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.<\/p>\n\n\n\n
Topic paths:<\/strong> for those who prefer a guided route instead of the full list, I\u2019ve gathered the articles into topic paths, each with its own reading guide: Basic Statistics<\/a>, Probability Distributions<\/a>, The Bayesian Approach<\/a>, Inferential Statistics<\/a>, Machine Learning Path<\/a> and Statistics for SEO<\/a>.<\/p>\n\n\n\n Before diving in:<\/em> A Brief (Personal) Manifesto for SEO<\/a> — a reflection on why statistical rigour matters in SEO work.<\/p>\n\n\n\n 1. The Data: The 4 Scales of Measurement<\/a><\/strong> 2. Descriptive Statistics: Measures of Position and Central Tendency<\/a><\/strong> 3. Descriptive Statistics: Measures of Variability (or Dispersion)<\/a><\/strong> 4. The Gini Index: What It Is, Why It Matters, and How to Compute It in R<\/a><\/strong> 5. First Steps into the World of Probability: Sample Space, Events, Permutations, and Combinations<\/a><\/strong> 6. Contingency Tables and Conditional Probability<\/a><\/strong> 7. Probability Distributions: Discrete Distributions and the Binomial<\/a><\/strong> 8. The Geometric Distribution<\/a><\/strong> 9. The Hypergeometric Distribution<\/a><\/strong> 10. The Negative Binomial Distribution (or Pascal Distribution)<\/a><\/strong> 11. The Poisson Distribution<\/a><\/strong> 12. The Beta Distribution Explained Simply<\/a><\/strong> 13. The Normal Distribution<\/a><\/strong> 14. The Central Limit Theorem: Why Statistics Works (Even When Data Isn’t Normal)<\/a><\/strong> 15. Hypothesis Testing: A Step-by-Step Guide<\/a><\/strong> 16. The t Distribution and Hypothesis Testing<\/a><\/strong> 17. The Two-Sample t-Test: How to Test a Hypothesis for Dependent or Independent Samples<\/a><\/strong> 18. Confidence Intervals: What They Are, How to Calculate Them (and What They Do NOT Mean)<\/a><\/strong> 19. Sampling and Sample Size: How Much Data Do You Really Need?<\/a><\/strong> 20. Statistical Parametric and Non-Parametric Tests<\/a><\/strong> 21. Non-Parametric Tests: The Wilcoxon Test for Non-Normal Data<\/a><\/strong> 22. The Chi-Square Test: Goodness of Fit and Test of Independence<\/a><\/strong> 23. Analysis of Variance, ANOVA. Explained Simply<\/a><\/strong> 24. Guide to Statistical Tests for A\/B Analysis<\/a><\/strong> 25. A\/B Testing: How to Run Statistically Valid Experiments (and the Mistakes to Avoid)<\/a><\/strong> 26. Effect Size and Power Analysis: How Big Is the Effect (and How Much Data You Need)<\/a><\/strong> 27. Bayesian Statistics: How to Learn from Data, One Step at a Time<\/a><\/strong> Bayesian Conversion Rate Estimation: how much can we trust limited data<\/a><\/strong> Bayesian A\/B Testing: not just “whether” B beats A, but “by how much”<\/a><\/strong> Multi-armed bandit: optimising the variants while the test is still running<\/a><\/strong> Naive Bayes: classifying search intent with Bayes\u2019 theorem<\/a><\/strong> 28. Time Series Analysis and Forecasting in R<\/a><\/strong> 29. Anomaly Detection: How to Identify Outliers in Your Data<\/a><\/strong> 30. Simpson’s Paradox in SEO: When Aggregate Data Can Lie<\/a><\/strong> 41. Regression to the Mean: the SEO Fix That Worked\u2026 by Accident<\/a><\/strong> 42. The Peeking Problem: Why Checking Your A\/B Test Early Inflates False Positives<\/a><\/strong> 31. Correlation: Pearson, Spearman and Kendall (and Why It Isn’t Causation)<\/a><\/strong> 32. Correlation and Regression Analysis – Linear Regression<\/a><\/strong> 33. Multiple Regression Analysis, Explained Simply<\/a><\/strong> 34. Multicollinearity, Heteroscedasticity, Autocorrelation: Three Difficult-Sounding Concepts (Explained Simply)<\/a><\/strong> 35. Logistic Regression: Predicting the Outcome of an Event<\/a><\/strong> 36. Understanding the Basics of Machine Learning: A Beginner’s Guide<\/a><\/strong> 37. How to Use Decision Trees to Classify Data<\/a><\/strong> 38. The Gradient Descent Algorithm Explained Simply<\/a><\/strong> 39. An Introduction to Principal Component Analysis (PCA)<\/a><\/strong> 40. The Monte Carlo Method Explained Simply with Real-World Applications<\/a><\/strong> 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)<\/strong><\/a>.<\/p>\n\n\n\n A\/B Test Sample Size Calculator<\/a><\/strong> A\/B Test Significance Calculator<\/a><\/strong> This blog is listed on R-bloggers.com<\/a>, an aggregator of R tutorials and news from the R community.<\/p>\n","protected":false},"excerpt":{"rendered":" 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 … Leggi tutto “Statistics and SEO”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-3452","page","type-page","status-publish","hentry"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"post-thumbnail":false},"uagb_author_info":{"display_name":"Paolo Gironi","author_link":"https:\/\/www.gironi.it\/blog\/author\/autore-articoli\/"},"uagb_comment_info":0,"uagb_excerpt":"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…","_links":{"self":[{"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/pages\/3452","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/comments?post=3452"}],"version-history":[{"count":5,"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/pages\/3452\/revisions"}],"predecessor-version":[{"id":3916,"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/pages\/3452\/revisions\/3916"}],"wp:attachment":[{"href":"https:\/\/www.gironi.it\/blog\/wp-json\/wp\/v2\/media?parent=3452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Statistics and SEO: The Topics<\/h2>\n\n\n\n
The Foundations: Describing Data<\/h3>\n\n\n\n
Quantitative and qualitative data | The 4 levels of measurement | Nominal scale | Ordinal scale | Interval scale | Ratio scale | Complexity levels of measurement types<\/p>\n\n\n\n
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<\/p>\n\n\n\n
Range | Mean deviation | Variance | Standard deviation | Coefficient of variation | Shape of a distribution | Kurtosis<\/p>\n\n\n\n
The Lorenz curve | Example | The concentration index R | Computing in R | The Gini index worldwide<\/p>\n\n\n\nFirst Steps into Probability<\/h3>\n\n\n\n
Probability | Additivity principle for incompatible events | Multiplication principle | Permutations | Combinations | The binomial distribution as an application<\/p>\n\n\n\n
Two-way tables and marginal distributions | Conditional probability | Dependence and independence<\/p>\n\n\n\nProbability Distributions<\/h3>\n\n\n\n
Discrete and continuous variables | Bernoulli random variable | Binomial distribution | Binomial coefficient | Mean, expected value, variance | The hypergeometric distribution<\/p>\n\n\n\n
How many attempts until the first success? | Examples | Computing in R<\/p>\n\n\n\n
Starting from the formula | The hypergeometric distribution explained with examples | The urn and balls example | Further reading<\/p>\n\n\n\n
Definition | Usage examples | Differences between the geometric and Pascal distributions<\/p>\n\n\n\n
Lambda: the average rate of events | Poisson vs Binomial | Practical examples | SEO applications<\/p>\n\n\n\n
An important probability distribution in Bayesian statistics | A practical example using R<\/p>\n\n\n\n
Visualizing the “normality” of data | Transforming data | The empirical rule | Standardization | Examples | Chebyshev’s inequality<\/p>\n\n\n\n
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<\/p>\n\n\n\nInference: Estimating and Testing<\/h3>\n\n\n\n
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<\/p>\n\n\n\n
A brief historical digression | Example | The p-value approach | Confidence intervals | The t-test with R<\/p>\n\n\n\n
Independent samples hypothesis test | Paired t-test for dependent samples | Example<\/p>\n\n\n\n
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<\/p>\n\n\n\n
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<\/p>\n\n\n\nTests in Practice: Comparisons and Categorical Variables<\/h3>\n\n\n\n
Parametric tests: the power of normality | Non-parametric tests: versatility and creativity<\/p>\n\n\n\n
Wilcoxon signed-rank test | Wilcoxon rank-sum test | Practical examples with R<\/p>\n\n\n\n
Goodness of Fit test | Understanding through examples | Using R | The Independence test<\/p>\n\n\n\n
ANOVA: a parametric test | Why ANOVA instead of multiple t-tests? | One-way ANOVA | The ANOVA table | Using R<\/p>\n\n\n\n
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<\/p>\n\n\n\n
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<\/p>\n\n\n\n
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”<\/p>\n\n\n\nThe Bayesian Path<\/h3>\n\n\n\n
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<\/p>\n\n\n\n
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<\/p>\n\n\n\n
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<\/p>\n\n\n\n
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<\/p>\n\n\n\n
From Bayes\u2019 theorem to the classifier | The naive independence assumption | Training by counting: Laplace smoothing | Classifying intent: informational or transactional<\/p>\n\n\n\nTraffic over Time: Time Series and Anomalies<\/h3>\n\n\n\n
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<\/p>\n\n\n\n
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<\/p>\n\n\n\nData Traps<\/h3>\n\n\n\n
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)<\/p>\n\n\n\n
Why extreme values revert on their own | Kahneman\u2019s flight-instructor anecdote | An R example on average position | The control group that exposes the illusion<\/p>\n\n\n\n
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<\/p>\n\n\n\nRegression and Models<\/h3>\n\n\n\n
From covariance to correlation | Pearson and linear association | Spearman and Kendall: monotonic association | The correlation matrix | Correlation is not causation | Try it yourself<\/p>\n\n\n\n
Simple Regression | Pearson’s R | R-squared | Spearman’s rank correlation | Regression equation | Outliers and leverage points | Model assumptions | Residual analysis | Other correlation coefficients<\/p>\n\n\n\n
The multiple regression equation | What information can I extract? | Prerequisites | Getting started | How good is my model? | Summary<\/p>\n\n\n\n
Multicollinearity | How to reduce the problem | Heteroscedasticity | Autocorrelation<\/p>\n\n\n\n
How logistic regression works | Example in R: Titanic survival probability | The logit equation | Summary | Resources<\/p>\n\n\n\nTowards Machine Learning<\/h3>\n\n\n\n
Introduction | What is ML | Supervised and unsupervised ML | Main stages | How to get started | Jupyter Lab and Google Colab<\/p>\n\n\n\n
Decision tree algorithm | Classification and regression trees | Practical examples<\/p>\n\n\n\n
How gradient descent works | Learning rate | Practical implementation<\/p>\n\n\n\nSimulation<\/h3>\n\n\n\n
The mathematical foundations | Practical applications across fields | PCA in web marketing, SEO and SEM | Implementing PCA in R | Interpreting the results<\/p>\n\n\n\n
What is Monte Carlo simulation | Random sampling | Practical applications | R examples<\/p>\n\n\n\n
\n\n\n\nThe Library<\/h2>\n\n\n\n
Interactive Tools<\/h2>\n\n\n
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.<\/p>\n\n\n\n
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.<\/p>\n\n\n\n
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