Inferential Statistics

To find out information about a population, we can do two things:

• CENSUS: Look at every object or individual in the population.
  • Advantages: We know everything exactly!
  • Disadvantages: It takes a lot of time and money, may even be impossible to do if measurements are destructive (e.g., average lightbulb lifetime).
• STATISTICAL INFERENCE: We sample the population (in a manner to ensure that the sample correctly represents the population). We then take measurements on our sample and infer (or generalize) back to the population.
  • Advantages: Less time and money.
  • Disadvantages: We no longer know everything exactly, we have some error.
• EXAMPLE: We may want to know the average height of all adults (over 18 years old) in the U.S. Our population is then all adults over 18 years of age. If we were to census, we would measure every adult and then compute the average. By using statistics, we can take a random sample of adults over 18 years of age, measure their average height, and then infer that the average height of the total population is ``close to'' the average height of our sample.

The goal of inferential statistics is to use sample statistics to make inference about population parameters.