Osijek, Croatia  ·  Established 2021

Research that has to hold up.

PEZ is the statistical practice of prof. dr. sc. Tena Velki — instrument validation, prevalence studies, mediation and moderation models, predictive and multivariate modelling for teams whose results will be reviewed, published, and acted on.

Risk & protective factors X Stress M Online risky behaviour Y a b c′
Fig. 1 — Simple mediation model. Indirect effect a×b tested by bootstrapped confidence interval.
After Velki & Milić (2021), Primenjena psihologija.
40+Peer-reviewed papers,
books & proceedings
12Research projects led
or analysed
5Measurement instruments
built or standardised
2012PhD in psychology,
University of Zagreb
A number is only as good as the instrument that produced it.

Much of this practice starts one step earlier than the analysis: checking that the questionnaire measures what it claims to, in this language, in this population. Five instruments have been developed, validated or standardised for Croatian use — and one has since been validated in Slovenian and tested against German samples.

About Tena Velki

How an engagement runs

01

Scope

A short call or email exchange about your research question, your sample, and your deadline. You get a written note on what is answerable with the data you have — and what would need to change if it isn’t.

02

Design

Before collection: sampling, power, instrument choice or adaptation, and a pre-specified analysis plan. This is the cheapest stage to fix a study and the most expensive one to skip.

03

Analysis

Data cleaning, assumption checks, the modelling itself, and the alternatives that were tested and rejected. Syntax files are kept so every result can be reproduced exactly.

04

Reporting & defence

Tables and figures formatted to APA or your journal’s template, a written interpretation in plain language, and support through peer review — including reviewers’ statistical comments.

About

prof. dr. sc.
Tena Velki

Psychologist · Full Professor · Owner of PEZ

I am a Full Professor of psychology at the Faculty of Education, Josip Juraj Strossmayer University of Osijek, and I have spent the past fifteen years doing the statistical work behind other people’s research as well as my own.

PEZ began in 2021 because the same request kept arriving: a team had collected good data and needed someone who could model it properly, explain what the model does and does not license them to say, and stay with the paper through review. That is the whole practice.

My own research covers peer violence and bullying, ADHD in the school environment, developmental screening in preschoolers, school climate, and the human side of information security. Across all of it, the recurring problem has been measurement — whether an instrument travels intact into another language, another age group, another country. Five instruments have come out of that work, including the Behavioural-Cognitive Internet Security Questionnaire, now validated in Slovenian and tested against German samples.

I teach statistics as well as use it. I founded three statistics courses at the University of Osijek, including the doctoral-level course in statistical analysis for the social sciences, and wrote the Croatian textbook on multivariate multilevel modelling. That matters for clients: an analysis you cannot explain to a reviewer, a ministry or a school board is not finished.

prof. dr. sc. Tena Velki

Appointments & education

2023 →
Full Professor of psychologyFaculty of Education, Josip Juraj Strossmayer University of Osijek
2021 →
Founder and owner, PEZStatistical consulting, research and education, Osijek
2018 – 2023
Associate Professor of psychologyFaculty of Education, University of Osijek · vice-dean for science, two terms
2013 – 2018
Assistant Professor of developmental psychologyFaculty of Education, University of Osijek
2008 – 2012
PhD in psychologyFaculty of Humanities and Social Sciences, University of Zagreb · EQF level 8
2003 – 2008
Master of PsychologyFaculty of Social Sciences, University of Osijek · EQF level 7

Methods training

2024
Structural equation modellingUniversity of Primorska, Koper · 12-day Erasmus+ training
2022
Instrument development & validationFaculty of Health Sciences, University of Primorska, Izola · 15 days
2019
Cyberpsychology & cybersecurityMasaryk University, Brno · 9 days
2018
R for psychological researchInstitute of Psychology, RWTH Aachen · 15 days

Recognition

2019
Best published scientific work, two-year periodFaculty of Philosophy, Novi Sad & the journal Applied Psychology
2018
„Marulić: Fiat Psychologia“Croatian Psychological Association, for contribution to applied psychology
2017
Croatian Psychological Association awardFor contribution to the Week of Psychology in Croatia
2016
UNESCO scholarship, WarsawInvited lecturer, UNESCO summer school

Software

SPSS advancedJASP advancedjamovi advanced AMOS SEMRPythonTableauExcel advanced

Working languages

Croatian nativeEnglish C2 · Cambridge AdvancedCroatian sign language B1

Teaching & professional roles

  • Founder of three statistics courses at the University of Osijek, including Basic statistical analysis in the social sciences at doctoral level (2022) and Data analysis using SPSS (2017)
  • Author of Multivariate multilevel modelling: application options in the social sciences (Osijek, 2020)
  • President of the Association of Psychologists Osijek since 2022, previously vice-president and secretary for ten years
  • Member of the Croatian Psychological Chamber, the Croatian Psychological Association and the European Federation of Psychologists’ Associations
  • Member of organising and scientific committees for national and international conferences

Services

What I can
take off your desk.

Engagements run from a two-hour consultation on a single model to full analytical partnership on a multi-year project. Every one includes the syntax, so the analysis stays reproducible after I hand it over.

01  /  Psychometrics

Psychological instrument validation

You have a questionnaire — newly written, translated from English, or borrowed from another field — and you need evidence that it measures what it claims to measure, in your language and your population. This is the most common reason people come to PEZ, and the area where five instruments now carry my name.

  • Item generation and expert review; pilot testing and item analysis
  • Exploratory and confirmatory factor analysis; competing factor structures compared
  • Reliability across the appropriate coefficients, not just Cronbach’s alpha out of habit
  • Convergent, divergent and criterion validity against established measures
  • Measurement invariance across gender, age, education level or country before any group is compared
  • Translation and cross-cultural adaptation, including back-translation protocols
  • Norms and standardisation for Croatian populations
You receive

A validation report with the full psychometric evidence, the final scored version of the instrument with its scoring key, and a methods section ready to submit.

02  /  Epidemiology of behaviour

Prevalence studies

How many, among whom, and how sure can we be? Prevalence work is where a sampling mistake is invisible in the output and fatal in the conclusion. I design the study so the estimate is defensible before anyone starts collecting.

  • Sampling frames, stratification and realistic power calculations
  • Prevalence and incidence estimates with confidence intervals, weighted where the sample requires it
  • Subgroup breakdowns by age, gender, county, school type or sector
  • Trend comparison against earlier waves and against national or EU benchmarks
  • Public-facing reports for institutions, county authorities and ministries
You receive

A full statistical report with tables and figures, an executive summary written for non-statisticians, and the underlying dataset documented and cleaned.

03  /  Process models

Mediation and moderation models

Knowing that X predicts Y is rarely the interesting part. The question is what carries the effect and for whom it holds — the mechanism and the boundary condition. These models are easy to run and easy to over-claim from; the value is in specifying them honestly.

  • Simple, serial and parallel mediation with bootstrapped indirect effects
  • Moderation and moderated mediation; conditional process models
  • Johnson–Neyman regions of significance rather than arbitrary median splits
  • Latent-variable mediation in SEM when measurement error would otherwise bias the estimate
  • Honest treatment of causal language: what a cross-sectional mediation model can and cannot support
You receive

Path diagrams, coefficient tables with confidence intervals and effect sizes, and a written interpretation that says what follows from the model and what does not.

04  /  Prediction

Statistical models of prediction

Which variables actually carry weight once the others are accounted for, how much variance they explain, and whether the same predictors work in different groups. This is the backbone of most applied research questions in education, health and organisational settings.

  • Multiple, hierarchical and logistic regression with full assumption diagnostics
  • Multilevel models for pupils within classes, staff within institutions, repeated measures within people
  • Multivariate multilevel modelling — the subject of my Croatian textbook on the method
  • Discriminant analysis and classification; risk-group identification
  • Model comparison, cross-validation and honest reporting of overfitting risk
You receive

Model comparison tables, diagnostics, effect sizes, and a clear statement of which predictors survived and how much practical difference they make.

05  /  Human factors in security

Consultation and data analysis for cybersecurity

Technical controls fail at the person using them. Since 2015 I have worked with information-security researchers and engineers to measure the behavioural side: what users actually do with passwords, devices and links, how aware they believe they are, and how far apart those two things sit.

  • Security-awareness and risky-behaviour measurement using validated instruments — UISAQ and BCISQ, both developed here
  • Studies comparing self-assessed risk against measured real behaviour
  • Sector-specific assessment: healthcare staff, university and school populations, ICT system users, employees
  • Cross-country comparison and translation of security instruments
  • Statistical support for engineering and informatics teams publishing in IEEE, MIPRO and applied security journals
  • Interpretation for management: which awareness gaps predict which behaviours, and where training changes outcomes
You receive

A measurement instrument suited to your population, the analysis, and a report that translates behavioural findings into security decisions.

06  /  Multivariate

Other multivariate analysis and modelling

The work that does not fit a standard label: several outcomes moving together, nested and longitudinal designs, latent structures, or a reviewer asking for a method the team has never run.

  • Structural equation modelling and path analysis
  • MANOVA, MANCOVA and repeated-measures designs
  • Cluster analysis and latent profile approaches for typologies
  • Longitudinal and cross-lagged models
  • Second opinions on an analysis already run, and responses to reviewers’ statistical objections
You receive

The analysis, the syntax, and a walkthrough so your team can defend and repeat it without me.

Ways to work together

Consultation

A focused session on one problem — a design decision, a model specification, a reviewer’s comment. Written summary afterwards so nothing is lost.

Full analysis

You hand over the data and the question. I return the cleaned dataset, the analysis, the syntax, and results formatted for your target journal or funder.

Project partnership

Named data analyst on the project from proposal to publication, including design, ethics documentation and co-authorship where the contribution warrants it.

Training

Workshops for research teams and doctoral students in SPSS, JASP, jamovi, multilevel modelling and SEM — taught with your data, not a textbook dataset.

Doctoral support

Methodological and statistical support for PhD candidates, from proposal design through to the defence. Support, not ghost-writing.

Instrument licensing

Use of validated instruments developed here, with scoring keys, norms and guidance on interpretation for your population.

Who this is for

University research teams · public health institutes and county authorities · schools, kindergartens and education agencies · NGOs running evaluated programmes · ICT and information-security groups · companies measuring employee behaviour · doctoral candidates.

Work is delivered in Croatian or English. Data-protection arrangements, ethics documentation and a signed confidentiality agreement are standard, not optional extras.

Ask about your project

Selected work

Projects, and
what came out of them.

Six engagements that show the range: an instrument that crossed three languages, a county-wide prevalence study, national monitoring for a ministry, and statistical support for an information-security group.

Instrument validation · Cybersecurity

BCISQ — an internet-security instrument that travels

With the Faculty of Electrical Engineering, Computer Science and IT, Osijek · 2015 → ongoing

Information-security researchers needed a way to measure what users actually do online, not only what they know. We built the Users’ Information Security Awareness Questionnaire, then the Behavioural-Cognitive Internet Security Questionnaire (BCISQ), through item generation, factor analysis and validation on student, secondary-school, healthcare and general ICT-user samples.

Outcome: BCISQ has since been cross-culturally validated in Slovenian, tested against German samples, and used in a study separating self-assessed risk from measured real online behaviour. Published in IJECES, Acta Polytechnica Hungarica, Elektrotehniški vestnik and Psychological Topics.
Standardisation · Developmental screening

ASQ-3 standardised for Croatian children

With Sveti Duh Clinical Hospital, Zagreb and the Catholic University of Croatia · 2016 – 2023

Croatian paediatric and preschool services were screening development with an instrument that had never been normed on a Croatian sample. Two consecutive projects — both led from here — validated and standardised the Ages & Stages Questionnaire for children aged three to five, and tested how far parents’ and preschool teachers’ assessments actually agree.

Outcome: Croatian norms published in Paediatria Croatica; the parent–teacher agreement study in Croatian Journal of Education. The screening tool is now usable in practice with population-appropriate cut-offs.
Prevalence study

Alcohol, gambling and technology addiction in Osijek-Baranja County

For the Teaching Institute of Public Health, Osijek-Baranja County · published 2024

A county-wide study of children and young people covering alcohol use, gambling and new-technology addiction: sampling design across school types, prevalence estimation with subgroup breakdowns, and interpretation aimed at people who allocate prevention budgets rather than at journal reviewers.

Outcome: A published county monograph used as the evidence base for local prevention planning.
National monitoring · Multilevel models

Croatian schools after the pandemic and the 2020 earthquake

Institute for Social Research in Zagreb, for the Ministry of Science and Education · 2021 – 2023

Two linked national projects tracked how the reorganisation of teaching affected the wellbeing, experience and aspirations of pupils and staff. The analytical problem was structure: pupils nested in classes nested in schools, repeated waves, and several outcomes moving together.

Outcome: Findings delivered to the Ministry and presented as a symposium at the Croatian psychologists’ annual conference, including work on media exposure, mental health and social-environment preference.
Applied research · Cybersecurity

Safer Internet Centre Croatia — national security research

Project leader for the Faculty of Education · 2016 – 2018

An EU-supported programme building a hotline, an awareness centre and systematic education for safer internet use by children. My part was the national research strand: measuring risky behaviour and security knowledge across age groups and feeding the results back into what the awareness centre actually taught.

Outcome: National results presented at plenary level; the Handbook for Information Security and Privacy (2018) and The Challenges of the Digital World (2019) edited and published from the project.
Prediction models · Education

Teacher expertise for inclusion of pupils with behavioural difficulties

University of Rijeka, UNIRI research support · 2019 – 2022

What predicts whether a teacher feels able to work with a pupil showing ADHD symptoms, and which disciplining strategies follow from that? The analysis modelled teacher self-efficacy against pupil symptom profiles and class characteristics, and tested whether the same predictors hold across school types.

Outcome: Papers in CEPS Journal and Društvena istraživanja, plus presentations at the END conferences in Porto and Lisbon.

Also led or analysed

2023 – 2025
IZDOS — key factors in implementing educational inclusionLead data analyst · research project IP-UNIZD-2023-01
2023 – 2024
Informal contact with English and foreign-language masteryFaculty of Education internal project
2020 – 2021
Evaluation of distance learning in Serbian and Croatian higher educationProject leader · with the University of Novi Sad
2016 – 2017
Implementation of inclusion in secondary schoolsProject leader · with Osijek-Baranja County
2015 – 2016
Interactive model of ADHD in the school environmentProject leader · University of Osijek

Publications

The record,
by method.

A selection of peer-reviewed output, grouped by the kind of statistical work it represents. Full list on CroRIS and ORCID.

2023
Velki, T., & Kuterovac Jagodić, G. Testing ecological validity of the Croatian School Climate Questionnaire for teachers from different educational levels. Društvena istraživanja, 32(3), 493–516. doi.org/10.5559/di.32.3.06
2022
Velki, T., Šolić, K., & Žvanut, B. Cross-cultural validation and psychometric testing of the Slovenian version of the Croatian Behavioral-Cognitive Internet Security Questionnaire. Elektrotehniški vestnik, 89(3), 103–108.
2021
Velki, T., Romstein, K., & Ružić, V. Agreement between the assessments of parents and preschool teachers for different developmental areas of preschoolers. Hrvatski časopis za odgoj i obrazovanje, 23(4), 1139–1169. doi.org/10.15516/cje.v23i4.4241
2021
Velki, T., & Romstein, K. Validation and standardisation of the Croatian version of ASQ-3 for children aged 3 to 5 years. Paediatria Croatica, 65(2), 95–101. doi.org/10.13112/PC.2021.15
2019
Velki, T., & Šolić, K. Development and validation of a new measurement instrument: the Behavioral-Cognitive Internet Security Questionnaire (BCISQ). International Journal of Electrical and Computer Engineering Systems, 10(1), 19–24. doi.org/10.32985/ijeces.10.1.3
2015
Velki, T., Šolić, K., & Nenadić, K. Development and validation of Users’ Information Security Awareness Questionnaire (UISAQ). Psychological Topics, 24(3), 401–424.
2014
Velki, T., Kuterovac Jagodić, G., & Antunović, A. Development and validation of Croatian school climate survey for students. Contemporary Psychology, 17(2), 151–166.
2024
Velki, T., Rotim, V., Kribl, M., Gorjanac Midžić, T., & Turić, N. Alcohol, gambling and new technology addiction among children and youth in the Osijek-Baranja County. Osijek: Teaching Institute of Public Health, Osijek-Baranja County.
2019
Velki, T. Comparison of prevalence and prediction of peer violence with bullying. Ljetopis socijalnog rada, 26(3), 363–390. doi.org/10.3935/ljsr.v26i3.218
2024
Velki, T. Can physical activities suppress the negative impact of stress on the mental health of adolescents? International Journal of Mental Health Promotion. doi.org/10.32604/ijmhp.2024.047950
2022
Velki, T. The mediating role of parents and school in peer aggression problems. Center for Educational Policy Studies Journal, 12(1), 169–188. doi.org/10.26529/cepsj.921
2021
Velki, T., & Milić, M. Stress as a mediator between risk and protective factors and online risky behavior in adolescents. Primenjena psihologija, 14(2), 149–171. doi.org/10.19090/pp.2021.2.149-171
2019
Velki, T., & Vrdoljak, G. Gender as moderator and age as mediator variables in prediction of school adjustment by self-evaluated symptoms of ADHD. Primenjena psihologija, 12(1), 65–83. doi.org/10.19090/pp.2019.1.65-83
2022
Vlah, N., Velki, T., & Zrilić, S. Positive and assertive disciplining of students with attention difficulties. Društvena istraživanja, 31(1), 155–174. doi.org/10.5559/di.31.1.08
2021
Vlah, N., Velki, T., & Kovačić, E. Teachers’ self-efficacy based on symptoms of attention deficit hyperactivity disorder in primary school pupils. Center for Educational Policy Studies Journal, 11(3), 141–161. doi.org/10.26529/cepsj.746
2020
Velki, T. Multivariate multilevel modelling: application options in the social sciences. Osijek: J. J. Strossmayer University of Osijek, Faculty of Education.
2020
Brust Nemet, M., & Velki, T. Relationship of some demographic and class characteristics and school climate and social support to teacher stress. Nova prisutnost, 18(3), 501–515. doi.org/10.31192/np.18.3.5
2019
Velki, T., Užarević, Z., & Dubovicki, S. Self-evaluated ADHD symptoms as risk adaptation factors in elementary school children. Društvena istraživanja, 28(3), 503–522. doi.org/10.5559/di.28.3.07
2018
Velki, T. Verifying the ecological model of peer aggression on Croatian students. Psychology in the Schools, 55(10), 1302–1320. doi.org/10.1002/pits.22178
2016
Velki, T., & Kuterovac Jagodić, G. Can we also predict electronic peer violence based on the predictors of traditional peer violence? Društvena istraživanja, 25(4), 523–545.
2015
Karlak, M., & Velki, T. Motivation and learning strategies as predictors of foreign language communicative competence. Croatian Journal of Education, 17(3), 635–658.
2024
Šolić, K., Idlbek, R., & Velki, T. An empirical study on differences between self-assessed and measured real risk in online behaviour. International Journal of Electrical and Computer Engineering Systems, 15(3), 297–304. doi.org/10.32985/ijeces.15.3.8
2024
Šolić, K., Velki, T., Fosić, I., & Vuković, M. Study on information security awareness using the Behavioral-Cognitive Internet Security Questionnaire. Acta Polytechnica Hungarica, 21(4), 49–68. doi.org/10.12700/APH.21.4.2024.4.3
2019
Šolić, K., Pleša, M., Velki, T., & Nenadić, K. Awareness about information security and privacy among healthcare employees. Southeastern European Medical Journal, 3(1), 21–28.
2019
Velki, T., & Šolić, K. (eds.) The challenges of the digital world. Osijek: J. J. Strossmayer University of Osijek, Faculty of Education.
2018
Velki, T., & Romstein, K. User risky behavior and security awareness through lifespan. International Journal of Electrical and Computer Engineering Systems, 9(2), 9–16. doi.org/10.32985/ijeces.9.2.2
2018
Velki, T., & Šolić, K. (eds.) Handbook for information security and privacy. Osijek: J. J. Strossmayer University of Osijek, Faculty of Education.
2015
Šolić, K., Velki, T., & Galba, T. Empirical study on ICT system’s users’ risky behavior and security awareness. MIPRO proceedings, 1623–1626.

Contact

Tell me about
the data.

The first exchange is free and usually short. What helps most: your research question, roughly what the sample looks like, whether the data is already collected, and when you need results.

Send a project brief

This opens a pre-filled message in your own email app — nothing is stored here.