Subject
Inferential Statistics
Reasoning from a sample to the population that produced it. Begins with the estimator as an object in its own right, a rule with a distribution, judged by where it is centred and how far it scatters, since the intervals and tests of classical inference are built on one, and the properties that make a procedure trustworthy are properties of the rule rather than of the number it happened to return.
Learning paths
Inferential Statistics
How a claim about a population is derived from a sample, starting from the rule that produces the estimate and the properties by which one rule is preferred to another.
What this subject develops
Build an estimator and defend the choice
Derive an estimator by matching moments or by maximising likelihood, and judge it by the properties of its sampling distribution rather than by the value it produced in one sample.
Test a claim about counts, and check the reference distribution
Compare observed counts with those a hypothesis predicts, determine the degrees of freedom implied by the table structure and by parameters estimated from the data, and check the expected-count condition before quoting the chi-square approximation.
See detailed outcomes
Build an estimator and defend the choice
- The learner can derive an estimator by the method of moments and by maximum likelihood, decompose its mean squared error into bias and variance, and judge competing estimators by unbiasedness, consistency and efficiency rather than by their value on one sample.
Test a claim about counts, and check the reference distribution
- The learner can carry out a chi-square goodness-of-fit test and a test of independence from a contingency table, determine the degrees of freedom from the table shape and the number of estimated parameters, check the expected-count condition, and select a nonparametric alternative when the assumptions of a parametric test fail.
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