Statistics and Sampling Techniques

• Statistics is the art and science of gathering, analyzing and making inferences from numerical information obtained in an experiment.
• Numerical information obtained from an experiment 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 collected.
• Read the forth paragraph on page 833.
• A population consists of all items under consideration.
• A sample is a subset of the population.
• It is important to pick a representative sample in order for predictions about the entire population to be correct.
• To find an unbiased sample a proper sampling technique must be used.
• I would like to determine if we should use student funds to build a new computer gaming room on campus.
• Sampling Techniques
  • Random: assure that the selection of each item in the population is equally likely.
    • Use a random process such as a random number generator.
    • Assign a number to all students, use a random number generator to select 100 students and survey this group.
  • Systematic Sampling: Select every n^th item.
    • Use a regular process to select samples.
    • Alphabetize the list of students, and use every 500^th name.
    • Can be problematic if the production process is periodic as well.
    • For example Every 100th item off of an assembly line which has 20 contributing machines.
  • Cluster Sampling: Divide the population into groups, randomly select the groups to sample, sample every member of the groups selected.
    • This is typically done by geographic area.
    • Select four dorm floors from all of the floors on campus. Ask everyone within that floor.
  • Stratified Sampling: Divide the population into groups, randomly sample within each group
    • Randomly sample within freshman, sophomores, juniors and seniors
    • Randomly sample within each department.
  • Convenience Sampling:
    • Take the sample in some convenient manner.
    • Ask everyone inside the computer lab.
    • Ask everyone at the Field House.

Misuses of Statistics

• We need to know details how the sampling was done.
• Use words such as average which has multiple meanings.
• Provide only partial data.
• Bad Graphs:
  • Condensed Y axis: 90% average in class 1, 92% in class 2.
  • Volume and Area: 3² ≠ 2×3³: Growth doubles, show 1x1 vs 2x2
  • Incorrectly constructed pie charts.