
AI tool usageMean of 11 AI tools Q25/Q290-5 (usage)
Adoption IndexComposite summative scaleobserved range 38-279

Method: Spearman correlation (ρ), two-tailed, α=0.05. Spearman was chosen over Pearson because of the ordinal nature of the Likert scales.

Correlation matrix (Law firms, n=72)

Infra.Herram.Herram. IACapacit.KPIConocim.Digital. %EfficiencyClienteImpacto IAEthicsAdapt.Index Infra. 1.00 0.23 0.19 0.40✱ 0.31✱ 0.32✱ 0.19 0.37✱ 0.31✱ 0.30✱ 0.44✱ 0.21 0.37✱ Herram. 0.23 1.00 0.45✱ 0.62✱ 0.63✱ 0.58✱ 0.09 0.46✱ 0.40✱ 0.41✱ 0.35✱ 0.10 0.73✱ Herram. IA 0.19 0.45✱ 1.00 0.39✱ 0.34✱ 0.50✱ -0.02 0.41✱ 0.47✱ 0.44✱ 0.33✱ 0.22 0.63✱ Capacit. 0.40✱ 0.62✱ 0.39✱ 1.00 0.59✱ 0.58✱ 0.03 0.49✱ 0.39✱ 0.31✱ 0.38✱ 0.00 0.66✱ KPI 0.31✱ 0.63✱ 0.34✱ 0.59✱ 1.00 0.59✱ 0.06 0.35✱ 0.33✱ 0.38✱ 0.54✱ 0.13 0.60✱ Conocim. 0.32✱ 0.58✱ 0.50✱ 0.58✱ 0.59✱ 1.00 0.17 0.48✱ 0.55✱ 0.53✱ 0.41✱ 0.07 0.73✱ Digital. % 0.19 0.09 -0.02 0.03 0.06 0.17 1.00 0.05 0.31✱ 0.26 0.16 -0.20 0.07 Efficiency 0.37✱ 0.46✱ 0.41✱ 0.49✱ 0.35✱ 0.48✱ 0.05 1.00 0.68✱ 0.54✱ 0.33✱ 0.06 0.63✱ Cliente 0.31✱ 0.40✱ 0.47✱ 0.39✱ 0.33✱ 0.55✱ 0.31✱ 0.68✱ 1.00 0.60✱ 0.41✱ -0.06 0.56✱ Impacto IA 0.30✱ 0.41✱ 0.44✱ 0.31✱ 0.38✱ 0.53✱ 0.26 0.54✱ 0.60✱ 1.00 0.26 0.13 0.64✱ Ethics 0.44✱ 0.35✱ 0.33✱ 0.38✱ 0.54✱ 0.41✱ 0.16 0.33✱ 0.41✱ 0.26 1.00 0.17 0.54✱ Adapt. 0.21 0.10 0.22 0.00 0.13 0.07 -0.20 0.06 -0.06 0.13 0.17 1.00 0.10 Index 0.37✱ 0.73✱ 0.63✱ 0.66✱ 0.60✱ 0.73✱ 0.07 0.63✱ 0.56✱ 0.64✱ 0.54✱ 0.10 1.00
−1 +1 ✱ significant (p < 0.05)

Correlation matrix (Legal departments, n=39)

Infra.Herram.Herram. IACapacit.KPIConocim.Digital. %EfficiencyClienteImpacto IAEthicsAdapt.Index Infra. 1.00 0.07 0.36 0.25 0.09 0.24 -0.02 0.11 0.23 0.14 0.28 0.05 0.13 Herram. 0.07 1.00 0.45✱ 0.39✱ 0.61✱ 0.39✱ 0.20 0.24 0.57✱ 0.38✱ 0.39✱ -0.10 0.76✱ Herram. IA 0.36 0.45✱ 1.00 0.69✱ 0.25 0.41✱ 0.04 0.25 0.33 0.69✱ 0.47✱ -0.23 0.69✱ Capacit. 0.25 0.39✱ 0.69✱ 1.00 0.30 0.37✱ 0.14 0.27 0.44✱ 0.48✱ 0.63✱ -0.19 0.56✱ KPI 0.09 0.61✱ 0.25 0.30 1.00 0.46✱ 0.28 0.27 0.53✱ 0.20 0.38✱ -0.06 0.53✱ Conocim. 0.24 0.39✱ 0.41✱ 0.37✱ 0.46✱ 1.00 0.37✱ 0.39✱ 0.50✱ 0.35 0.44✱ -0.06 0.55✱ Digital. % -0.02 0.20 0.04 0.14 0.28 0.37✱ 1.00 -0.04 0.17 -0.04 0.08 -0.24 0.12 Efficiency 0.11 0.24 0.25 0.27 0.27 0.39✱ -0.04 1.00 0.48✱ 0.43✱ 0.26 0.10 0.33✱ Cliente 0.23 0.57✱ 0.33 0.44✱ 0.53✱ 0.50✱ 0.17 0.48✱ 1.00 0.56✱ 0.42✱ -0.06 0.56✱ Impacto IA 0.14 0.38✱ 0.69✱ 0.48✱ 0.20 0.35 -0.04 0.43✱ 0.56✱ 1.00 0.48✱ 0.04 0.62✱ Ethics 0.28 0.39✱ 0.47✱ 0.63✱ 0.38✱ 0.44✱ 0.08 0.26 0.42✱ 0.48✱ 1.00 -0.28 0.70✱ Adapt. 0.05 -0.10 -0.23 -0.19 -0.06 -0.06 -0.24 0.10 -0.06 0.04 -0.28 1.00 -0.18 Index 0.13 0.76✱ 0.69✱ 0.56✱ 0.53✱ 0.55✱ 0.12 0.33✱ 0.56✱ 0.62✱ 0.70✱ -0.18 1.00
−1 +1 ✱ significant (p < 0.05)

Significance summary

Of 156 pairs analyzed, 89 are significant (p < 0.05), that is 57%. In law firms, 53 of 78 (68%). In legal departments, 36 of 78 (46%).

The correlation structure is much denser in law firms than in legal departments. This suggests that in law firms, the dimensions of technology adoption form a more integrated ecosystem (improving one dimension tends to correlate with improvements in the others). In legal departments, the structure is more fragmented, possibly because technology decisions are distributed between the legal department and the corporate IT areas.

The 5 strongest correlations per dataset

Law firms

  • Conocim. ↔ Index: ρ=0.731 (p=<0.0001)
  • Herram. ↔ Index: ρ=0.729 (p=<0.0001)
  • Efficiency ↔ Cliente: ρ=0.681 (p=<0.0001)
  • Capacit. ↔ Index: ρ=0.661 (p=<0.0001)
  • Impacto IA ↔ Index: ρ=0.637 (p=<0.0001)

Legal departments

  • Herram. ↔ Index: ρ=0.760 (p=<0.0001)
  • Ethics ↔ Index: ρ=0.703 (p=<0.0001)
  • Impacto IA ↔ Herram. IA: ρ=0.695 (p=0.0001)
  • Herram. IA ↔ Index: ρ=0.692 (p=0.0001)
  • Capacit. ↔ Herram. IA: ρ=0.687 (p=0.0002)

Complete table of significant correlations

The 89 significant correlations, ordered by strength (|ρ|).

PopulationVariable AVariable Bρpn
Legal departments Herram.Index 0.760 <0.0001 39
Law firms Conocim.Index 0.731 <0.0001 72
Law firms Herram.Index 0.729 <0.0001 72
Legal departments EthicsIndex 0.703 <0.0001 28
Legal departments Impacto IAHerram. IA 0.695 0.0001 25
Legal departments Herram. IAIndex 0.692 0.0001 25
Legal departments Capacit.Herram. IA 0.687 0.0002 24
Law firms EfficiencyCliente 0.681 <0.0001 71
Law firms Capacit.Index 0.661 <0.0001 72
Law firms Impacto IAIndex 0.637 <0.0001 53
Law firms Herram. IAIndex 0.634 <0.0001 53
Law firms EfficiencyIndex 0.631 <0.0001 71
Legal departments EthicsCapacit. 0.627 0.0005 27
Law firms KPIHerram. 0.626 <0.0001 72
Law firms Capacit.Herram. 0.620 <0.0001 72
Legal departments Impacto IAIndex 0.616 0.0005 28
Legal departments KPIHerram. 0.607 <0.0001 39
Law firms ClienteImpacto IA 0.600 <0.0001 53
Law firms KPIIndex 0.598 <0.0001 72
Law firms KPIConocim. 0.594 <0.0001 72
Law firms KPICapacit. 0.591 <0.0001 72
Law firms Conocim.Capacit. 0.579 <0.0001 72
Law firms Conocim.Herram. 0.578 <0.0001 72
Legal departments ClienteHerram. 0.570 0.0002 39
Law firms ClienteIndex 0.565 <0.0001 72
Legal departments ClienteImpacto IA 0.563 0.0018 28
Legal departments ClienteIndex 0.562 0.0002 39
Legal departments Capacit.Index 0.561 0.0003 38
Legal departments Conocim.Index 0.550 0.0003 39
Law firms ClienteConocim. 0.549 <0.0001 72
Law firms EthicsIndex 0.540 <0.0001 53
Law firms EfficiencyImpacto IA 0.537 <0.0001 52
Law firms EthicsKPI 0.536 <0.0001 53
Legal departments ClienteKPI 0.533 0.0005 39
Legal departments KPIIndex 0.531 0.0005 39
Law firms Impacto IAConocim. 0.529 <0.0001 53
Legal departments ClienteConocim. 0.502 0.0011 39
Law firms Conocim.Herram. IA 0.497 0.0002 53
Law firms EfficiencyCapacit. 0.488 <0.0001 71
Legal departments Impacto IACapacit. 0.483 0.0107 27
Law firms EfficiencyConocim. 0.482 <0.0001 71
Legal departments EfficiencyCliente 0.477 0.0028 37
Legal departments Impacto IAEthics 0.477 0.0104 28
Law firms ClienteHerram. IA 0.474 0.0003 53
Legal departments EthicsHerram. IA 0.471 0.0176 25
Law firms EfficiencyHerram. 0.461 0.0001 71
Legal departments KPIConocim. 0.460 0.0032 39
Law firms Herram.Herram. IA 0.453 0.0007 53
Legal departments Herram.Herram. IA 0.447 0.0252 25
Law firms Impacto IAHerram. IA 0.444 0.0009 53
Legal departments ClienteCapacit. 0.444 0.0052 38
Legal departments EthicsConocim. 0.443 0.0184 28
Law firms Infra.Ethics 0.436 0.0012 52
Legal departments EfficiencyImpacto IA 0.426 0.0267 27
Legal departments ClienteEthics 0.418 0.0268 28
Law firms ClienteEthics 0.414 0.0021 53
Legal departments Conocim.Herram. IA 0.413 0.0403 25
Law firms Impacto IAHerram. 0.410 0.0023 53
Law firms EfficiencyHerram. IA 0.410 0.0026 52
Law firms EthicsConocim. 0.407 0.0025 53
Law firms ClienteHerram. 0.399 0.0005 72
Law firms Infra.Capacit. 0.396 0.0006 71
Law firms ClienteCapacit. 0.395 0.0006 72
Legal departments EthicsHerram. 0.391 0.0395 28
Legal departments EfficiencyConocim. 0.390 0.0171 37
Law firms Capacit.Herram. IA 0.388 0.0041 53
Legal departments Conocim.Herram. 0.386 0.0151 39
Legal departments Capacit.Herram. 0.386 0.0166 38
Law firms EthicsCapacit. 0.379 0.0051 53
Legal departments EthicsKPI 0.378 0.0476 28
Legal departments Impacto IAHerram. 0.377 0.0482 28
Law firms Impacto IAKPI 0.375 0.0057 53
Law firms Infra.Index 0.370 0.0015 71
Legal departments Conocim.Digital. % 0.369 0.0208 39
Legal departments Conocim.Capacit. 0.366 0.0240 38
Law firms Infra.Efficiency 0.365 0.0017 71
Law firms EfficiencyKPI 0.348 0.0029 71
Law firms EthicsHerram. 0.345 0.0114 53
Law firms KPIHerram. IA 0.336 0.0140 53
Law firms EfficiencyEthics 0.332 0.0161 52
Legal departments EfficiencyIndex 0.330 0.0462 37
Law firms EthicsHerram. IA 0.326 0.0173 53
Law firms ClienteKPI 0.325 0.0053 72
Law firms Infra.Conocim. 0.319 0.0066 71
Law firms Infra.Cliente 0.311 0.0084 71
Law firms Impacto IACapacit. 0.308 0.0247 53
Law firms Infra.KPI 0.307 0.0091 71
Law firms ClienteDigital. % 0.305 0.0091 72
Law firms Infra.Impacto IA 0.304 0.0286 52

Patterns that emerge from the complete matrix

  1. Professional adaptation is orthogonal: it has no significant correlation with any other variable in either dataset. It is a construct of professional values independent of the technology adoption dimension.
  2. Digitalization (%) predicts nothing: the reported percentage of digitized documents does not correlate significantly with efficiency, client experience, or the Adoption Index. Digitalization without process transformation is an empty metric.
  3. The efficiency ↔ client cycle (ρ=0.681): it is the strongest inter-block correlation in law firms, suggesting a virtuous feedback cycle.
  4. Infrastructure decoupled in legal departments: it does not correlate significantly with any variable in legal departments (IT infrastructure is corporate, not owned by the legal department).
  5. Correlation density differs: law firms have considerably more significant pairs than legal departments (53 versus 36), indicating a more integrated adoption ecosystem in law firms.

Corrected item-total correlation of the Adoption Index

Because the Adoption Index sums its components, correlating each component with the full index inflates it by construction (part-whole correlation). The table below reports, for each component, the raw correlation (against the full index) and the corrected one (against the index excluding that component). The corrected version is the one used by the Index chapter.

PopulationComponentρ rawρ correctedΔ (inflation)Strength (corrected)Sig.
Law firms Conocim. 0.731 0.724 0.006 strong ✱
Law firms Herram. 0.729 0.631 0.098 strong ✱
Law firms Efficiency 0.631 0.621 0.010 strong ✱
Law firms Impacto IA 0.637 0.592 0.045 moderate ✱
Law firms KPI 0.598 0.588 0.009 moderate ✱
Law firms Capacit. 0.661 0.564 0.097 moderate ✱
Law firms Herram. IA 0.634 0.560 0.074 moderate ✱
Law firms Cliente 0.565 0.532 0.033 moderate ✱
Law firms Ethics 0.540 0.467 0.073 moderate ✱
Law firms Infra. 0.370 0.382 -0.012 weak ✱
Law firms Adapt. 0.100 0.072 0.028 very weak —
Law firms Digital. % 0.075 0.053 0.022 very weak —
Legal departments Ethics 0.703 0.617 0.087 strong ✱
Legal departments Herram. 0.760 0.594 0.166 moderate ✱
Legal departments Impacto IA 0.616 0.536 0.080 moderate ✱
Legal departments Conocim. 0.550 0.534 0.016 moderate ✱
Legal departments Herram. IA 0.692 0.534 0.159 moderate ✱
Legal departments Cliente 0.562 0.524 0.037 moderate ✱
Legal departments KPI 0.531 0.523 0.008 moderate ✱
Legal departments Capacit. 0.561 0.435 0.126 moderate ✱
Legal departments Efficiency 0.330 0.261 0.069 weak —
Legal departments Infra. 0.132 0.151 -0.019 very weak —
Legal departments Digital. % 0.116 0.084 0.032 very weak —
Legal departments Adapt. -0.178 -0.195 0.017 very weak —

The components with the greatest inflation (Δ) are, logically, those with the greatest weight in the index (tool usage, AI usage, training). After correction, the team's knowledge remains the strongest predictor in law firms, and in legal departments ethical practices and tool usage emerge as the most central factors.

Profile, maturity and adoption correlations

At the request of the editorial committee, additional relationships were computed among profile variables (size, budget), management maturity (KPI, knowledge) and AI adoption.

PopulationRelationshipρpnStrengthSig.
Law firms Firm size ↔ % tech budget 0.059 0.6399 66 very weak —
Law firms Firm size ↔ KPI maturity 0.442 0.0001 72 moderate ✱
Law firms % tech budget ↔ KPI maturity 0.426 0.0004 66 moderate ✱
Law firms Knowledge ↔ % tech budget 0.534 <0.0001 66 moderate ✱
Law firms Knowledge ↔ KPI maturity 0.594 <0.0001 72 moderate ✱
Law firms Implemented AI ↔ KPI maturity 0.196 0.0994 72 very weak —
Law firms Implemented AI ↔ knowledge 0.327 0.0051 72 weak ✱
Legal departments Company size ↔ legal department size 0.431 0.0070 38 moderate ✱
Legal departments Legal department size ↔ % tech budget -0.144 0.4100 35 very weak —
Legal departments Legal department size ↔ KPI maturity 0.237 0.1516 38 weak —
Legal departments % tech budget ↔ KPI maturity 0.322 0.0558 36 weak —
Legal departments Knowledge ↔ % tech budget 0.391 0.0182 36 weak ✱
Legal departments Knowledge ↔ KPI maturity 0.460 0.0032 39 moderate ✱
Legal departments Implemented AI ↔ KPI maturity 0.165 0.3358 36 very weak —
Legal departments Implemented AI ↔ knowledge 0.184 0.2836 36 very weak —

Reading these correlations

  • The team's knowledge is related to management maturity (with KPI maturity and with the % of budget in technology), in both audiences. Knowing more goes hand in hand with measuring better and investing more.
  • Size does not determine technology investment: the relationship between size and % of technology budget is very weak. Large and small organizations invest in similar proportions.
  • Having implemented AI is related only weakly to management maturity or knowledge: AI adoption is fairly spread out and is not exclusive to the organizations most mature in metrics.
  • Underuse: among those who have already adopted AI, only around 1 in 5 uses it daily, and a relevant proportion does not evaluate its ethical risks consistently (see the AI chapter).

Concentration by organization type

The questionnaire does not include a direct classification of "boutique vs. full-service" for law firms. As an approximation, we use the number of practice areas that each firm declares (more areas ≈ full-service profile). For legal departments, the requested equivalent is the type of industry, which does exist but with very small cells (several industries have 1–2 respondents), so it only supports a descriptive and exploratory reading, not significance tests.

Law firms, "full-service" profile (no. of practice areas) versus maturity:

RelationshipρpStrengthSig.
No. of practice areas ↔ KPI maturity 0.427 0.0002 moderate ✱
No. of practice areas ↔ Knowledge 0.233 0.0490 weak ✱
No. of practice areas ↔ % tech budget 0.116 0.3545 very weak —

Firms with more practice areas (a more full-service profile) tend to have greater metrics maturity (moderate relationship) and somewhat more knowledge. With budget the relationship is very weak. It is a signal of concentration, with the caveat that it is a proxy, not a declared classification.

Legal departments, profile by industry (descriptive, small cells):

IndustrynMean KPI (1-5)Mean knowledge (1-5)Budget (ord. 0-3)Legal size (ord.)
Otro12 2.252.58 1.421.50
Otras (n<3)9 3.112.33 1.251.56
Servicios financieros7 2.141.71 1.603.00
Technology (software, hardware)4 2.503.25 2.001.00
Food and beverage4 3.254.00 2.501.50
Pharmaceutical3 2.003.00 1.001.00

With these caveats, no marked concentration of KPI maturity or of budget in a specific industry is observed. The largest visible difference is that financial services tends to have larger legal departments, while sectors such as food and beverage or technology report greater self-assessed knowledge. It is offered as exploration, not as a confirmed finding.

Method bias in the efficiency ↔ client link (CMV)

The efficiency ↔ client experience correlation is the strongest in the study, but both variables come from the same respondent, same instrument and same session, and in law firms part of it does not genuinely measure client satisfaction (the variable captures the partner's belief, not measured satisfaction). To gauge the risk of common method variance, we compared those who measure satisfaction against those who do not:

GroupnMean efficiencyMean client exp.ρ efficiency↔clientStrength
Measures satisfaction48 3.583.53 0.734strong
Does not measure / does not know24 3.303.23 0.559moderate

About a third of law firms do not measure client satisfaction (or do not know), and none use NPS. The efficiency ↔ client relationship persists even among those who do not measure satisfaction, which confirms that part of its strength is a method artifact (two perceptions of the same respondent) rather than a purely empirical link. That is why, throughout the report this relationship is described as an association that "goes hand in hand", avoiding causal language.

How to cite

Prince Tritto, P., Villa Berger, P., Salmon, L., Muñoz Ponce, M., & Limón González, J. B. (2026). Technology Maturity Index for the Legal Industry: pilot study (data from Mexico, 2025). Law and Artificial Intelligence Laboratory, Universidad Panamericana; KermaPartners; Lemontech. https://labderia.up.edu.mx/en/legaltech-report