An easy non-computerized demo is have everyone in the class put their height in inches or cm on a slip of paper into a hat, and then sample one by one and plot them on the whiteboard (sample with replacement). How you "figure" the standard deviation depends .. I like to have the actual values in advance, but if not, the "idea" of the standard deviation can be eye-balled from the plot, as well as the mean.
Then you can do the same thing by having someone take out 2 slips of paper at a time and get repeated averages of two heights, plotting the averages on a separate plot on the whiteboard. Again, I like to know the means and standard deviations in advance so I can stack one plot above the other with the means and x-axis values lining up. It can be done with means of 4 or 8 too, but that takes more time. If done carefully, it's easy to see that roughly 2/3 (68%) of X fall within one SD on the X plot, and 2/3 of means lie within one SE on the means plot - with the usual caveat "individual results may vary". When I do this is a stats class (different audience), I sometimes generate random data on MINITAB for a few different sample sizes and pop the histograms out of the computer, and often use sample sizes 1 to 4 to 16, as I can wing the standard error in my head (SE gets chopped in half every time N increases 4-fold, so, if you use IQ scores you can jump from 15 to 7.5 to 3.75 without calculators or computers). If all else fails, my moment of Zen (I do one every stat class). On this topic: "Standard Deviation is to X as Standard Error is to X bar". ========================== John W. Kulig Professor of Psychology Plymouth State University Plymouth NH 03264 ==================================================================== GALILEO GALILEI: I do not feel obligated to believe that the same God who has endowed us with sense, reasons, and intellect has intended us to forgo their use. ==================================================================== ----- Original Message ----- From: "Stuart McKelvie" <[email protected]> To: "Teaching in the Psychological Sciences (TIPS)" <[email protected]> Sent: Thursday, May 6, 2010 1:34:03 PM Subject: RE: re:[tips] standard deviation versus standard error Dear Tipsters, And once the idea of the standard error is understood in the context of the mean, it can be generalized to other statistics. Sincerely, Stuart _____________________________________________________ "Floreat Labore" "Recti cultus pectora roborant" Stuart J. McKelvie, Ph.D., Phone: 819 822 9600 x 2402 Department of Psychology, Fax: 819 822 9661 Bishop's University, 2600 rue College, Sherbrooke, Québec J1M 1Z7, Canada. E-mail: [email protected] (or [email protected]) Bishop's University Psychology Department Web Page: http://www.ubishops.ca/ccc/div/soc/psy Floreat Labore" _______________________________________________________ -----Original Message----- From: Mike Palij [mailto:[email protected]] Sent: May 6, 2010 1:28 PM To: Teaching in the Psychological Sciences (TIPS) Cc: Mike Palij Subject: re:[tips] standard deviation versus standard error On Thursday, May 06, 2010 11:29 AM, Annette Taylor wrote: >I am trying to explain to students with no or minimal stats knowledge >the difference between standard deviation and standard error. They >get SD pretty well because I can talk about average deviation about >a mean for a set of scores. SE, the more commonly accepted error >term these days, is a bit more complicated. Anyone have an "easy" >way to describe it to students? As others have pointed out, you can say that the standard error is a standard deviation but of deviations of sample means relative to the population mean (or our best estimate of the population mean, the mean of the sample means). The key idea is that all of the sample means estimate the population mean but because they are based on subsets from the population, the sample means contain sampling error. If the samples were the same size as the population, there would be no sampling error and the sample means would always be equal to the population mean (standard deviation of sample means = 0). . But as the sample size gets smaller than the population size, the sampling error goes from zero to some measurable amount because some values are not included in the samples used to calculate that sample means.. In small samples, the amount of sampling error can be quite large and the standard deviation of the differences among sample means provides a measure of the amount of sampling error -- thus, the standard deviation for deviations of sample means around the population mean is a measure of error which we refer to as the "standard error of the mean". It might be useful to point out that standard errors can be calculated for most sample statistics and one will see standard errors for statistics like skewness and kurtosis when one uses SPSS for detailed descriptive statistics. -Mike Palij New York University [email protected] --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13510.2cc18398df2e6692fffc29a610cb72e3&n=T&l=tips&o=2492 or send a blank email to leave-2492-13510.2cc18398df2e6692fffc29a610cb7...@fsulist.frostburg.edu --- You are currently subscribed to tips as: [email protected]. 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