Populations, Parameters, Statistics, and Sampling

Sampling Distributions
• When taking N samples (observations) from the
population, we are interested in is a statistic across all
possible samples of N
– sampling distribution: for an assumed population parameter, the
probability distribution for all possible samples of size N
• e.g., sampling N times from a Bernoulli population with parameter P
• If N=1, the sampling distribution is the population distribution
– sampling distribution of the mean
• just like the population, sampling distributions are theoretical, and
have “true” parameters
– standard deviation of the sampling distribution of the mean is the
standard error of the mean (σ M )
• The statistics from a particular sample give a “point
estimation” for the population parameters
– in general these will be different due to random effects