Explore statistics, one topic at a time.
Discover statistics from fundamentals and probability to inference, regression, advanced methods, data science and research. Choose a topic to explore its course outline and lessons as they become available.
Statistics topics and courses
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Introduction to Statistics
Understand what statistics is and how it helps us make sense of data.
Importance and Applications of Statistics
Explore real-world uses of statistics across science, business and policy.
Types of Data: Qualitative and Quantitative
Distinguish between different kinds of data and choose appropriate methods.
Population and Sample
Learn the difference between a population and a sample and why sampling matters.
Types of Variables
Identify discrete, continuous, independent and dependent variables.
Data Collection Methods
Compare surveys, experiments, observational studies and other collection methods.
Primary and Secondary Data
Understand when to collect new data and when to use existing sources.
Data Classification and Tabulation
Organise raw data into meaningful categories and tables.
Frequency Distribution Tables
Construct frequency tables to summarise large sets of numerical data.
Charts and Graphs in Statistics
Choose and create appropriate graphical displays for different types of data.
Bar Charts and Pie Charts
Display categorical data clearly using bars and pie slices.
Histograms and Frequency Polygons
Visualise the shape of continuous data distributions.
Measures of Central Tendency
Get an overview of the main ways to describe the centre of a data set.
Arithmetic Mean
Calculate and interpret the arithmetic mean as a measure of centre.
Median and Mode
Use the median and mode when the mean is not the best summary.
Geometric Mean and Harmonic Mean
Apply specialised averages for growth rates and rates of change.
Measures of Dispersion
Describe how spread out the values in a data set are.
Range, Variance and Standard Deviation
Calculate the most common measures of variability in a data set.
Quartiles, Deciles and Percentiles
Locate positions within an ordered data set using quantiles.
Coefficient of Variation
Compare relative variability across data sets with different units or scales.
Introduction to Probability
Build an intuitive understanding of chance and uncertainty.
Basic Rules of Probability
Apply the fundamental rules for combining and calculating probabilities.
Conditional Probability
Calculate the probability of an event given that another has occurred.
Independent and Dependent Events
Distinguish events whose occurrence does or does not affect each other.
Bayes' Theorem
Update probabilities in light of new evidence using Bayes’ formula.
Permutations and Combinations
Count arrangements and selections of objects systematically.
Random Variables
Assign numerical values to the outcomes of random experiments.
Discrete and Continuous Random Variables
Distinguish variables that take countable values from those that take any value in a range.
Probability Mass and Density Functions
Describe the probability structure of discrete and continuous random variables.
Expected Value and Variance
Calculate the mean and spread of a probability distribution.
Bernoulli Distribution
Model a single trial with two possible outcomes—success or failure.
Binomial Distribution
Model the number of successes in a fixed number of independent trials.
Poisson Distribution
Model the number of rare events occurring in a fixed interval.
Geometric Distribution
Model the number of trials needed until the first success occurs.
Uniform Distribution
Study distributions where every value in a range is equally likely.
Normal Distribution
Master the most important continuous distribution in statistics.
Exponential Distribution
Model waiting times between events in a Poisson process.
Student's t-Distribution
Use the t-distribution for inference when sample sizes are small.
Chi-Square Distribution
Apply the chi-square distribution to tests of fit and independence.
F-Distribution
Use the F-distribution to compare variances and in analysis of variance.
Introduction to Statistical Inference
Learn how to draw conclusions about populations from sample data.
Sampling Methods
Choose appropriate methods for selecting representative samples.
Sampling Distributions
Understand the distribution of sample statistics across repeated samples.
Central Limit Theorem
Discover why sample means tend toward a normal distribution.
Point Estimation
Obtain single-number estimates of unknown population parameters.
Properties of Estimators
Evaluate estimators using unbiasedness, consistency and efficiency.
Confidence Intervals
Construct intervals that capture population parameters with stated confidence.
Introduction to Hypothesis Testing
Learn the formal framework for testing claims about populations.
Null and Alternative Hypotheses
Formulate the competing claims that a statistical test will evaluate.
Type I and Type II Errors
Understand the two kinds of mistakes possible in hypothesis testing.
P-Values and Significance Levels
Interpret p-values and choose appropriate significance levels for tests.
Z-Tests and T-Tests
Test hypotheses about means and proportions using z and t procedures.
Chi-Square Tests
Test goodness of fit and independence in categorical data.
ANOVA: Analysis of Variance
Compare means across three or more groups using analysis of variance.
Statistical Power and Effect Size
Plan studies that can detect meaningful effects with adequate power.
Covariance and Correlation
Measure the strength and direction of linear association between variables.
Pearson Correlation
Calculate and interpret the Pearson product-moment correlation coefficient.
Spearman Rank Correlation
Measure monotonic association using ranks instead of raw values.
Simple Linear Regression
Model the linear relationship between one predictor and one response.
Multiple Linear Regression
Extend regression to include several explanatory variables at once.
Regression Assumptions and Diagnostics
Check the assumptions underlying linear regression and diagnose problems.
Logistic Regression
Model binary outcomes and estimate the probability of an event occurring.
Polynomial Regression
Fit curved relationships using polynomial terms in the regression model.
Residual Analysis
Examine residuals to assess model fit and detect unusual observations.
Multicollinearity and Heteroscedasticity
Detect and address common problems that invalidate regression results.
Analysis of Categorical Data
Analyse relationships among categorical variables using contingency tables.
Experimental Design Fundamentals
Learn the principles that make experiments valid and efficient.
Randomized Controlled Experiments
Design experiments that support strong causal conclusions.
Factorial Design
Study the effects of multiple factors and their interactions simultaneously.
Design of Experiments and Sampling Bias
Avoid bias and confounding through careful design and sampling.
Multivariate Statistics
Analyse data involving several response variables simultaneously.
Multivariate Normal Distribution
Extend the normal distribution to multiple dimensions.
Principal Component Analysis (PCA)
Reduce the dimensionality of data while retaining most of the variation.
Factor Analysis
Uncover latent factors that explain correlations among observed variables.
Cluster Analysis
Group observations into clusters based on similarity.
Discriminant Analysis
Classify observations into predefined groups using measured variables.
Nonparametric Statistics
Use methods that do not rely on strong distributional assumptions.
Rank-Based Statistical Tests
Perform hypothesis tests based on ranks rather than raw data values.
Bootstrap Methods
Estimate sampling distributions by resampling from the observed data.
Permutation Tests
Conduct exact tests by rearranging the observed data under the null.
Bayesian Statistics
Update beliefs about parameters using prior knowledge and observed data.
Bayesian Inference
Perform parameter estimation and hypothesis evaluation in the Bayesian framework.
Markov Chain Monte Carlo (MCMC)
Sample from complex posterior distributions using MCMC algorithms.
Survival Analysis
Analyse time-to-event data in the presence of censoring.
Reliability and Quality Control Statistics
Apply statistical methods to ensure product reliability and process quality.
Time Series Analysis
Analyse data collected over time and account for temporal dependence.
Trend and Seasonality
Decompose time series into trend, seasonal and residual components.
Forecasting Methods
Generate future predictions from historical time series data.
Econometrics and Statistical Modelling
Apply statistical models to economic and social science data.
Missing Data Analysis
Handle incomplete data sets using principled statistical methods.
Outlier Detection
Identify and appropriately handle unusual or anomalous observations.
Statistical Computing with R
Perform statistical analysis using the R programming language.
Statistical Analysis with Python
Carry out statistical computing and analysis using Python libraries.
Data Visualization and Statistical Storytelling
Communicate statistical findings clearly through effective graphics and narrative.
Machine Learning: Statistical Foundations
Connect classical statistics to modern machine learning methods.
Statistical Learning and Model Validation
Train, validate and assess predictive models using statistical principles.
Causal Inference
Move beyond association to estimate causal effects from data.
Big Data Analytics
Apply statistical methods to massive and complex data sets.
Statistical Research Methods and Academic Writing
Design studies and communicate results in clear academic prose.
Statistics Research Project and Dissertation
Plan, execute and present a substantial independent research project in statistics.
Choose a category. Build your statistics knowledge step by step.
This directory organises statistics from fundamentals and probability through inference, regression, advanced methods, data science and research. Each topic can have its own course overview, chapter pages, examples, and practice questions. Some course pages still need to be created.