Sampling Techniques and the Misuses of Statistics

• statistics is the art and science of gathering, analyzing and making predictions from numerical information obtained in an experiment.
  • In probability, we look at all of the possible outcomes to decide what the chances of an event are.
  • In statistics, we look at the results of a few experiments and determine what the outcomes must look like.
• Consider a magic 8-ball
  • The probability approach is to crack it open and count the number of good, neutral and negative responses and then calculate the probability of each.
  • A statistics approach is to check it a number of times and try to predict the number of each type of response.
• The population is the collection of items studied.
• A sample is a subset of the population, frequently used to predict properties of the population.
• Statisticians sample the population because
• It might be
  • Impractical
  • Impossible
  • Very inconvenient
  to look at the entire population.
• To get a good prediction of the entire population it is important to have a representative or unbiased sample
• In order to accomplish this, statisticians have identified a number of sampling techniques
  • Random Sampling: samples are selected in such a way that each item in the population has an equal chance of being drawn
    • Assign a unique number to each member of the population and use a random number generator to select the sample.
    • Hard to achieve in some cases.
    • This is the gold standard.
  • Systematic Sampling: Starting at some position, select every n^th item.
    • If multiple items are producing the population, make sure that you hit all items.
  • Cluster Sampling : Randomly select a group or groups of the population. Then either observe the entire group, or use another sampling technique on the groups.
  • Stratified Sampling: divide the population based on some characteristic. Sample each group proportionally.
  • Convenience sampling: pick a sample based on what is easy.
  • Biased Sampling: Pick a group that agrees with what you are trying to demonstrate.
• When reading statistics
  • It is important to know the sampling techniques, are the data valid?
  • Make sure words have meaning
    • What is the "biggest" retailer in the nation?
    • This is especially true with the word "average"
  • Be careful with graphs
    • Y axis should start at 0
    • In a circle chart, percent should add to 100
    • EVERYTHING should be labeled.
    • Careful changing two/three dimensional areas
  • Don't draw correlations where they don't exist