Statistics Online Course

Lesson 1 • Types of Data and Variables

Classifies variables as categorical or numerical and distinguishes discrete from continuous. Correct classification drives every subsequent analytical choice.

Lesson 2 • Introduction to Statistical Software

Orients learners to a statistical computing environment for data entry and basic operations. Hands-on practice from the start reinforces conceptual lessons throughout the course.

Lesson 3 • What Statistics Is and Why It Matters

Defines statistics as a discipline and contrasts descriptive with inferential goals. Anchors the chapter by establishing why data-driven decisions outperform intuition.

Lesson 4 • Populations, Samples, and Parameters

Distinguishes population parameters from sample statistics and explains why sampling is necessary. Establishes the inferential logic used throughout the course.

Lesson 1 • Graphical Displays for Numerical Data

Builds histograms, stem-and-leaf plots, and box plots to reveal shape, spread, and outliers. These tools directly support the probability concepts introduced in Chapter 3.

Lesson 2 • Graphical Displays for Categorical Data

Creates bar charts, pie charts, and Pareto charts to communicate categorical distributions. Choosing the right chart type is emphasised as a professional communication skill.

Lesson 3 • Measures of Central Tendency

Computes mean, median, and mode and explains when each measure is most appropriate. Selecting the right centre measure depends on data type and distribution shape.

Lesson 4 • Frequency Distributions and Tables

Constructs frequency, relative frequency, and cumulative frequency tables for both variable types. Tables are the foundation for all graphical displays covered next.

Lesson 1 • Conditional Probability and Bayes' Theorem

Defines conditional probability and applies Bayes' theorem to update beliefs with new evidence. Bayesian reasoning recurs in advanced inference and decision-making chapters.

Lesson 2 • Basic Probability Concepts

Introduces sample spaces, events, and the classical, empirical, and subjective probability approaches. These definitions are the language of every inferential method in the course.

Lesson 3 • Addition and Multiplication Rules

Derives the general addition rule and both forms of the multiplication rule for joint events. Mastery here enables correct probability calculations in hypothesis testing later.

Lesson 4 • Discrete Probability Distributions

Defines random variables and constructs probability distributions for discrete outcomes. Expected value and variance of distributions bridge probability to inferential statistics.

Lesson 1 • Normal Distribution Properties

Describes the bell-curve shape, symmetry, and empirical rule for the normal distribution. The normal model is the cornerstone of all confidence intervals and tests ahead.

Lesson 2 • Binomial Distribution

Derives the binomial formula from Bernoulli trials and computes probabilities for fixed-trial experiments. The binomial model is the basis for proportion-based inference in Chapter 6.

Lesson 3 • Normal Distribution Applications

Converts raw scores to Z-scores and finds areas under the normal curve for applied problems. Fluency with normal calculations is required for every inferential chapter.

Lesson 4 • Other Useful Distributions

Introduces the uniform, exponential, and t-distributions as practical modelling tools. The t-distribution is essential for small-sample inference covered in Chapter 5.

Lesson 1 • Central Limit Theorem

States and demonstrates the Central Limit Theorem for non-normal populations. CLT justifies normal-based inference for large samples regardless of population shape.

Lesson 2 • Sampling Distribution of the Mean

Defines the sampling distribution of the sample mean and derives its mean and standard error. This concept is the theoretical engine behind all confidence intervals and tests.

Lesson 3 • Confidence Intervals for Proportions

Builds confidence intervals for population proportions and determines required sample sizes. Proportion intervals are applied directly in quality and survey analysis chapters.

Lesson 4 • Confidence Intervals for Means

Constructs Z-based and t-based confidence intervals for a population mean. Learners interpret interval width and confidence level in practical decision contexts.

Lesson 1 • Tests for a Single Mean

Conducts one-sample Z-tests and t-tests for a population mean and computes p-values. Learners practise the full five-step testing procedure with real datasets.

Lesson 2 • Two-Sample Tests for Means

Compares two independent or paired population means using appropriate t-tests. Choosing between independent and paired designs is a critical applied skill.

Lesson 3 • Logic and Structure of Hypothesis Tests

Establishes null and alternative hypotheses, significance levels, and the decision rule framework. This structure is applied identically across every test type in the chapter.

Lesson 4 • Two-Sample Tests for Proportions

Tests equality of two population proportions and constructs difference intervals. These methods are directly applied in A/B testing and quality comparison scenarios.

Lesson 1 • Chi-Square Goodness-of-Fit Test

Tests whether observed categorical frequencies match a hypothesised distribution. This test extends the chi-square distribution introduced in Chapter 6.

Lesson 2 • Chi-Square Test of Independence

Assesses association between two categorical variables using a contingency table. Results are linked to conditional probability concepts from Chapter 3.

Lesson 3 • Two-Way ANOVA and Interaction Effects

Analyses two categorical factors simultaneously and tests for interaction between them. Interaction plots reveal whether factor effects depend on the level of the other factor.

Lesson 4 • One-Way ANOVA Fundamentals

Partitions total variation into between-group and within-group components to test mean equality. ANOVA avoids the inflated error rate of running multiple pairwise t-tests.

Lesson 1 • Simple Linear Regression Model

Derives the least-squares regression line and interprets slope and intercept in context. The simple model is the building block for multiple regression in the next section.

Lesson 2 • Inference in Simple Regression

Tests the significance of the slope and constructs confidence and prediction intervals. Regression inference integrates hypothesis testing and interval estimation from Chapters 5 and 6.

Lesson 3 • Regression Diagnostics and Assumptions

Checks linearity, independence, normality, and equal variance through residual plots. Detecting and addressing violations ensures reliable predictions and valid inference.

Lesson 4 • Correlation and Scatterplots

Quantifies linear association with Pearson's r and visualises relationships through scatterplots. Correlation analysis motivates and precedes the regression model development.