Sampling Distributions

statistics

See also: Hypothesis Testing

Definitions:

• parameter :: numerical descriptive measure of a population. (usually unknown b/c populations are big)
• sample statistic :: numerical descriptive measure of a sample (like variance, stddev, etc)
• probability distribution :: the probability of every event in a population
• sampling distribution :: get statistics for a bunch of samples and model the statistic as a probability distribution
• point estimator :: rule/formula which says how to use sample data to to estimate a population parameter
• biased/unbiased estimates :: if a sample statistic is equal to the population parameter, it’s unbiased. Otherwise, it’s biased.

Population parameters vs sample statistics

	population param	sample stat
mean	$\mu$	$\bar{x}$
median	$\eta$	$M$
variance	${\sigma }^2$	$s^2$
standard deviation	$\sigma$	$s$
binomial proportion	$p$	$\hat{p}$