Sampling Techniques

• Probability- given knowledge of the experiment, can we predict the chances for a given outcome?
• Statistics given some outcomes, can we tell something about the population of the experiment?
• Statistics is the art and science of gathering, analyzing, and making inferences (predictions) from numerical information obtained in an experiment.
• The numerical information is called data
• Descriptive Statistics is concerned with collecting, organizing and analysis of data
• Inferential Statistics is concerned with making predictions based on the data.
• The data we analyze comes from a population or the entire collection of things.
• We sample the data, or remove a subset to examine.
• We use statistics because it is often impossible to study the entire population.
• Example 1: We wish to determine if the formula in Coke is correct at a bottling plant for the last week. If we open all of the cans, we won't have anything to sell, so we select a number of cans to test.
• Example 2: We want to know if the students at Edinboro are interested in building an ice arena. We could ask everyone on campus, but this would be time consuming and difficult, so we ask 100 people at random.
• There are a number of ways we form a sample:
  • Random -
    • Use some random process to select items from the population
    • Use a table of random numbers (computer generated for example)
    • This may cause problems if we are not careful.
      • For example, a random sample of people in the library will be vastly different from a random sample of people in the field house.
      • Or a sampling of people at noon will be different from a sample of people at 6:00 pm, or even 6:00 am.
    • We may need a way to sample things that are not uniform - marbles vs a bag of sports balls.
  • Systematic
    • Select every n^th item.
    • For example, talk to every 7^th person waling through Doucette hall.
    • Or remove every 100^th can on an assembly line.
    • Some of the same problems as above.
    • And make sure that you don't have 7 people doing the same job on the assembly line, and you always select the work of person number 4
  • Cluster
    • Divide an area into regions
    • Perform a sample in each region
    • In some cases the entire region is selected
    • In others a random sample is performed witin the region
    • Select 5 city blocks in a town and survey all the residents of the block
    • Select a box of items, and look at all the items in the box.
  • Stratified
    • Divide the population into classes or stratum based on knowledge of the population
    • Draw a representative sample from each strata
    • You need to know something about the population to do this.
  • Convenience
    • Use data that has already been collected
    • This is likely to be biased
    • Often you hear about this in medical studies.

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