Over the years, I’ve been writing a series of posts that I hope can serve as an introduction to the main “foundational” topics of statistics applied to working with data: from descriptive statistics to inference, from time series to the first steps into machine learning. I’m grouping them here by theme, so they can form a path: the order is the one I would follow myself, but each section can also stand on its own.
Topic paths: for those who prefer a guided route instead of the full list, I’ve gathered the articles into topic paths, each with its own reading guide: Basic Statistics, Probability Distributions, The Bayesian Approach, Inferential Statistics, Machine Learning Path and Statistics for SEO.
Before diving in: A Brief (Personal) Manifesto for SEO — a reflection on why statistical rigour matters in SEO work.
1. The Data: The 4 Scales of Measurement
Quantitative and qualitative data | The 4 levels of measurement | Nominal scale | Ordinal scale | Interval scale | Ratio scale | Complexity levels of measurement types
2. Descriptive Statistics: Measures of Position and Central Tendency
Measures of central tendency | Arithmetic mean | Weighted mean | Geometric mean | Harmonic mean | Trimmed mean | Median | Mode | Relationship between mean, median and mode | Quartiles, deciles and percentiles | The five-number summary | Box-plot
3. Descriptive Statistics: Measures of Variability (or Dispersion)
Range | Mean deviation | Variance | Standard deviation | Coefficient of variation | Shape of a distribution | Kurtosis
4. The Gini Index: What It Is, Why It Matters, and How to Compute It in R
The Lorenz curve | Example | The concentration index R | Computing in R | The Gini index worldwide
5. First Steps into the World of Probability: Sample Space, Events, Permutations, and Combinations
Probability | Additivity principle for incompatible events | Multiplication principle | Permutations | Combinations | The binomial distribution as an application
6. Contingency Tables and Conditional Probability
Two-way tables and marginal distributions | Conditional probability | Dependence and independence
7. Probability Distributions: Discrete Distributions and the Binomial
Discrete and continuous variables | Bernoulli random variable | Binomial distribution | Binomial coefficient | Mean, expected value, variance | The hypergeometric distribution
8. The Geometric Distribution
How many attempts until the first success? | Examples | Computing in R
9. The Hypergeometric Distribution
Starting from the formula | The hypergeometric distribution explained with examples | The urn and balls example | Further reading
10. The Negative Binomial Distribution (or Pascal Distribution)
Definition | Usage examples | Differences between the geometric and Pascal distributions
11. The Poisson Distribution
Lambda: the average rate of events | Poisson vs Binomial | Practical examples | SEO applications
12. The Beta Distribution Explained Simply
An important probability distribution in Bayesian statistics | A practical example using R
13. The Normal Distribution
Visualizing the “normality” of data | Transforming data | The empirical rule | Standardization | Examples | Chebyshev’s inequality
14. The Central Limit Theorem: Why Statistics Works (Even When Data Isn’t Normal)
What is the CLT | Why it matters | Simulation in R | The practical rule: how large should n be? | Standard error | Daily organic traffic example | When the CLT is not enough
15. Hypothesis Testing: A Step-by-Step Guide
Statistical hypotheses | Type I and II errors | One-tailed or two-tailed? | Setting null and alternative hypotheses | Significance level | Choosing the distribution | Drawing conclusions | Power of a test | Determining sample size
16. The t Distribution and Hypothesis Testing
A brief historical digression | Example | The p-value approach | Confidence intervals | The t-test with R
17. The Two-Sample t-Test: How to Test a Hypothesis for Dependent or Independent Samples
Independent samples hypothesis test | Paired t-test for dependent samples | Example
18. Confidence Intervals: What They Are, How to Calculate Them (and What They Do NOT Mean)
What is a CI | The 95% misconception | CI for means | CI for proportions | CI vs hypothesis testing | Confidence levels: 90%, 95%, 99% | What affects CI width | Practical example: organic CTR
19. Sampling and Sample Size: How Much Data Do You Really Need?
Types of sampling (simple random, stratified, systematic) | Sample size: the math behind the estimation | R and Python examples | From estimation to A/B testing | Sampling error vs bias
20. Statistical Parametric and Non-Parametric Tests
Parametric tests: the power of normality | Non-parametric tests: versatility and creativity
21. Non-Parametric Tests: The Wilcoxon Test for Non-Normal Data
Wilcoxon signed-rank test | Wilcoxon rank-sum test | Practical examples with R
22. The Chi-Square Test: Goodness of Fit and Test of Independence
Goodness of Fit test | Understanding through examples | Using R | The Independence test
23. Analysis of Variance, ANOVA. Explained Simply
ANOVA: a parametric test | Why ANOVA instead of multiple t-tests? | One-way ANOVA | The ANOVA table | Using R
24. Guide to Statistical Tests for A/B Analysis
Z test | Student’s t-test | Welch’s t-test | Chi-square test | Analysis of Variance (ANOVA) | Mann-Whitney U test | Fisher’s exact test | Regression analysis | Comparative overview table
25. A/B Testing: How to Run Statistically Valid Experiments (and the Mistakes to Avoid)
What an A/B test is | Setting it up correctly | The two-proportion z-test in R | Common mistakes | Frequentist vs Bayesian | Practical SEO example
26. Effect Size and Power Analysis: How Big Is the Effect (and How Much Data You Need)
Beyond the p-value: statistical significance is not practical relevance | Cohen’s d for means, Cohen’s h for proportions (CTR, conversions) | The power of a test and the type II error | Power analysis in R with pwr: how much data you need | A practical SEO case: the underpowered A/B test that “didn’t work”
27. Bayesian Statistics: How to Learn from Data, One Step at a Time
Frequentist vs Bayesian | Bayes’ theorem: derivation and components (prior, likelihood, posterior, evidence) | Numerical example in R: ad campaign click rate | Sequential updating | Informative and non-informative priors | Credible interval vs confidence interval | When to use the Bayesian approach
Bayesian Conversion Rate Estimation: how much can we trust limited data
The Beta-Binomial model: conjugate prior for proportions | Non-informative vs informative prior | Credible interval with direct interpretation | Sequential updating: today's posterior is tomorrow's prior
Bayesian A/B Testing: not just “whether” B beats A, but “by how much”
Two Beta posteriors, one per variant | The probability that B wins: P(B>A) | The distribution of the difference: by how much it's better | When to stop: expected loss and the peeking problem
Multi-armed bandit: optimising the variants while the test is still running
The hidden cost of the fixed A/B test | Exploration versus exploitation | Thompson sampling: sampling from each arm's posterior | The regret avoided: converting more on the same traffic
Naive Bayes: classifying search intent with Bayes’ theorem
From Bayes’ theorem to the classifier | The naive independence assumption | Training by counting: Laplace smoothing | Classifying intent: informational or transactional
28. Time Series Analysis and Forecasting in R
What is a time series | Classical analysis and decomposition | The four classic components | Creating time series in R | Smoothing techniques | SEO applications | Moving averages | LOESS decomposition | Holt-Winters exponential smoothing | ARIMA models
29. Anomaly Detection: How to Identify Outliers in Your Data
Why recognizing anomalies matters | Working dataset: simulated sessions with injected anomalies | Method 1: z-score and the empirical rule | Method 2: IQR and Tukey’s method | Method 3: Grubbs’ test and iterative approach | Comparing the three methods on web traffic data
30. Simpson’s Paradox in SEO: When Aggregate Data Can Lie
When the aggregate tells the opposite of the segments | The Berkeley admissions case | An example with Search Console data | How to spot it (and protect yourself)
41. Regression to the Mean: the SEO Fix That Worked… by Accident
Why extreme values revert on their own | Kahneman’s flight-instructor anecdote | An R example on average position | The control group that exposes the illusion
42. The Peeking Problem: Why Checking Your A/B Test Early Inflates False Positives
What peeking is | The Optimizely story (2015) | An R simulation: from 5% to 25% false positives | The fixed horizon and sequential methods | Try it yourself
31. Correlation: Pearson, Spearman and Kendall (and Why It Isn’t Causation)
From covariance to correlation | Pearson and linear association | Spearman and Kendall: monotonic association | The correlation matrix | Correlation is not causation | Try it yourself
32. Correlation and Regression Analysis – Linear Regression
Simple Regression | Pearson’s R | R-squared | Spearman’s rank correlation | Regression equation | Outliers and leverage points | Model assumptions | Residual analysis | Other correlation coefficients
33. Multiple Regression Analysis, Explained Simply
The multiple regression equation | What information can I extract? | Prerequisites | Getting started | How good is my model? | Summary
34. Multicollinearity, Heteroscedasticity, Autocorrelation: Three Difficult-Sounding Concepts (Explained Simply)
Multicollinearity | How to reduce the problem | Heteroscedasticity | Autocorrelation
35. Logistic Regression: Predicting the Outcome of an Event
How logistic regression works | Example in R: Titanic survival probability | The logit equation | Summary | Resources
36. Understanding the Basics of Machine Learning: A Beginner’s Guide
Introduction | What is ML | Supervised and unsupervised ML | Main stages | How to get started | Jupyter Lab and Google Colab
37. How to Use Decision Trees to Classify Data
Decision tree algorithm | Classification and regression trees | Practical examples
38. The Gradient Descent Algorithm Explained Simply
How gradient descent works | Learning rate | Practical implementation
39. An Introduction to Principal Component Analysis (PCA)
The mathematical foundations | Practical applications across fields | PCA in web marketing, SEO and SEM | Implementing PCA in R | Interpreting the results
40. The Monte Carlo Method Explained Simply with Real-World Applications
What is Monte Carlo simulation | Random sampling | Practical applications | R examples
Every article along this path closes with one or two recommended books. I have gathered them all on a single page, with the reason each title earned its place on the shelf: The Statistics and SEO Library: the Books I Recommend (and Why).
A/B Test Sample Size Calculator
Calculate the required sample size for your A/B test in real time. Enter baseline conversion rate, minimum detectable effect, significance level and power to get the exact number of users per variant.
A/B Test Significance Calculator
The complement of the calculator above: once the test is over, enter visitors and conversions for the two variants to get the p-value, a significance verdict and the confidence interval of the difference.
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