Eikosstatistics & data science

Experimental Design & Data Collection · Survey Design & Psychometrics

Survey Design: Basic Probabilistic Sampling Designs and Estimation Theory

Public introduction · full guide in Eikos

Introduction

What this guide covers

An expert-level reference on the mathematical foundations of finite populations, design-based inference, and advanced estimation methods.

Overview

Topics covered

  • Introduction
  • Inference in Finite Populations and Design-Based Inference
  • The Horvitz-Thompson Estimator
  • Simple Random Sampling (MAS): Variance Derivations and Estimators
  • Simple Random Sampling Without Replacement (MAS-SR)
  • Estimation of the Mean and the Total

Related concepts

Main connections

  • Variance & standard deviation
  • Mean & expected value
  • Unsupervised learning & clustering
  • Survey sampling methods
  • Linear regression
  • Calculus & differentiation

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

p(s)≥0∀s∈𝒮Y∑s∈𝒮p(s)=1
View LaTeX sourcep(s) \geq 0 \quad \forall s \in \mathcal{S} \quad \text{Y} \quad \sum_{s \in \mathcal{S}} p(s) = 1