5 Statsmodels Functions That Give You the "Why" Behind the "What"

Statsmodels answers the questions sklearn was never built to answer: is this coefficient real or noise, does this added complexity earn its keep, can I trust these p-values in the first place, and which specific data points are quietly running the whole show.

Note: Run a regression in scikit-learn, and you get exactly two things back: a set of coefficients and a .predict() method. Ask it for a p-value on any of those coefficients, and there’s no built-in way to get one. This isn’t a missing feature scikit-learn’s maintainers overlooked; it’s a deliberate design choice they’ve stated directly: scikit-learn is built for prediction, not statistical inference…

Reversing Factorio's RNG

This post details how Factorio's random number generation works, how it can be reversed and how I used that knowledge to predict and manipulate the RNG with pure in‑game mechanics.

How is it possible for a deterministic game like Factorio to have a random mechanic?

PRNG

Ngram error rate

An example illustrating the large amount of error in Ngram data.

Bayesian textbook list

Exactly what the title says.

rubygems distribution docs

Documenting RubyGems, Stdlib, and GitHub Projects

3 Real-World Distributions That Refuse to Follow the Bell Curve

Explore how Pareto, log-normal, and Cauchy distributions differ from normal and why confusing them is costly.

Note: pareto, log-normal, cauchy

Starting Hand Frequencies and Pre-Flop Statistics in Texas Hold 'Em

Learn how starting hand frequencies and table position shape every pre-flop decision in Texas Hold 'Em.

In Praise of Observational Evidence

Everyone knows RCTs are the gold standard of evidence. ….Right?

It is a rare randomized trial (studying a particular intervention with a sufficiently large and well-distributed sample population) that can detect an 0.3% difference in a binary random variable — but Laplace could, more than 200 years ago.

You can be relatively sure that a p-value in one clinical trial conveys the same information as it does in another clinical trial, at least as far as the mathematical model is concerned.

Using the Gini Coefficient to Plan Edge Capacity | Fastly

Discover how Fastly uses the Gini coefficient, a metric usually reserved for economics, to model edge traffic inequality, improve cache efficiency, and plan capacity.

Major events change the shape of the traffic we serve.

traffic inequality -> cache behavior -> CPU utilization -> headroom

Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones? | Quanta Magazine

A decades-old proof showed that seven shuffles are enough to mix up a deck of cards. But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle.

MLE (max likelihood estimation) (@probabilityandstatistics)

Maximum Likelihood Estimation is the quiet engine underneath almost everything in ML, DL, and RL. Most people learn it once in a stats class and move on. They shouldn't. It's not just a parameter-fitting trick — it's the philosophical foundation of why our models work at all…

How to Estimate the Average Treatment Effect (ATE) with DoWhy How to Estimate the Average Treatment Effect (ATE) with DoWhy

Estimate the Average Treatment Effect in Python using DoWhy with regression and propensity score matching on real data.

Getting Started with DoWhy, the Python Causal Inference Library

Learn how to build and test causal inference models in Python using the DoWhy library.

Understanding Probability in Texas Hold 'Em

Learn how probability, outs, and card removal drive every decision in Texas Hold 'Em.

7 Everyday Distributions Explained Simply

This article is a quick, everyday tour of seven distributions you'll actually recognize once you know what to look for. No heavy math. No gatekeeping.

The "Everything's Equally Likely" Pattern

The "How Many Successes?" Counter

Calculating The Process Capabilities Of Cleaning Processes: A Primer

The industry has begun the movement to science-, risk-, and statistics-based approaches to cleaning process development and validation. Process capability has become an important measure for demonstrating acceptable cleaning processe performance. Explore process…

The Concise Guide to the Law of Large Numbers

Understand the law of large numbers and why larger datasets produce results closer to theoretical truth.

he more times an experiment is repeated, the closer the average of its results will be to the expected theoretical result.

The false positive paradox explains why you misjudge risk

Here’s how a mathematical paradox distorts our view of news, safety and statistics

Welsh police learned this lesson the hard way during the 2017 Union of European Football Associations Champions League final. They deployed cameras throughout Cardiff, where the soccer event was held, and used automated facial-recognition software to analyze the footage. The software scanned the…

Understanding Standard Deviation vs Standard Error

Understand the key differences between standard deviation and standard error with clear examples and practical applications.

The standard deviation measures the spread of individual data points in a sample from a population.

The standard error measures how well a sample mean represents the actual population mean—in other words, how uncertain we are about the sample mean.

Why 52 Cards Is the Perfect Number for Poker—Mathematically

A traditional card deck happens to dodge a tricky poker paradox. Other poker variants aren’t so lucky

Implementing Softmax From Scratch: Avoiding the Numerical Stability Trap - MarkTechPost

Learn about implementing Softmax from scratch and discover how to avoid the numerical stability trap in deep learning projects.

This function implements the Softmax activation in its most straightforward form.

numerically unstable—large positive logits can cause overflow, and large negative logits can underflow to zero. As a result, this version should be avoided in real training pipelines

Why Mean-Variance Fails: Alternative Portfolio Risk Metrics with Python

5 Effect Size Measures You’ll Actually Use

Learn to calculate and interpret five essential effect size measures with Python examples and clear guidance.

Cohen’s d — the standardized difference between two group means r (correlation coefficient) — the strength of a relationship between variables Odds ratio — how much more likely an outcome is in one group than another η² (eta squared) — how much of the total variance your variable explains Cliff’s…

Explaining Gibrat's Law: Why Growth Creates Lognormal Distributions

Gibrat's Law explains why proportional growth processes create lognormal distributions across economics, biology, and social systems.

Softmax in Statistics: Turning Scores into Probabilities

Learn how softmax converts raw scores into probability distributions that power AI decision-making.

How to Calculate and Interpret the Covariance Matrix with NumPy

In this article, we will explore how to calculate and interpret the covariance matrix using NumPy.

p-values Explained in Plain English (with Visuals)

In this article, we'll explore what p-values really mean, what they do not mean, and how to interpret them correctly.

Understanding Occam's Razor: Why Simpler Models Usually Win

Learn why simpler statistical models often outperform complex alternatives and when to apply this principle.

Information criteria like Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) formalize this trade-off using specific formulas:

5 Real-Life Examples of the Poisson Distribution

Image by Editor | ChatGPT The Poisson distribution might sound like one of those things you only deal with in a stats class, but it actually shows up in

How to Visualize Skewness and Kurtosis in Python

In this article, you will learn how to visualize skewness and kurtosis using Python.

10 Python One-Liners to Run Common Statistical Tests

In this article, we'll explore 10 Python one-liners that showcase the progression from basic statistical tests to sophisticated analyses.

7 Statistical Concepts Machine Learning Engineers Misunderstand

Let’s break down seven statistical concepts that even seasoned machine learning engineers often trip over — and why getting them right matters more than you think.

Concise Guide to Survival Analysis

So, if you’ve ever asked, “How long until X happens?” and wanted to back that up with solid data, you’re in the right place.

Introduction to statsmodels

This article explains its features, installation, and how to use it with examples.

The Concise Guide to Chi-Square Distribution

Let's clarify this important statistical pattern and understand its significance in analysis.

The Concise Guide to Poisson Distribution

The Poisson distribution is a discrete probability distribution that expresses the likelihood of a specific number of events occurring within a fixed time or space interval.

A Complete Guide to Understanding Probability Distributions

This article is your ultimate guide to understanding them gently and illustratively.

Statistical Formulas For Programmers – Evan Miller

What is Hellinger distance? - Dataconomy

Hellinger Distance is a statistical measure that quantifies the similarity between two probability distributions, useful in data analysis and machine learning applications.

Learning curve: The Kaplan-Meier estimator | The Actuary

The Kaplan-Meier survival curve estimator is one of the most cited ideas in science

The Concise Guide to Leverage

Leverage helps us identify observations that could significantly influence our regression results, even in ways that aren't immediately obvious.

The Concise Guide to Heteroscedasticity

Heteroscedasticity might seem like just the opposite of homoscedasticity, but understanding it in its own right is crucial for any data analyst.

The Concise Guide to Homoscedasticity

Homoscedasticity stands as one of those statistical terms that can seem unnecessarily complex at first glance.

Time Series Decomposition: Extracting Seasonal, Trend, and Residual Components

Still, the exact application, challenges and shortcuts related to this technique are relatively unknown, and that’s what this article seeks to change.

The Concise Guide to Statistical Power

Statistical power might be the most frequently misunderstood concept in research design. While many researchers know they "need" it, few truly understand

Understanding Degrees of Freedom in Statistics

Degrees of freedom (df) represent the number of independent values in a dataset that are free to vary while still satisfying the statistical constraints imposed on the data.

Statology's Most Popular Articles of 2024

Have a look at Statology's most popular articles of the year!

Note: Here are some of the most popular articles from Statology in 2024, along with brief summaries: 1. **5 of the Most Cited Statistical Papers of All Time** This article highlights five landmark statistical papers that have significantly influenced the field, including works by Kaplan and Meier, Cox, Bland and Altman, Duncan, and Marquardt. 2. **10 Essential Statistical Tests Explained in One…

Beyond the Mask: A Comprehensive Study of Discrete Diffusion Models

Masked diffusion has emerged as a promising alternative to autoregressive models for the generative modeling of discrete data. Despite its potential, existing research has been constrained by overly complex model formulations and ambiguous relationships between different…

Square roots and maxima

A brief numerical and graphical check on a 3Blue1Brown video.

Distribution Calculator Guide: From Basic Probabilities to Statistical Tests

The calculators in this guide follow a natural progression, starting with basic probabilities and z-scores, moving through hypothesis testing tools, and concluding with specialized distributions.