From personal insights to professional assessments, our cognitive tests are trusted for their accuracy. Individual users get immediate feedback and can opt for detailed reports. Pro users can get bulk solutions for institutional applications, a dedicated dashboard for monitoring results, and advanced data analytics to enhance decision-making.
Assess your cognitive skills with our free tests. Instantly receive a certificate showing your score range or request a more detailed report for personalized insights.
Whether you're a researcher, student, or enthusiast, our user-friendly tools will assist you in various statistical computations.
Assess the reliability of your scale with the Cronbach Alpha coefficient.
Calculate the Lambda-6 reliability coefficient for your assessments.
Gain a refined estimate of test reliability with Jouve's advanced randomized reliability analysis.
Compute and interpret the KR-20, a measure of internal consistency for dichotomous choice assessments.
Create custom datasets for research using Item Response Theory.
Optimize test reliability by adjusting it using the Spearman-Brown Prophecy formula.
Utilize the Tellegen-Briggs Formula for advanced psychometric scale creation and analysis.
Quickly correct correlations for range restriction using the renowned Thorndike's formula.
Standardize scores from different tests for direct comparison with Z-Score Equating.
Not sure where to start? Try our Z-Score Equating Calculator now!
This paper develops a mathematical framework for integrating group-theoretic symmetry constraints into Item Response Theory (IRT) parameter estimation. Group actions on item parameters define algebraic structures that capture latent regularities, thereby reducing the effective dimensionality of the parameter space. Specifically, group actions on item difficulty and discrimination parameters are formalized through permutation matrices, inducing coset decompositions that collapse symmetrically related items into equivalence classes. This symmetry-enforced regularization ensures parameter estimates remain consistent with both empirical data and the underlying algebraic structures. Additionally, the model incorporates data-driven dynamic bounds for discrimination parameters, derived from the empirical distribution of point-biserial correlations, enabling the model to capture item-level variability while maintaining theoretical consistency. While the focus is on the two-parameter logistic (2PL) model, the approach generalizes to more complex models, such as the three-parameter logistic (3PL) and four-parameter logistic (4PL) models, by including additional constraints on guessing and upper asymptote parameters. Future work will address empirical validation, computational scalability, and alternative group-theoretic structures in psychometric modeling.
This paper provides a theoretical formulation of the hierarchical Two-Parameter Logistic (2PL) Item Response Theory (IRT) model within a Bayesian framework. The model introduces hierarchical priors on respondent abilities theta, and informative priors for item discrimination a and difficulty b, allowing for more flexible and realistic modeling of latent traits and item characteristics. To overcome the computational challenges posed by the high-dimensional posterior, we employ Automatic Differentiation Variational Inference (ADVI), which offers a scalable and efficient alternative to traditional Markov Chain Monte Carlo (MCMC) methods. We present a complete derivation of the model's probabilistic structure, including both prior and likelihood functions, and detail the variational inference process central to ADVI. The mathematical foundations are carefully developed, providing a clear and formal account of the inferential methodology. This work focuses on theoretical aspects, offering a comprehensive mathematical exposition without empirical applications or simulation studies.
High intelligence is a pivotal research area, influencing the intellectual development of societies. This treatise explores the nuanced territory of cognitive ability studies. Beginning with a historical evolution from earlier conceptions of intelligence to modern definitions, the manuscript delves into the semantic roots of intelligence, a term derived from the Latin intelligere, which translates to "to understand". Challenges inherent in assessing high levels of intelligence, such as ceiling effects in well-known measures like the Stanford-Binet and WAIS, are discussed. An exploration of neuroimaging uncovers neural underpinnings associated with elevated cognitive abilities. Moreover, the convoluted relationship between genetics and environment in the context of cognitive abilities is examined. The treatise not only addresses salient critiques of IQ measures but also underscores the imperative for sophisticated psychometric instruments tailored for the highly gifted.
Since its inception in 2010, Cogn-IQ has been a trusted provider of cognitive assessment tools for individuals and professionals alike. Our platform offers a wide array of free, reliable IQ and cognitive potential tests, empowering users to gain insights into their mental abilities. For deeper analysis, we provide affordable, comprehensive individual reports that can be used for personal growth and development.
For clinical professionals, including psychologists and medical doctors, Cogn-IQ offers advanced, paid assessment solutions designed to aid in diagnostic processes and therapeutic planning. We also supply researchers with specialized measurement tools that ensure precision and reliability for studies in cognitive sciences and related fields.
Human resources and recruitment professionals benefit from our tailored assessment services, enabling informed hiring decisions and helping to match candidates with roles that align with their cognitive strengths. Whether you're an individual looking for personal insights or a professional seeking robust cognitive evaluation tools, Cogn-IQ is your partner in cognitive assessment and intelligence measurement.
Founder & Head of Research
Assessment Development Enhancer
Client Relations Gentleman
Educational Content Scribe
Dev & Tech Wizard
