Statistics in a Nutshell, 2nd Edition

Chapter 3. Inferential Statistics

Statistical inference is the science of characterizing or making decisions about a population by using information from a sample drawn from that population. Most of the practice of statistics is concerned with inferential statistics, and many sophisticated techniques have been developed to facilitate this type of inference. The concept of inferential statistics can be a bit tricky, so it’s worth taking a few minutes to think about what it means to use statistics for inferential reasoning.

The term “inference” is given two definitions by the Merriam-Webster online dictionary:

a) The act of passing from one proposition, statement, or judgment considered as true to another whose truth is believed to follow from that of the former

b) The act of passing from statistical sample data to generalizations (as of the value of population parameters) usually with calculated degrees of certainty

The second meaning, which is specific to statistics, is closely related to the first. Inference in general is a method of making judgments about an unknown, drawing on what is already known to be true. Statistical inference is a specific kind of inference in which you make judgments about a population, as stated earlier.

People are sometimes confused about the difference between descriptive statistics (discussed in Chapter 4) and inferential statistics, in part because some statistical procedures are used in both types of statistics, although there can be subtle differences ...