Biostatistics

10.

Statistical Inference

10.1.

Estimation Theory

10.1.1.

Point Estimation

10.1.1.1.

Estimators and Estimates

10.1.1.2.

Properties of Estimators

10.1.1.2.1.

10.1.1.2.2.

10.1.1.2.3.

10.1.1.2.4.

10.1.2.

Interval Estimation

10.1.2.1.

Confidence Intervals

10.1.2.1.1.

Concept and Interpretation

10.1.2.1.2.

Construction Methods

10.1.2.1.3.

Confidence Level Selection

10.1.2.2.

Confidence Intervals for Means

10.1.2.2.1.

Known vs Unknown Variance

10.1.2.2.2.

Large vs Small Samples

10.1.2.3.

Confidence Intervals for Proportions

10.1.2.3.1.

Normal Approximation

10.1.2.3.2.

10.1.2.3.3.

Continuity Correction

10.1.2.4.

Factors Affecting Interval Width

10.1.2.4.1.

10.1.2.4.2.

Confidence Level

10.1.2.4.3.

Population Variability

10.2.

Hypothesis Testing Framework

10.2.1.

Null and Alternative Hypotheses

10.2.1.1.

Formulation and Types

10.2.1.2.

One-Sided vs Two-Sided Tests

10.2.2.

Test Statistics

10.2.2.1.

Definition and Properties

10.2.2.2.

Sampling Distributions

10.2.3.

Critical Values and Rejection Regions

10.2.3.1.

Determination Methods

10.2.3.2.

Relationship to Significance Level

10.2.4.

10.2.4.1.

Definition and Calculation

10.2.4.2.

Interpretation Guidelines

10.2.4.3.

Common Misinterpretations

10.2.5.

Type I and Type II Errors

10.2.5.1.

Definitions and Consequences

10.2.5.2.

Error Rate Control

10.2.5.3.

Relationship to Power

10.2.6.

Statistical Power

10.2.6.1.

Definition and Calculation

10.2.6.2.

Factors Affecting Power

10.2.6.3.

Power Analysis Applications

10.3.

Tests for Single Populations

10.3.1.

Tests for Population Mean

10.3.1.1.

One-Sample Z-Test

10.3.1.1.1.

Assumptions and Applications

10.3.1.1.2.

Test Statistic and P-Value

10.3.1.2.

One-Sample t-Test

10.3.1.2.1.

Assumptions and Applications

10.3.1.2.2.

Degrees of Freedom

10.3.1.2.3.

Comparison to Z-Test

10.3.2.

Tests for Population Proportion

10.3.2.1.

One-Sample Proportion Test

10.3.2.1.1.

Normal Approximation

10.3.2.1.2.

Exact Binomial Test

10.3.2.1.3.

Continuity Correction

10.4.

Tests for Two Populations

10.4.1.

Comparing Two Means

10.4.1.1.

Independent Samples t-Test

10.4.1.1.1.

Equal Variances Assumption

10.4.1.1.2.

Unequal Variances (Welch's Test)

10.4.1.1.3.

Effect Size Measures

10.4.1.2.

Paired Samples t-Test

10.4.1.2.1.

10.4.1.2.2.

Assumptions and Interpretation

10.4.1.2.3.

Advantages over Independent Samples

10.4.2.

Comparing Two Proportions

10.4.2.1.

Two-Sample Proportion Test

10.4.2.1.1.

Pooled vs Unpooled Estimates

10.4.2.1.2.

Chi-Square Test

10.4.2.1.3.

Fisher's Exact Test

10.4.2.2.

10.4.2.2.1.

Paired Proportions

10.4.2.2.2.

Applications in Before-After Studies

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9. Bias and Confounding

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11. Analysis of Variance (ANOVA)