Detection Theory: A User's Guide

By Neil A. Macmillan; C. Douglas Creelman | Go to book overview
Save to active project

Appendix 1
Elements of Probability and Statistics

In this appendix, we offer a brief survey of the parts of probability theory and its application to statistics that are most relevant to psychophysics. Because our aim is to make references to these ideas in the body of book more comprehensible, we frequently allude to psychophysical applications. Most concepts would be covered in a one-semester behavioral statistics course, but some ideas (e.g., random variable) are not usually found at that level. We do not believe, of course, that we have exhausted in this brief chapter topics usually covered in a semester or two. Our incomplete discussion is also relatively informal. Hays (1994) provided a thorough treatment of all issues raised here.


Probability for Finite Sets

Definition of Probability. In the simplest probabilistic situation, an elementary event is chosen at random from the sample space S. If A is a subset of S, then the probability that an elementary event that is in A will occur is

where the function n counts the number of elementary events in a set. For example, when a fair coin is tossed, the probability of a Head occurring is 1/2, as is the probability of a Tail. When a die is tossed, the probability of a “2” is 1/6, and the probability of an Even outcome (“2, “4, or “6”) is 3/6 or 1/2.

Some important characteristics of probabilities are evident from these examples: All probabilities must lie between 0 and 1, and the sum of probabilities for all elementary events must be 1.


Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
Loading One moment ...
Project items
Cite this page

Cited page

Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited page

Bookmark this page
Detection Theory: A User's Guide


Text size Smaller Larger
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

While we understand printed pages are helpful to our users, this limitation is necessary to help protect our publishers' copyrighted material and prevent its unlawful distribution. We are sorry for any inconvenience.
Full screen
/ 492

matching results for page

Cited passage

Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.

Are you sure you want to delete this highlight?