Course
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.
Finishing this course means you have demonstrated the required skills with the level of support this course currently assesses.
- Modules
- 2
- Lessons
- 2
- Skills
- 2
- Starting here
- Assumes 3 prior topics
The route
Module 1: Estimation
The estimator as a random variable, the two standard ways of constructing one, and the properties that decide between competitors, including the case where the unbiased estimator is the worse 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.
Module 2: Testing counts
Comparing observed counts with those a hypothesis predicts: the statistic, the degrees of freedom that account for anything fitted along the way, the condition under which the reference distribution can be trusted, and the exact procedure available when it cannot.
- 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.
What finishing means
Finishing this course means you have demonstrated the required skills with the level of support this course currently assesses.
2 required skills. If you reach a lesson without the background it assumes, you are pointed at the prerequisite first, and returned here afterwards.
How progress is measured
Progress is inferred from evidence you produce, not from pages you have opened. Each required skill moves through states as evidence accumulates: met, practicing with help, performed unassisted, then performed again after a delay.
This course counts a skill as finished atguided. Where the system cannot admit evidence for a stronger claim — for instance when the only available scoring is your own judgment of your written answer — the skill stays at the state the evidence supports, and the reason is shown rather than hidden.