Introduction to Statistics

• Statistics is the art and science of gathering, analyzing, and making inferences (predictions) from numerical information.
• The numerical information is called data
• Descriptive statistics is concerned with collecting, organizing and analyzing data.
• Inferential statistics is concerned with making generalizations, or predictions, from the data.
• "If a probability expert and a statistician find identical boxes, the probability expert might 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 predictions as to the total contents of the box."
• The universal set is called the population in statistics.
• Statisticians form a sample or a subset of the population for study.
• Samples are studied because
  • It is sometimes impossible to study the entire population: Think mosquitoes
  • Studying the population might destroy it: Think testing cans of food for quality of canning process.
  • It would be too expensive to study the entire population: Think talk to every single student at Edinboro.
• We use different symbols for some statistical information to indicate that we are dealing with a population or a sample.
  • Mean: x̄ for sample, μ for population
  • Standard Deviation: s for sample, σ for population
• Generally you can assume we are looking at a sample.
• The goal of honest statistics is to construct an unbiased sample or a sample that is representative of the population.
• The book lists a number of sampling techniques
  • Biased Sampling: Select a population that agrees with what you want to show.
    • Biased by definition
    • Dishonest
    • Worthless scientifically
  • Convenience Sampling: Select whatever data is handy
    • Probably biased
    • Probably not very useful
  • Random Sampling: Select randomly from the population
    • The gold standard.
    • Each item has an equally likely chance of being selected.
    • Draw numbers from a hat, ...
      • Number each element of the population.
      • Select n random numbers
      • Elements corresponding to these numbers are selected.
  • Systematic sampling
    • Select every n^th item that passes by the sampling point.
    • Make sure that the entire population is sampled.
    • This is some times a problem due to systematic processes.
  • Cluster Sampling
    • Divide physically separated data into geographic regions.
    • Randomly select a number of these regions to sample.
    • Use all data within the region, or conduct another sampling technique on the region.
  • Stratified sampling: Divide the population into classes based on some identifying characteristic
  • Sample each of the class
• Do some problems page 778