Glossary/Jargon
- Reference distribution - the standardized distribution used to compute probabilities. Examples include the Normal distribution, Chi-squared distribution, T distribution, and F distribution.
- Sampling distribution - the true distribution of a statistic drawn from data randomly sampled from a distribution. For a test statistic, it may not be the same as the reference distribution if we are using approximations or assumptions are violated.
- Statistic - a random variable computed as a function of a random sample.
- Test statistic - the standardized value, which is assumed to follow the reference distribution.
- One/two tailed hypothesis
- Paired/unpaired test
- One/two sample test
- Skew
- Type 1 error rate - the probability of falsely rejecting the null when it is true.
- Type 2 error rate - the probability of falsely retaining the null when it is false.
- Power - the probability of correctly rejecting the null.
- Wald statistic - A statistic derived as the estimator minus the parameter divided by the variance of the estimator times square root of \(n\), \(\frac{\sqrt{n}(\hat\mu - \mu)}{\text{Var}(\sqrt{n} \hat\mu)}\).
- Parameter - an unknown population value.
- Estimator - a statistic used to estimate a parameter.
- Estimate - a function of an observed sample used to estimate a parameter (not random).
- Coverage - The proportion of the time that an interval captures the true value of the parameter.
- Width/Length - The expected width/length of a confidence interval is the distance between the upper and lower bounds.
- Consistent estimator - an estimator that converges to the target parameter as the sample size gets bigger.
- Standard error - the standard deviation of a statistic.