Sampling Techniques

• Probability is about predicting what might happen in an experiment based on the nature of the experiment
• Statistics is the art and science of gathering, analyzing and making predictions from numerical information obtained in an experiment.
• The data is the numerical information obtained from the experiment.
• Descriptive Statistics is concerned with collecting, organizing and analysis of data.
• Inferential Statistics is concerned with making generalizations, or predictions about the data that was collected.
• Look at paragraph 4 on page 833.
• The population is the set of everything under consideration.
• The sample is the subset of the data that is studied.
  • Using a sample may lead to errors.
  • Consider a box holding 100 marbles.
  • 10 are red and 90 are blue.
  • A random sample of 10 marbles could yield 10 red marbles, leading one to believe that all of the marbles are red.
• Samples are used for a number of reasons
  • It might not be possible to look at everything. Look at every mosquito to see if it has malaria.
  • It might not be practical to look at everything. Open every can of Dog Foot at Dads to see if it has the proper nutritional mixture.
  • It might not be affordable to look at everything. Call every eligible voter in the US to find their stance on health care.
• It is important to select an unbiased sample
• There are a number of ways samples can be performed, these are called Sampling Techniques
• Random Sampling
  • Select items from a population in such a way that each item is equally likely.
  • The best way to perform this is associate the entire population with a unique number and use a random number generator to sample the population.
  • This is a good, if not always practical technique.
• Systematic Sampling
  • Select every n^th item on a list or off an assembly line or ....
  • The list, however, must contain all items.
  • There must not be a periodic process related to n in the assembly line.
• Cluster Sampling
  • Divide a region into equal sections
  • Random sample in those sections.
  • Divide a city into blocks. Pick a random sample from each block
  • Looking at a lot of many boxes of screws, select some of the boxes and determine how many screws are defective in the boxes, use that to predict how many screws are defective in the lot.
• Stratified Sampling
  • Used when the population is naturally divided into groups.
  • Freshman, Sophomores, Juniors, and Seniors.
  • Undergraduates, Graduates, Faculty, Staff, Administrators
  • This requires knowledge of the population.
• Convenience Sampling
  • Use data that is easily obtained.
  • The people that harass you in the mall.
  • Talk to everyone in the library.
  • This is probably the least effective sampling technique.
• Do problems 15 through 24 page 838

Misuse of Statistics

• You should be cautious when examining statistical information.
• Was the sample conducted properly?
• Was the sample adequate?
• Is the data presented properly?
• Were there other influences that changed the results?
• It turns out that the word "average" has a bunch of different meanings, as we will see later.
• This is true of largest, smallest, and other words. Their use can be ambiguous.
  • What is the largest store?
  • Largest volume sales?
  • Largest inventory?
  • Physically largest building?
  • Largest profit?
• Are any graphs or charts that accompany the data accurate?
• Look at graphs and charts very carefully.
• Look at the pictures on page 840, 841
• Look at some 3-16 page4 942.
• 17, 21