Mean, Median and Sample Size for Dummies

Sample size vs population

One of the things we've noticed quite often while searching the halls of eHow.com for bogus freelance jobs is that DotD candidates may do a fairly good job of rewording some very specific information while completely missing the point of the question they're supposed to answer. Say, for instance, going into detail about the habitat and growth habit of Solidago canadensis while neglecting to mention that the flower's color is the source of the name for goldenrod paper. Such is the case of today's candidate, repeat offender Jack Ori (sometimes known as Stephanie Silberstein), caught attempting to explain "The Effect of Sample Size on Mean & Median" for Synonym Science (now at Sciencing.com).

If you, like many of our staffers, remember the basics of your statistics class; you know that the most important effect of sample size on those two stats is in how closely they may approximate the analogous parameters of the population as a whole. Unfortunately, Ori's post fails to use the word "population" at all. Oops.

While much of what Jack / Stephanie says in the post is more or less correct, some is a little "off." Take, for instance, the claims that

"If the sample size is too small, the mean scores will be artificially inflated or deflated... Similarly, the median scores will be unduly influenced by a small sample size." Clearly, Ori does not understand statistics: you cannot "artificially inflate" or "deflate" the mean value -- it is either correctly calculated, using the method Jack mentions, or it isn't. What you can change by changing sample size is your confidence in the measurement's accuracy. That's what the post's only reference says, but it's highly technical and very likely caused "Jack's" eyes to glaze over by the end of the abstract.

Ori / Silberstein finishes by opining that

"Small sample sizes are problematic because the results of experiments involving them are not usually statistically significant..."

...which, our house statistician says, is essentially correct. However, Jack never says a word about large sample sizes. Since, at least as far as anyone here can remember, about half of statistics is spent determining optimum sample size, we'd like to have known more about that aspect... but Ori's not forthcoming. Darn: and here we thought he'd avoided picking up his fifth Dumbass of the Day award. Sorry, Jack. Sorry, Stephanie.

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