[Posted only to the edstat list. -- DFB.] On Mon, 1 Sep 2003, in reply to Eric Bohlman <[EMAIL PROTECTED]>'s remark:
>>Another way to put it is that the OP's original distribution is >>discrete, but he's approximating it with a continuous distribution, >>and the area under the appropriate part of the curve of a continuous >>distribution doesn't have to evenly divide that of a discrete one. Stan Brown <[EMAIL PROTECTED]> wrote: > I started to write that at first, but I don't think it's true. The > scores on the test may very well be continuous. You were right the first time, Stan. It is true: scores on a test are NOT continuous. Ever. (1) Scores on a test are nearly always the number of items correct, or a (usually linear) transformation thereof; and the number of items right is necessarily an integer, not a continuous measure. (2) Even if the scores are transformed (via norms tables or otherwise) to some kind of "scaled score", there are a finite number of scores, not exceeding the number of items on the test nor the number of examinees in the data set. (3) The scores are stored and and manipulated using digital computers; it is not possible for a digital instrument to deal with a continuous quantity except by approximation, and ALWAYS to a finite number of significant digits of precision. This would be true EVEN IF the original measuring instrument reported values on a continuum. I usually refer to test scores and such as "quasi-continuous", just to emphasize the fact that they are not in fact continuous a well as to allow a courteous nod in the direction of those who like to think of test scores as reflecting (however imperfectly) a continuous latent trait. The existence of the latent trait, as well as its supposed continuity, are of course both articles of faith, not demonstrable empirical characteristics. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
