How to Calculate Standard Error in Python with Scipy & Numpy

🧠 Don’t miss out! Get FREE access to my Skool community — packed with resources, tools, and support to help you with Data, Machine Learning, and AI Automations! 📈 https://www.skool.com/data-and-ai-automations-4579 Want to measure how precise your sample mean is? In this tutorial, you’ll learn how to calculate the standard error (SE) using Python, with real code examples using NumPy and SciPy. Perfect for students, researchers, and data analysts! Code: https://ryanandmattdatascience.com/python-standard-error-of-the-mean/ 🚀 Hire me for Data Work: https://ryanandmattdatascience.com/data-freelancing/ 👨‍💻 Mentorships: https://ryanandmattdatascience.com/mentorship/ 📧 Email: [email protected] 🌐 Website & Blog: https://ryanandmattdatascience.com/ 🖥️ Discord: https://discord.com/invite/F7dxbvHUhg 📚 *Practice SQL & Python Interview Questions: https://stratascratch.com/?via=ryan 📖 *SQL and Python Courses: https://datacamp.pxf.io/XYD7Qg 🍿 WATCH NEXT Statistics for Data Science Playlist: https://www.youtube.com/playlist?list=PLcQVY5V2UY4LF-eHg0tfTpWHhgpX9XF4S One Sample T Test: https://youtu.be/1I3JKTAwfcY Levene's Test: https://youtu.be/CkNGg64f20w Confidence Interval: https://youtu.be/zy8T4hWms1M In this Python tutorial, we dive deep into the standard error of the mean and show you exactly how to calculate it using both manual methods and SciPy. We start by explaining what the standard error is and why it matters in statistics, then walk through four practical examples that range from simple manual calculations to advanced visualizations showing how sample size impacts standard error. First, I demonstrate the manual calculation using NumPy with a baseball strikeout dataset, breaking down the formula step by step. Then I show you how SciPy makes this incredibly easy with just one line of code using stats.sem(). The third example uses simulated marathon times to illustrate how standard error decreases as sample size increases, from 50 to 5,000 samples. Finally, we create a matplotlib visualization that clearly shows the relationship between sample size and standard error. By the end of this video, you'll understand the central limit theorem connection, know when to use standard error, and be ready for our next video on confidence intervals. This is essential knowledge for anyone working with statistics in Python, whether you're analyzing data, running experiments, or building machine learning models. All code is available in the description, and make sure to watch the confidence intervals video next to see how we use standard error in practice. TIMESTAMPS 00:00 Introduction to Welch's T-Test 01:15 Background on Independent Two Sample T-Test 02:00 Pooled vs Welch's T-Test 02:50 Using Levene's Test for Equal Variance 03:25 Hypotheses and Test Setup 04:00 Manual Calculation Example 05:35 Coding Setup and Example 1 07:30 Calculating Means and Variances 09:00 T-Statistic Calculation 10:45 Degrees of Freedom Formula 12:00 P-Value and Hypothesis Conclusion 12:45 Example 2: Running Club Data 14:15 Using SciPy for Welch's T-Test 15:10 Example 3: One-Tailed Test 17:30 Professional vs College Runners Analysis 18:45 Final Results and Wrap-Up OTHER SOCIALS: Ryan’s LinkedIn: https://www.linkedin.com/in/ryan-p-nolan/ Matt’s LinkedIn: https://www.linkedin.com/in/matt-payne-ceo/ Twitter/X: https://x.com/RyanMattDS Who is Ryan Ryan is a Data Scientist at a fintech company, where he focuses on fraud prevention in underwriting and risk. Before that, he worked as a Data Analyst at a tax software company. He holds a degree in Electrical Engineering from UCF. Who is Matt Matt is the founder of Width.ai, an AI and Machine Learning agency. Before starting his own company, he was a Machine Learning Engineer at Capital One. *This is an affiliate program. We receive a small portion of the final sale at no extra cost to you.