From: JSmelser@aol.com
Date: Thu Jul 25 1996 - 11:57:24 EDT
In a message dated 96-07-25 06:07:51 EDT, Erik Van Halsema wrote:
<<Perhaps someone of you in the past did have the need of statistical
analysis.
Could you advice me on basic literature? For instance: suppose that in 1 Cor.
8-10 the average sentence length is 15 (bypassing the problem: 'what is a
sentence'??...). Is it then statistically crorrect to say that a sentence of
e.g., 45 words is something special? 35? 25? 5? I recall there were some
pretty simple rules about that. >>
Erik, averages don't tell us anything about the likelihood of a specific
value. Consider 10 men, five of whom are 200 centimeters tall, and five of
whom are 160 centimeters tall. The average height of these ten men is 180 cm.
Is a height of 200 cm unusual in this group? Clearly not. On the other hand,
the average, 180 cm, is very unusual! None of the men in the group is 180 cm.
If we have knowledge of the variance, in addition to the average, we know
something about how widely dispersed the data is. However we still don't know
what we need to know. Not all distributions are uniform. In other words, if
the "average sentence length" is 10 words, the likelihood of a 15 word
sentence is not necessarily the same as the likelihood of a 5 word sentence.
Therefore, we also need to know the type of distribution that best models the
data in order to comment on the likelihood of specific values. With reference
to modeling a sentence length distribution, it is conceivable that the most
appropriate distribution type might vary from one writer to another.
My B.S. degree is in Actuarial Science, a discipline based heavily on
statistics, and I worked as an actuarial analyst for three years. One thing
that impressed me as I learned more about statistics was the degree to which
statistics are misused by non-mathematicians. I would advise linguists to
exercise caution when tempted to draw conclusions based on statistical
analysis.
With regard to literature on the subject, do you have in mind works that
specially discuss the use of statistics in linguistical analysis, or are you
interested in text books on statistics per se? With regard to the former
category, I have had no occasion to become familiar with such. Perhaps
someone else on this list could better advise you of such. I could mention
some text books in the latter category, but these assume a background in
mathematics.
-Jeff Smelser
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