Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Spring 2010 MATH 1300-101
Sampling from chapter 13
Good sampling of good data for statistical purposes may look boring and easy.
It certainly is not easy.
In this chapter we see examples of sampling data from large populations,
and then see some failed attempts at drawing good conclusions about the
population by misreading the meaning of the sample or by overrating the value
of the sample or by having a badly developed sample from the beginning.
What follows are some concepts that are of relevance in trying to sample good
data.
- The N-value is the size of the population, from which we are to
sample data.
This value N need not be constant, thereby complicating our ability to draw
conclusions from our sample(s).
- The population can often be clearly partitioned into subpopulations
called strata.
When we build a sample, we may divide the elements of the sample into sample
strata that reflect from which stratum of the population each sample element
originates.
In some sense we sample the different strata somewhat independently, although
the total collection is still called a sample or a stratified sample.
- The most basic sampling technique is simple random sampling, followed
by the slightly more sophisticated stratified random sampling.
Guaranteeing randomness is not easy, even the meaning of what is a random
sample is not easy.
- A parameter is a true value about a population that we would like
to know, or at least like to know approximately.
- A statistic is a value that we derive from our sample, and that
we hope is a good approximation of a parameter.
- The difference between statistic and parameter is called the sampling
error.
There are two main causes of sampling error.
- Chance error.
- Sampling bias.
The sampling proportion is the fraction (n / N) (sample size n over
population size N).
In general, a larger sampling proportion implies a smaller chance error.
- The capture-recapture method is often a way to get a good statistical
approximation of the population size N.
Last updated: February 2010
Comments and suggestions: Email wimr@mscs.mu.edu