Populations and Samples
Descriptive and Inferential Statistics

Illustrated with the "Immediate Memory Span" Project

GFE Questions:

  1. What are the three basics of measurement?
  2. In this reading, what is meant by "inference"?
  3. Is "inference" similar to inferential or deductive reasoning? You may recall that deductive reasoning is going from the general to the particular; inferential reasoning is going from the particular to the general.
  4. Which is more correct? To say the Monte Carlo technique verifies the validity or reliability of the value measured by the sample?
  5. Whats the difference betweenf a statistic and a parameter.
  6. How is the use of the term "population" different when used by a mathematician/statistician than when used by a scientist/researcher?
  7. When using infential statistical theory to generalize from the sample to the population, what is the scientist's goal?
  8. How can a researcher be sure the prediction/generalization they make is correct?

What I (a scientist) wants to know: These questins are answered scientifically by observing (empiricism).

What do I observe?

I can't measure everyone in order to find out the answer to my question. Its absurd to think that I could. Can I measure relatively few people and use that information as a substitute for measuring everyone?

Perhaps if I measure the memory span on a small set of people (a sample), that will tell me something useful about the memory span of everyone (the population).

Inferential statistics is an area of mathematics where the process of infering population characteristics from sample values has been formalized and made rigorous.

The development of inferential statistics has led to two sets of specialists using similar terms but for different reasons.

By measuring IMS for digits and letters from a small sample of subjects, a scientist can determine memory span for "people in general" However, the scientist, in using inferential statistics knows the generalizations (predictions) will be wrong a certain proportion of the time because some samples are "further away" [have a larger sampling error] than others.

Is there any way to make predictions (generalizations) without error? Yes there is and its really very very simple. Never test your predictions. Never state predictions (theoretical statements) in a way in which they can be disproven. You'll never be wrong.

© 2002 by BurrtonWoodruff. All rights reserved. Modified Friday, June 7, 2002