Re: SD Woes

[Dr. Bob Wildblood]

In a little book that a colleague and I wrote nearly 30 years ago (and 
for some completely unknown reason was not picked up by a publisher) we 
said:

     "As a means of comparing dispersion among distributions, the 
average deviation has some value since, simply stated, the greater the 
average3 deviation, the greater the dispersion; however, when using the 
average deviation to interpret scores within a distribution, it is less 
useful since there is not precise mathematical relationship between the 
average deviation and the actual locationof values within the deviation.
     Since the average deviation is of such limited value, why is it 
discussed in this text at all?  The primary reason is because of the 
historical relationship the average deviataion has with the variiance 
and standard deviation, and second, and understanding of the concept of 
deviation as espressed by the average deviation allows us to begin to 
understand errors in prediction.  That is, if you were to try to predict 
the score of a given individual on a test, what is the single best 
guess?  Well, assuming that the data come from a normally distributed 
population and that you are given no other information that the mean (or 
some other measure of central tendency, it turns out that the mean is 
the best predictor.
     When we use the mean as the predicted score, the largest error you 
can make is equal to the most expteme score minus the mean.  Using any 
other score, the maximum possible error is larger."

I think that the text written by Runyon, Haber, (and I don't remember 
who the third author is) has a reasonably good description of what we 
used to call back in the early 70's the Average Deviation.

*********************
----- Original Message -----
From: "Wallace E. Dixon, Jr." <[EMAIL PROTECTED]>
To: "Teaching in the Psychological Sciences"
<[EMAIL PROTECTED]>
Sent: Tuesday, February 25, 2003 12:40 PM
Subject: SD Woes


Speaking of z-score woes, does anyone know how psychology ended up
with standard deviations rather than mean absolute differences from
the mean.  Is it just because of ease of calculation?


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