13.1, Sampling Techniques

• Statistics: The art and science of gathering, analyzing and making inferences (predictions) from numerical information obtained from an experiment.
• Numeric information is called data.
• Descriptive statistics is concerned with collecting, organizing and analyzing data.
• Inferential statistics is concerned with making predictions from the data collected.
• "If a probability expert and a statistician find identical boxes, the probability expert will open the box, observe the contents, replace the cover, and proceed to compute the probability of randomly selecting a specific object from the box. The statistician might select a few items from the box without looking at the contents and make a prediction as to the total contents of the box."
• A population are all of the items of interest (the universal set)
• Frequently we can not effectively study the entire population so we look at a subset of the population called a sample
• We wish to do our best to make sure that the sample is representative of the population.
• Sampling Techniques are methods used to produce a sample.
• Random Sampling: select elements of the population at random to form the sample.
• Systematic Sampling: Select every n^th item.
• Cluster Sampling: Divide the population into sections, sample EVERYTHING is a few of the randomly selected sections.
• Stratified Sampling: break the population into groups based on some quality, sample each group.
• Convenience Sampling: use any readily available sample of items.

Misuse of Statistics

• To truly judge some statistical evidence we need to know
  • That the sample size was sufficient.
  • That a reasonable sampling technique was used
  • The definitions of the words used.
  • Is all of the data included?
• Examples:
  • What does average mean? We will see at least three different definitions.
  • What is the biggest store in the world?
• Careful with graphs. Do problem 19 page 842