Sampling Methods | Stratified | Random | Solved Example | Data Mining

In this tutorial, we explore Sampling, one of the most essential concepts in statistics, data science, and machine learning — forming the foundation for everything from surveys and experiments to model training and evaluation.

We begin by understanding what sampling is, why it’s needed, and where it’s applied — from large-scale data collection and randomized controlled trials to class balancing in machine learning datasets. Then, we dive into a practical theoretical problem that highlights two important sampling approaches:

1️⃣ Proportional Stratified Sampling — where we divide the population into groups (or strata) and sample a fixed number of elements from each group based on their size. We’ll derive how this ensures balanced representation, compute inclusion probabilities, and show why it often leads to lower variance and more stable estimates.

2️⃣ Simple Random Sampling (SRS) — where we draw all samples from the dataset as a whole, ignoring group structure. We’ll see how group counts now follow a multinomial distribution, making representation random, and compare its statistical behavior to the stratified method through intuitive reasoning and examples.

Along the way, we’ll derive the key mathematical expressions for inclusion probability, expected counts, and variance under both schemes, explaining why proportional stratification is often superior when groups differ significantly in size or variability.

We’ll then discuss extensions and modifications — such as Neyman allocation for variance minimization, oversampling rare classes for ML fairness, and stratified k-fold cross-validation — all of which stem from the same foundational idea of structured sampling.

Finally, we’ll look ahead to advanced sampling designs, including cluster sampling, probability proportional to size (PPS), and streaming stratified sampling, showing how these build on the core concepts introduced in this tutorial.

By the end of this session, you’ll not only understand the difference between proportional stratified and simple random sampling, but also gain deep insight into when and why to use each, and how sampling design directly affects accuracy, fairness, and representativeness in your data-driven projects.

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Chapters in the video:
0:00 Introduction
0:42 Problem Statement
1:45 Concept Introduction
2:40 Applications
4:50 Core Knobs
5:38 Comparing the Schemes
13:58 Example
16:15 Implementation
17:49 Inference
19:10 Modifications
20:44 Conclusion

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