Statistical Inference

Learning about a population from a sample, and quantifying the uncertainty.

In suggested reading order:

1. Sampling Distributions. The distribution of a statistic, such as the sample mean, over all the samples that could have been drawn.
2. Law of Large Numbers. As a sample grows, its average gets closer and closer to the expected value.
3. Central Limit Theorem. The mean of many independent observations is approximately normally distributed, whatever the shape of the population.
4. Point Estimation. Using a single number computed from a sample to estimate an unknown population parameter, and judging how good that rule is.
5. Likelihood and Maximum Likelihood Estimation. The likelihood measures how well each parameter value explains the observed data; the maximum likelihood estimate is the value that explains them best.
6. Confidence Intervals. A range of plausible values for a parameter, produced by a procedure that captures the true value in a stated fraction of repeated samples.
7. Hypothesis Testing. A procedure for deciding whether data are inconsistent enough with a default claim about a population to reject that claim.
8. P-values and Statistical Significance. The probability, assuming the null hypothesis and the model are true, of a result at least as extreme as the one observed.