Statistics for Scientific Research Course

Lesson 1 • Probability Fundamentals for Researchers

Introduces probability rules, conditional probability, and independence as the mathematical basis for inference. Connects probability theory to p-values and confidence intervals introduced later.

Lesson 2 • Types of Data and Measurement Scales

Classifies nominal, ordinal, interval, and ratio data and links scale type to permissible analyses. Correct classification prevents invalid statistical operations downstream.

Lesson 3 • Descriptive Statistics Essentials

Covers measures of central tendency, dispersion, and distribution shape for summarising datasets. These summaries form the baseline for all inferential work in later chapters.

Lesson 4 • Common Probability Distributions

Surveys normal, binomial, Poisson, and t-distributions and their research applications. Understanding distributional assumptions is prerequisite to valid hypothesis testing.

Lesson 1 • Sampling Theory and Strategies

Covers probability and non-probability sampling methods and their effect on generalisability. Proper sampling strategy is foundational to unbiased population-level inference.

Lesson 2 • Bias, Confounding, and Internal Validity

Identifies selection, information, and confounding biases and statistical strategies to address them. Controlling these threats is essential before applying inferential methods.

Lesson 3 • Randomisation and Blinding Techniques

Details simple, block, stratified, and adaptive randomisation and their role in eliminating confounding. Blinding procedures protect against performance and detection bias.

Lesson 4 • Experimental vs. Observational Designs

Contrasts randomised controlled trials, quasi-experiments, cohort, case-control, and cross-sectional designs. Design choice determines which causal claims are statistically defensible.

Lesson 1 • Parametric Tests for Means

Covers one-sample, independent, and paired t-tests and one-way ANOVA with assumption verification. These tests address the most common mean-comparison questions in research.

Lesson 2 • Hypothesis Formulation and Test Logic

Establishes null and alternative hypothesis construction and the logic of statistical decision-making. Correct formulation prevents misaligned tests and misinterpreted outcomes.

Lesson 3 • Chi-Square and Categorical Data Tests

Applies chi-square goodness-of-fit and independence tests and Fisher's exact test to categorical outcomes. These methods are essential for frequency and proportion comparisons in research.

Lesson 4 • Non-Parametric Alternatives

Introduces rank-based tests for data violating parametric assumptions, including Wilcoxon, Kruskal-Wallis, and Friedman tests. Selecting non-parametric methods preserves validity when assumptions fail.

Lesson 1 • Multiple Linear Regression

Extends regression to multiple predictors, addressing multicollinearity, variable selection, and adjusted R-squared. Multivariate control is central to observational research analysis.

Lesson 2 • Simple Linear Regression Principles

Derives the least-squares regression line, interprets slope and intercept, and assesses model fit. This section establishes the conceptual core for all regression extensions.

Lesson 3 • Logistic Regression for Binary Outcomes

Models binary outcomes using logistic regression, interpreting log-odds, odds ratios, and model discrimination. Logistic regression is the standard tool for dichotomous research endpoints.

Lesson 4 • Generalized Linear Models Overview

Introduces Poisson, negative binomial, and gamma regression for count and skewed outcomes. Extends the regression framework to non-normal response distributions common in research.

Lesson 1 • Single and Multiple Imputation Methods

Applies mean, regression, and multiple imputation by chained equations to handle missing values. Multiple imputation preserves uncertainty and produces unbiased estimates under MAR.

Lesson 2 • Missing Data Mechanisms and Patterns

Distinguishes MCAR, MAR, and MNAR mechanisms and their consequences for analysis validity. Correct mechanism identification determines which remediation strategies are statistically justified.

Lesson 3 • Data Cleaning and Outlier Management

Establishes systematic procedures for detecting errors, inconsistencies, and outliers before analysis. Clean data is a prerequisite for reproducible and defensible statistical results.

Lesson 1 • Cluster Analysis Techniques

Groups observations using hierarchical and k-means clustering to reveal natural data structures. Cluster analysis supports subgroup identification in epidemiological and behavioural research.

Lesson 2 • Structural Equation Modelling Basics

Introduces path diagrams, measurement models, and structural models for testing complex theoretical frameworks. SEM integrates factor analysis and regression into a unified confirmatory approach.

Lesson 3 • Principal Component and Factor Analysis

Reduces dimensionality using PCA and identifies latent constructs through exploratory factor analysis. These methods are foundational for scale development and data compression in research.

Lesson 4 • Multivariate Analysis of Variance

Extends ANOVA to multiple dependent variables simultaneously, controlling familywise error. MANOVA is essential when outcomes are theoretically related and should not be tested separately.

Lesson 1 • Competing Risks and Advanced Survival Methods

Addresses competing events using cause-specific and subdistribution hazard models. Standard survival methods produce biased estimates when competing risks are present.

Lesson 2 • Cox Proportional Hazards Regression

Models covariate effects on hazard rates using the Cox model, including assumption testing and interpretation. The Cox model is the dominant regression tool for survival outcomes in research.

Lesson 3 • Repeated-Measures and Longitudinal Designs

Covers within-subject designs, sphericity assumptions, and mixed-model approaches for longitudinal data. Proper handling of correlated observations is critical for valid longitudinal inference.

Lesson 1 • Peer Review and Statistical Critique

Develops skills to critically evaluate statistical methods and results in submitted manuscripts. Statisticians serving as reviewers protect the integrity of the published scientific record.

Lesson 2 • Tables and Figures for Statistical Results

Designs effective tables for descriptive statistics, regression outputs, and survival results. Well-constructed visuals accelerate reader comprehension and reduce manuscript word count.

Lesson 3 • Reporting Standards and Guidelines

Applies CONSORT, STROBE, PRISMA, and related reporting checklists to ensure transparent methods disclosure. Adherence to reporting standards is required by most peer-reviewed journals.

Lesson 4 • Interpreting and Communicating Uncertainty

Teaches accurate verbal and written interpretation of p-values, confidence intervals, and effect sizes. Misinterpretation of uncertainty is a leading source of errors in published research.