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" ========================== John W. Kulig, Ph.D. Professor of Psychology Director, Psychology Honors Plymouth State University Plymouth NH 03264 ========================== ----- Original Message ----- From: "michael sylvester" <msylves...@copper.net> To: "Teaching in the Psychological Sciences (TIPS)" <tips@fsulist.frostburg.edu> Sent: Sunday, June 19, 2011 10:48:16 AM Subject: [tips] What's normal about the normal curve? Michael --- You are currently subscribed to tips as: ku...@mail.plymouth.edu . To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13338.f659d005276678c0696b7f6beda66454&n=T&l=tips&o=11063 (It may be necessary to cut and paste the above URL if the line is broken) or send a blank email to leave-11063-13338.f659d005276678c0696b7f6beda66...@fsulist.frostburg.edu --- You are currently subscribed to tips as: j.cl...@uwinnipeg.ca. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13251.645f86b5cec4da0a56ffea7a891720c9&n=T&l=tips&o=11068 or send a blank email to leave-11068-13251.645f86b5cec4da0a56ffea7a89172...@fsulist.frostburg.edu --- You are currently subscribed to tips as: arch...@jab.org. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=11071 or send a blank email to leave-11071-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
