On Mon, 12 Oct 2009 02:45:28 -0700, Martin Bourgeois wrote: >Nothing hard to understand about it; you dummy code a dichotomous >variable and correlate it with a continuous one. On test items, you can >dummy code a question as right/wrong and correlate it with test scores >to see if people who get it right tend to do better on the test.
To add to what Martin has written: (1) The point-biserial coefficient is the Pearson r calculated on a "truly" dichotomous variable (e.g., an item is right or wrong, gender/sex coded 0=female, 1=male, illness status, 0=not ill, 1=ill, life status, 0=dead, 1=alive, etc.) and an interval or ratio scale continuous variable (e.g., total score on a test, height, weight, number of years of smoking, degree of depression, etc.) The specific equation for the point-biserial is simplify hand calculation, simplifications that arise from dealing with dichotomies in form of zero and one. The Wikipedia entry provides additional background as well as the point-biserial's relationship to tests which appear similar but are not based on the Pearson r (e.g., the biserial coefficient and the rank-biserial); see: http://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient (2) The point-biserial coefficient is now often covered in introductory statistics textbooks. For example, Gravetter & Wallnau include it and present it as a way of obtaining an effect size measure from the two-sample t-test. One version of the formula is the following: point biserial r**2 = t**2/(t**2 + df-TOTAL) where **2 means raised to the power of 2. Taking square roots of both sides provides the point-biserial r. I like Glass & Hopkins (3rd ed) coverage of correlations and suggest it for additional background: Gene V. Glass and Kenneth D. Hopkins (1995). Statistical Methods in Education and Psychology (3rd edition ed.). Allyn & Bacon. ISBN 0205142125 This book is available on books.google.com but only in a "snippet view" (I believe that it continues to be a popular book that is used in a variety of undergraduate statistics courses); see: http://books.google.com/books?lr=&num=100&id=SFmdAAAAMAAJ&dq=%22Glass+%26+Hopkins%22&q=point-biserial#search_anchor or http://tinyurl.com/yg2ftct -Mike Palij New York University [email protected] ________________________________ On Monday, October 12, 2009 4:45 AM, Michael S wrote: > >I never did understand the point-biserial statistic.I came across >it at Mizzou when I was in charge of grading lots of scantrons. >It had something to do with test items but I never figured out why. --- To make changes to your subscription contact: Bill Southerly ([email protected])
