Category: statistics

What is the Monte Carlo method

The story of the Monte Carlo method begins in the most unlikely way: with a mathematician in bed playing cards. In 1946, Stanisław Ulam, a Polish mathematician recovering from surgery, found himself playing solitaire to pass the time. Being a mathematician, he wondered: what are the chances of winning a game?

The problem was theoretically solvable: just enumerate every possible combination of cards and count the favorable ones. In practice, however, the number of combinations was so enormous that an exact calculation was completely impractical. Ulam then had an insight as simple as it was powerful: instead of computing the exact probability, why not simulate hundreds of games and count how many times you win?

One of the most common questions when planning an A/B test is: how many users do I need to get a reliable result? The answer is not a magic number: it depends on the size of the effect we want to detect, the baseline conversion rate, and the level of statistical certainty we require.

Calculating the sample size in advance is essential to avoid two classic mistakes: stopping the test too early and declaring a winner that does not exist, or letting it run too long, wasting traffic and time. In other words, it is about finding the right balance between resources and rigour.

If you have read the article on A/B Testing, you will recall that power analysis is the statistical method that lets us determine this threshold. And if you have studied confidence intervals, you already know that significance level and test power are not abstract concepts but operational levers that directly affect sample size.

Continue reading “A/B Test Sample Size Calculator”

Introduction

Machine Learning is changing the way we see the world around us. From weather prediction to medical diagnosis, from content recommendations on streaming platforms to financial fraud detection, Machine Learning is increasingly present in our daily lives.

But what exactly is it, and how does it work? In this post, we will explore the fundamental concepts of Machine Learning and see how it can be used to solve real-world problems. We will also look at how to get started with Machine Learning, what resources are available, and how to use this technology to improve both work and everyday life.

Continue reading “Understanding the Basics of Machine Learning: A Beginner’s Guide”

Ever noticed how just a handful of pages on your site get the lion’s share of traffic?
The homepage, the blog, the product page — and then a long tail of pages that together weigh less than those few.

It’s the Pareto principle, we know it well. But “80% of traffic comes from 20% of pages” is a heuristic, not a measurement.
How do we know if our site is more or less concentrated than average? And what if we want to compare two sites — or the same site at two different points in time?

We need an index that quantifies concentration in a single number.
A number that equals 0 when everything is evenly distributed, and 1 when a single page takes it all. In between, the space of all real distributions.

That number exists. It’s called the Gini index, and it measures the concentration of a transferable quantitative variable (a quantity that can be redistributed without changing its total: income, traffic, market share). It was introduced in 1912 by the Italian statistician Corrado Gini specifically to study inequality in income distribution.
Since then, it has become one of the most widely used indicators in economics, sociology — and yes, in SEO analysis too.

Let’s see how it works.

Have you ever noticed how mobile users behave differently from desktop users? It’s not just a feeling — it’s a relationship between two categorical variables. The variable “device” (mobile or desktop) and the variable “converted” (yes or no) — when we cross them in a table, we can see if there’s a systematic link.

Contingency tables (also called two-way tables or cross-tabulations) are the basic tool for this. They allow us to evaluate the interaction between two categorical variables and to quantify conditional probability — how likely an event is “given that” another has occurred.

The question about mobile vs desktop differences, for example, translates into a conditional probability: is P(conversion | device = mobile) different from P(conversion | device = desktop)? If yes, there’s a relationship. If not, the two variables are independent.

Let’s see how this works, starting with a deliberately light-hearted example.