Sampling Theory

4.

Estimation from Samples

4.1.

Point Estimation

4.1.1.

Estimator Properties

4.1.1.1.

4.1.1.2.

4.1.1.3.

4.1.1.4.

4.1.1.5.

Minimum Variance

4.1.2.

Population Mean Estimators

4.1.2.1.

4.1.2.2.

4.1.2.3.

Ratio Estimators

4.1.3.

Population Total Estimators

4.1.3.1.

Expansion Estimators

4.1.3.2.

Weighted Total Estimators

4.1.4.

Population Proportion Estimators

4.1.4.1.

Sample Proportion

4.1.4.2.

Weighted Proportion

4.1.5.

Population Variance Estimators

4.1.5.1.

Sample Variance

4.1.5.2.

Unbiased Variance Estimators

4.2.

Interval Estimation

4.2.1.

Confidence Interval Concepts

4.2.1.1.

Confidence Level

4.2.1.2.

Margin of Error

4.2.1.3.

Coverage Probability

4.2.2.

Confidence Intervals for Means

4.2.2.1.

Known Population Variance

4.2.2.2.

Unknown Population Variance

4.2.2.3.

t-Distribution Applications

4.2.3.

Confidence Intervals for Proportions

4.2.3.1.

Normal Approximation

4.2.3.2.

4.2.3.3.

Continuity Corrections

4.2.4.

Confidence Intervals for Totals

4.2.4.1.

Expansion from Mean Intervals

4.2.4.2.

Direct Total Estimation

4.2.5.

Central Limit Theorem Role

4.2.5.1.

Asymptotic Normality

4.2.5.2.

Sample Size Requirements

4.2.6.

Confidence Level Interpretation

4.2.6.1.

Frequentist Interpretation

4.2.6.2.

Common Misconceptions

4.3.

Variance and Standard Error

4.3.1.

Variance of Sample Mean

4.3.1.1.

Simple Random Sampling

4.3.1.2.

Stratified Sampling

4.3.1.3.

Cluster Sampling

4.3.2.

Variance of Sample Proportion

4.3.2.1.

Binomial Variance

4.3.2.2.

Design-Based Variance

4.3.3.

Standard Error Concepts

4.3.3.1.

Standard Error of Mean

4.3.3.2.

Standard Error of Proportion

4.3.3.3.

Standard Error of Total

4.3.4.

Finite Population Correction

4.3.4.1.

FPC Factor Calculation

4.3.4.2.

When to Apply FPC

4.3.4.3.

Impact on Standard Errors

4.3.5.

Variance Estimation in Complex Designs

4.3.5.1.

Linearization Methods

4.3.5.2.

Replication Methods

4.3.5.3.

Bootstrap Methods

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3. Non-Probability Sampling Methods

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5. Advanced Estimation Techniques