Basics
Fundamental concepts every learner starts with
Expectation and Variance
Learn how to compute the expectation and variance of random variables in both discrete and continuous cases, with clear definitions and examples.
Boxplot and IQR
Learn how to read boxplots, calculate IQR, and detect outliers in data.
Descriptive Statistics
Instead of listing raw data, descriptive statistics use summary measures to convey the big picture quickly.
Histogram Bin Size
An introduction to frequency distributions, histograms, and how to choose an appropriate bin width for visualization.
Mean, Median, and Mode
Learn the basics of mean, median, and mode with clear examples and bar chart visualizations.
Types of Data
The very first step in learning statistics is understanding types of data. This article introduces qualitative vs. quantitative data, with clear examples of nominal, ordinal, discrete, and continuous variables.
Variance and Standard Deviation
A beginner-friendly guide to variance and standard deviation: definitions, calculation formulas, unbiased estimation, and why we square deviations.
One-Way ANOVA
A beginner-friendly walkthrough of one-way ANOVA with visual insight into between- and within-group variance.
Probability
Core probability theory and foundations
Discrete Distributions
An introduction to key discrete probability distributions: the uniform, Bernoulli, and binomial distributions, with examples, expectations, and variances.
Probability Distributions and Densities
Building on Laplace and Kolmogorov’s definitions of probability, this article explains the basics of probability distributions and density functions in a beginner-friendly way.
Events and Sigma-Algebras
A beginner-friendly explanation of 'events' and 'σ-algebras' in probability theory, with examples and visual aids to help you understand how probability is defined mathematically.
Laplace and Kolmogorov Definitions of Probability
From Laplace's classical probability to Kolmogorov's modern axiomatic definition, explained step by step for beginners.
Distributions
Probability distributions and their properties
Gamma Distribution
A gentle introduction to the gamma distribution, including its definition, special cases, real-world medical applications, and the additive property that reveals its intuitive meaning.
Exponential Family
A beginner-friendly introduction to exponential family distributions, with examples like Bernoulli, Poisson, and Normal. Learn how to rewrite distributions in exponential form and understand their components visually.
Regression & Modeling
From simple regression to generalized models
Multiclass Logistic Regression
Extend logistic regression from binary to multiclass classification using the softmax function, cross-entropy loss, and gradient descent — with full derivation and interactive demo.
Logistic Regression
Understand logistic regression from the sigmoid function to maximum likelihood estimation and cross-entropy loss, with an interactive demo.
ATE, ATT, and ATC
A clear explanation of ATE, ATT, and ATC in causal inference, using a regression-based example with visual illustrations.
Generalized Linear Models (GLM)
A step-by-step introduction to Generalized Linear Models (GLMs) starting from basic linear regression, explaining distributions, link functions, and model construction with an interactive tool.
Least Squares Regression
A gentle explanation of simple linear regression by combining the mathematical derivation with a visual demo of best-fit lines.
Simple Linear Regression
Understand linear regression through relatable examples, clear math, and a visual demo.
Hypothesis Testing
Statistical testing and evaluation methods
Power Curve and Sample Size
Learn how statistical power curves change with sample size through formulas and interactive visualization.
Alpha Error, Beta Error, and Statistical Power
Learn the meaning of alpha error, beta error, and power through visual demonstrations using normal distributions.
Sensitivity, Specificity, and ROC
How to evaluate medical test performance using a 2×2 table, ROC curves, and AUC calculations.
Linear Algebra & ML
Mathematical tools and machine learning
K-means Clustering
An interactive visual comparison of k-means clustering performance on circular Gaussian blobs vs. non-circular moon-shaped data.
Principal Component Analysis (2D)
From centering the data to deriving Var(z) = w^T S w and solving the eigenvalue problem, this article explains PCA step-by-step using the maximum variance approach.
Eigenvalues and Eigenvectors
An intuitive introduction to eigenvalues and eigenvectors, explained with the idea of direction and length change, plus real-world applications like PCA.
Advanced Theory
Measure theory, estimation, and beyond
Carathéodory Extension Theorem
From outer measure to Lebesgue measure: why not every set can be measured, with Cantor and Vitali sets as examples.
Probability Measures and Random Variables
An intuitive introduction to probability measures and measurable random variables, starting from lengths and areas.
Borel Sigma-Algebra
An intuitive explanation of the Borel sigma-algebra, the key structure for defining probability on continuous sample spaces like the real line.