Where Do the Numbers Come From?

"Seventy-five percent of women are wearing the wrong sized bra."
                                    -- Variously quoted in different places

Now that I've got your attention, I've got a problem: where did that exact percentage come from?  Were those presumably uncomfortable ladies asked how their bras feel?  Was this empirically determined?  Is this an inappropriately precise quantification of a less precise amount (e.g., about three out of four).  Writing as a wearer (mostly), I can declare that proper fitting is a complex activity; made more complicated by the fact that there is some variation among brands as to what a specific size means.  Also, the type of bra to be considered.

But, anyway, this is not about bras: it's about numbers.

"There are three kinds of lies: lies, damned lies, and statistics."
                                                  -- Benjamin Disraeli

There are two kinds of statistics: the kind you look up and the kind you make up."
                                                         --Rex Stout

The print media loves numbers; as a matter of fact, it wallows in them.  But very often the numbers provide only very flimsy support for a particular statement.

"He uses statistics like a drunk uses a lightpost; not for illumination, but for support."

Consider the Best and Worst Cities lists.  More defensible criteria might employ crime data, health statistics, economic indices such as income, types of jobs available, recreational opportunities, and others.  But when you do that, you're metaphorically mixing apples and oranges.  If your abiding passion is golf, then being in a golfless community negatively impacts your life.  Also, the impact of some indices impacts certain parts of town more than others.  And certain age groups.  As a matter of fact, it might be appropriate to categorize cities as "Best for Single Women" or "College Students" or "Granolas and Earth Mothers"!

But most of those lists use very limited data, and stretch their conclusions overly much.

The same can be said for "Most Corrupt States."  Now this sticks in my craw a bit: the roll call here has the usual suspects: Louisiana, Illinois, New Jersey, California, and a few others.  Political corruption can be latent or manifest: evidences of political corruption are largely dependent on publicity and seriousness of law enforcement.  Let's face it: some states really fly under the radar: I know far less about Vermont, for example, than I do about Honduras!

But there's also what the numbers represent.  Here we come to the distinction between a population and a sample.  A population is the totality of cases of a particular category.   A sample is a subset of a population.  To go back to the bra issue, the population includes all women wearing bras.  The sample is the number of cases upon which we get our statistic.  So how much credence should we give the sample?  It depends.  Obviously, having a larger-sized sample would help make it more like the population.  But also very important is what type of sample used.  A convenience sample is just that: a group of people surveyed.  This is the cheapest and least powerful type.  A representative sample is one in which some important characteristics of the population (e.g., age, weight, etc.) is approximately replicated in the composition of the sample.  That's a better type, if you chose the dimensions of representativeness well.  A random sample is one in which all possible members of the population have an equal likelihood of being surveyed.  (In that way, you, your next door neighbor, Snooki, Hilary Clinton, some Manhattan socialite, some nutcase living in a cabin in Idaho, and Jon Stewart have an equal likelihood of being surveyed.)

As a final jibe:  when the New York Times reported on the Times-Picyaune soon to come out three days a week, the writer characterized New Orleans as being a dystopia.  That would have been news to New Orleanians, if they gave a damn about what the New York Times wrote.  My point is this: it is the actual residents who get to decide whether their community is working or not.

To end this meandering discourse, I close with this intriguing chart:

Apparently, Italians are happy with their culture; more so than us or other Europeans.  For them, Italy seems to be working; even though it might not seem to be that way to me.