Just to dot some i's and cross some t's, a couple of points: (1) As far as I can tell, it is unclear why the "normal" distribution is called the normal distribution. Wikipedia has an entry on the normal distribution (yadda-yadda) and, in the history section, it is pointed out that de Moivre in 1783 first suggested the possibility of what we call the normal distribution. It was Gauss (1809) and Laplace (1774) who would provide a basis for thinking about the normal distribution as a probability distribution and this is why "really old school" statisticians refer to the normal distribution as a Gaussian distribution or Laplace-Gaussian distribution. See: http://en.wikipedia.org/wiki/Normal_distribution#Development
(2) The Wikipedia entry also provides some of the history for the different names that have been used for this distribution. Quoting from the entry: |Naming | |Since its introduction, the normal distribution has been known |by many different names: the law of error, the law of facility of |errors, Laplace’s second law, Gaussian law, etc. By the end of |the 19th century some authors[nb 6] had started using the name |normal distribution, where the word “normal” was used as an |adjective — the term was derived from the fact that this distribution |was seen as typical, common, normal. Peirce (one of those authors) |once defined “normal” thus: “...the ‘normal’ is not the average |(or any other kind of mean) of what actually occurs, but of what |would, in the long run, occur under certain circumstances.”[49] |Around the turn of the 20th century Pearson popularized the term |normal as a designation for this distribution.[50] http://en.wikipedia.org/wiki/Normal_distribution#Naming Why it should continue to be called the "normal distribution" is a puzzlement especially since we know that there are many different probability distributions and these may describe behavioral and/or psychological variables better than the normal/guassian/whatever. (3) I think that the use of the "normal distribution" in psychological testing, especially for IQ and other intelligence tests, promotes the use of the word "normal" because it is expected that "normal" intelligence is variable but extreme values in either direction are rare. So, 2 standard deviations above and below the mean in the normal distribution contain slightly more than 95% of the values in the distribution (thus "normal" or commonly expected) but values beyond this range have less than a 5% chance of occurring by chance (thus, "exceptional" or "special" or whatever euphemism we're using today to refer to people with intelligence way below "normal" or way above "normal"). Similar points can be made for other psychological variables (such as continuous measures of psychopathology). (4) Somebody should mention that what John Kulig and Jim Clark allude to below relates to the "central limit theorem". The Wikipedia entry on the normal distribution also coverts this topic; see: http://en.wikipedia.org/wiki/Normal_distribution#Central_limit_theorem and there is a separate entry on it (yadda-yadda) as well: http://en.wikipedia.org/wiki/Central_limit_theorem (5) I'm surprised no one asked Prof. Sylvester what he mean by "normal" or "normal distribution". It is possible that his definition is not consistent with common or "normal" definitions of those terms. -Mike Palij New York University m...@nyu.edu ------------ Original Message ----------- On Sun, 19 Jun 2011 21:12:41 -0700, Jim Clark wrote: Hi Here's a simple spss simulation of John's point about sums of multiple discrete factors being normally distributed. Just cut and paste into spss syntax window. input program. loop o = 1 to 1000. end case. end loop. end file. end input program. compute score = 0. do repeat v = v1 to v25. compu v = rv.uniform(0,1) > .5. end repeat. compute score1 = v1. compute score2 = sum(v1 to v2). compute score3 = sum(v1 to v3). compute score4 = sum(v1 to v4). compute score9 = sum(v1 to v9). compute score16 = sum(v1 to v16). compute score25 = sum(v1 to v25). freq score1 to score25 /form = notable /hist norm. Take care Jim James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax j.cl...@uwinnipeg.ca >>> John Kulig <ku...@mail.plymouth.edu> 20-Jun-11 4:38 AM >>> Well, most things in psychology have numerous independent causes. Height is caused by at least several genes, your score on an exam is caused by answers to many individual questions, etc. The sum (i.e. adding) of independent events gets "normal" -- faster the more things you add (among other things). Example: Toss ONE coin, and record 0 for tails and 1 for heads. If this experiment - tossing one coin - is repeated long enough, you get about 50% heads and 50% tails (a flat or uniform distribution). Next toss two coins and record the total number of heads - it will either be 0, 1 or 2 heads. Repeat this experiment - two coins in one toss - and 25% of time you'll get 0 heads (TT) 50% of the time you'll get one head (since 1 head can be either TH or HT) and 25% of the time you'll get 2 heads (HH). With 0 1 and 2 heads on the X axis, it's not exactly a normal distribution but it is peaked at 1 head. When this is done by summing, say, number of heads when 5 or 6 coins are tossed in a single experiment, the resultant distribution (number of heads in one experiment) gets "normal" very fast (slower if the probability of a 'heads' is different than the probability of "tails" but it will still get to normal with enough coins in the experiment). Life is like coin tosses, no? Most everything we measure has multiple causes, so it should be no surprise that many things in the natural world are distributed "normally" .. though sometimes when a distribution has deviations from normality it's a clue about different underlying processes. IQ is somewhat normally distributed, though there is a little hump at the lower end (single gene effects?) and a slight bulge in the upper half (high IQ marrying other high IQ people?). Even when you measure the same exact thing over and over - like having all your students measure your height, their measurements will look normal .. classic psychological measurement theory would say that any measurement is the result of your "true" score added to an error component, and in many situations they assume "error" is unbiased, itself normally distributed, yaddy yaddy yaddy ... gets complicated quickly but the bottom line is that many things in the real world simply ARE normally distributed, or at least close enough to assume normality. A google search of the "central limit theorem" will give more precise information than this. On the other hand, I always tell my students to never take normality for granted, and merely LOOKING at data is the first step in determining if we can assume normality. Or at Yogi Berra put it, "you can observe a lot by looking" --- You are currently subscribed to tips as: arch...@jab.org. 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