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Led by R.A. Fisher Simulacrum
Probability and statistical thinking from frequentist, Bayesian, and subjective interpretations through distributions, hypothesis testing, correlation and causation, and Bayesian reasoning.
Led by R.A. Fisher Simulacrum
The question
Probability is a number between 0 and 1 that expresses how likely something is — but what does "likely" mean? Three interpretations compete. The frequentist says: probability is the long-run frequency of an event (flip a fair coin 10,000 times; it lands heads approximately 5,000 times; the probability of heads is 0.5).
Outcome
The student can describe the three interpretations of probability (frequentist, Bayesian, subjective), state the three Kolmogorov axioms, define independence and conditional probability, and explain the difference between P(A|B) and P(B|A). (Probability as a language)
Sub-units
Led by R.A. Fisher Simulacrum
The question
A single number tells you almost nothing. The average income in a country could be £30,000 — but if half the population earns £10,000 and half earns £50,000, the average is misleading. The distribution tells you everything: not just where the centre is (the mean), but how spread out the values are (the variance), whether they are symmetrical (the normal distribution) or skewed (the income distribution), and how extreme the extremes can be (the tails).
Outcome
The student can describe three measures of centre and when each is appropriate, describe the normal distribution and the 68-95-99.7 rule, explain skewness and why it makes the mean misleading, and state the Central Limit Theorem and why it is foundational. (Distributions and the CLT)
Sub-units
Led by R.A. Fisher Simulacrum
The question
A pharmaceutical company claims its new drug reduces blood pressure. A clinical trial shows a 5 mmHg reduction in the treatment group compared to the placebo group. Is this a real effect, or could it have happened by chance? Hypothesis testing is the framework for answering this question — and the p-value is the number at its centre. The p-value is also the most misunderstood number in science: it does NOT tell you the probability that the drug works.
Outcome
The student can define the null and alternative hypotheses, correctly interpret a p-value, distinguish statistical significance from practical significance, describe Type I and Type II errors, and explain three common misinterpretations of the p-value. (Hypothesis testing)
Sub-units
Led by Pearson Simulacrum
The question
Correlation is not causation — every statistics student learns this. But few can explain precisely why, and fewer still can identify the mechanisms by which correlation misleads. Ice cream sales correlate with drowning deaths — but ice cream does not cause drowning (both increase in summer).
Outcome
The student can compute and interpret r, explain three causal structures (direct, confounding, mediation), explain why only RCTs establish causation, and describe Simpson's Paradox with an example. (Correlation and causation)
Sub-units
Led by R.A. Fisher Simulacrum
The question
A test for a rare disease has 99% accuracy. You test positive. What is the probability you have the disease? If you answered "99%," you have committed base rate neglect — the most common and consequential error in probabilistic reasoning. If the disease affects 1 in 10,000 people, the true probability is approximately 1%. This module teaches the Bayesian framework for updating beliefs with evidence — the antidote to base rate neglect.
Outcome
The student can define base rate neglect, apply Bayes' theorem to a medical test scenario, convert between probabilities and natural frequencies, describe iterative Bayesian updating, and apply Bayesian reasoning to an everyday decision. (Bayesian thinking)
Sub-units