Innumeracy is to mathematics and statistics as illiteracy is to reading with understanding. Alas for this country, innumeracy runs rampant thanks to our public school system, which is more concerned about indoctrinating our children with the worship of our Dear Leader (where is the separation of church and state when you really need it???) and generating the entitlement mindset than it is with the basics of life, the reading, writing, and arithmetic that led this country to the greatness it once had and that will result in true freedom (including freedom from the tyranny of the elite, which liberals dread because they are the elite, at least in their own minds). The issue is a systemic one, crossing multiple presidencies and the dominance of both political parties. Our current President is merely utilizing the tools already created for him, tools created by the leftist ideology of those we have allowed to brainwash our children in our education institutes.

The particularly pernicious problem is less with the mindless fools behind the cash registers of our nation who can’t give change without their cash registers telling them what to do and more with The Innumerati of the statistical kind in the MSM and government. These are the ones who make and/or take the statistics they find at face value and do not think critically about them as they seek to make public policy and national legislation based on the alleged “facts” of the numbers before them. And then “The simple believes every word….” (Proverbs 14:15) Since thinking critically is such a lost art and a root cause of many of the issues we face today, we here at The Interface continually rail against common errors usually exposed in Basic Statistics 101 as they appear to support various and sundry of the claims of liberals.

Just recently I attended a statistical software conference and was introduced to an author whose works would go a long way in addressing this issue if they were actually read and used intelligently by those who did so. Dr. Joel Best is a sociologist, a discipline that requires a thorough understanding of statistical analysis given the nature of the data which describes the behavior of humans in groups. I just finished reading his book, Stat-Spotting: A Field Guide to Identifying Dubious Data (2008), and I highly recommend it to the point of summarizing it below. He has authored two other books that I have yet to read, but which likewise look interesting: Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists (2001), and More Damned Lies and Statistics: How Numbers Confuse Public Issues (2004). (Full disclosure statement: I do not get any remuneration at all for my recommendations of his work. I doubt he even knows I exist!) These books are replete with specific examples, yet they span the ideological spectrum and generally are ideologically neutral so as to demonstrate the problem without concomitant emotional complications to obscure the issue.

Very well done indeed.

THE CONTEXT

In his introduction, Dr. Best notes [editorial comment added]:

This book is guided by the assumption that we are exposed to many statistics that have serious flaws [an assumption that he proves true in his examples both in this book and his others]. This is important, because most of us have a tendency to equate numbers with facts, to presume that statistical information is probably pretty accurate information. If that’s wrong – if lots of the figures that we encounter are in fact flawed – then we need ways of assessing the data we’re given. We need to understand the reasons why unreliable statistics find their way into the media, what specific sorts of problems are likely to bedevil those numbers, and how to decide whether a particular figure is accurate. (page 5)

Probably one of his primary points about statistics is that

Every statistic is the product of a series of choices made by the people who produce, process, and report the data. In particular, when we see statistics in media coverage, we need to appreciate that those numbers are the products of choices made not just by the folks who actually gathered the data but also by those who brought the story to the attention of the media and by the people in the media who selected this story for coverage and who then chose how to repackage the information as news. (page 111)

Now, one of the things Piker (our resident liberal who honestly tries to make sense of my ramblings and respond with some intelligence, which makes him an outlier of that population) likes to try to catch me on is my use of generalizations which apparently do not allow for exceptions or a spectrum of behaviors rather than a black and white approach. (I would contend that this merely means he does not understand the role of generalizations, but that is another argument.) This is particularly true when it comes to discussions of motive, and here I think Dr. Best strikes a good balance that even Piker would approve:

Sometimes, of course, the people who present numbers intend to deceive us: they deliberately present false figures or statistics that give a misleading impression. But bad statistics often have more mundane explanations: the people who prepare or present numbers may themselves be confused and fail to understand the figures’ flaws. And, although they may not set out actually to lie, they would prefer that their figures be at least interesting enough to capture attention among the cacophony of competing claims for publicity. A source’s sincerity is no guarantee of a number’s accuracy. (page 112)

Having pointed this out, he then notes the proper attitude with which to approach The Innumerati in their lair:

This means we need to approach the statistics we encounter with a certain skepticism, an appreciation that numbers are produced by people – people who have their own agendas, people who can’t always be counted on to criticize figures that seem to support their views, people who sometimes make mistakes. Taking a moment to think critically about statistics can be time well spent. (page 112)

So, how does one go about doing this? What are the specifics? Again, let me encourage you to get the book. It is well worth it to see the examples he uses to illustrate the guidelines he puts forth. Be not afraid of the statistics…there are no formulas whatsoever in this book, and it is written in a simple and engaging style that is an excellent example of good didactic method. His sure signs of numerical problems are listed in the next section by category.

COMMON SIGNS OF DUBIOUS DATA (pages 103-105)

BACKGROUND

• Numbers seem inconsistent with benchmark figures (basic, familiar facts).
• Severe examples are used to illustrate a supposedly common problem.

BLUNDERS

• Numbers that seem too high or too low may be caused by a misplaced decimal point.
• Botched translations convert statistics into simpler but incorrect language.
• Misleading graphs distort the reader’s visual interpretation of the data.
• Errors in strings of calculations affect the final figures.

SOURCES

• Big round numbers may be a sign of guessing.
• Hyperbole (“the biggest,” “the worst”) may reveal exaggeration.
• Claims that seem unbelievably shocking may indeed be unbelievable.
• A problem is given a disturbing name, calculated to arouse concern.

DEFINITIONS

• Broad definitions lead to big numbers.
• Expanding a problem’s definition makes the problem seem larger.
• Changing a problem’s definition distorts measures of change.
• A problem’s definition may exclude less disturbing cases.

MEASUREMENTS

• New statistics invite the question, How was this measure created?
• Unusual units of analysis can lead to questionable conclusions.
• Surveys may use loaded questions that encourage particular responses.
• Changes in measurements may affect the resulting statistics.
• Competing methods of measurement may produce different results.

PACKAGING

• Numbers are presented in the most impressive format (percentages for the most common problems, absolute numbers for this less common).
• Generalizations may be based on a biased or misleading sample.
• Time frames are chosen to emphasize a particular trend.
• An odd base is used to calculate percentages.
• The number involves a selective comparison (looking only at those cases most likely to be affected).
• A claim reports that some statistical milestone has been passed.
• The word average may refer to either the mean or the median.
• Apparent epidemics may be caused by problems receiving closer attention than before.
• Correlation is implied as proof of causation.
• Dramatic discoveries my prove incorrect.

DEBATES

• Rival explanations identify different causes of the problem.
• Opposing sides disagree about the nature of equality.
• Advocates debate policy choices.

The categories above are those provided by Dr. Best, and this is by no means an exhaustive list of possible issues of innumeracy that can be encountered. However, this is the list he specifically discusses, and it is both entertaining and enlightening to see his specific examples of each. They are all “real life” examples, and he has no shortage thereof.

Now one may ask, if there are so many things that could go wrong with the utilization of numbers and statistics, is there any hope of understanding the numbers thrown at us daily? Are any statistics reliable? Dr. Best also gives us three signs or characteristics of good data which in and of themselves don’t guarantee the correctness of the numbers or their interpretation, but which significantly increase the probabilities that they are accurate. (pages 106-110)

First, “better statistics come with information about the methods used to produce them.” While MSM news snippets obviously don’t have the time to do so, the reports on which such news stories are based should. So, it should be possible to locate the original research report and that document should give sufficient information so that anyone could reproduce the same work with the same results. Information such as the source of the data, how it was measured, and how were the terms defined allow for a more accurate assessment of the reliability of the data, the methods, and thus, of the conclusions. One of the advantages of the Internet is the available of sources and the ability to link to them so immediate verification and evaluation can take place…if one wants such. It is certainly a standard The Interface tries to maintain. (This is not to say that if you see it on the Internet, it must be true!)

Second, “better statistics tend to be subject to competing pressures.” What he means here is that it is better when people who disagree participate in producing and interpreting the statistics, and thus present both sides of the issue. This would be especially important regarding controversial matters. Numerous instances could be cited from the current cultural landscape where one side has announced that their conclusions are indisputable and are “fact” and so any discussion thereof is meaningless and that to doubt them is logically impossible, if not downright illegal! They “won” and all opposition should just sit down and shut up and let them, the geniuses who came to this conclusion, run the show. The AlGorians come to mind, as do evolutionists. Don’t get me started….

Third, “better statistics tend to use consistent measures.” Since better statistics allow us to follow trends across time and space, it is necessary to have a common unit of measure to allow accurate comparisons.

Let’s close this post now with one more recommendation to get, read, study, and apply this book, and as one further incentive, here is one of his examples (pages 19-20; there are footnotes in the book for his sources; get it to verify) [editorial comment added]:

EXAMPLE: HOW MANY MINUTES BETWEEN TEEN SUICIDES?

“Today, a young person, age 14-26, kills herself or himself every 13 minutes in the United States.” - Headline on a flyer advertising a book

When I first read this headline, I wasn’t sure whether the statistic was accurate. Certainly, all teen suicide is tragic; whatever the frequency of these acts, it is too high. But could this really be happening every 13 minutes?

A bit of fiddling with my calculator showed me that there are 525,600 minutes in a year (365 days x 24 hours per day x 60 minutes per hour = 525,600). Divide that by 13 (the supposed number of minutes between young people’s suicides), and we get 40,430 suicides per year. That sure seems like a lot – in fact, you may remember from our discussion of statistical benchmarks that the annual total number for suicides for people of all ages is only about 32,000. So right away we know something’s wrong.

In fact, government statistics tell us that there were only 4,010 suicides by young people age 15-24 in 2002. That works out to one every 131 – not 13 – minutes. Somebody must have dropped a decimal point during their calculations [or failed to use their calculator right when doing the division; thank you public school system!] and, instead of producing a factoid, created what we might call a fictoid – a colorful but completely erroneous statistic. (Sharp-eyed readers may have noticed that, in the process, the age category 15-24 [fairly standard in government statistical reports] morphed into 14-26.)

You’ve probably seen other social problems described as occurring “every X minutes.” This is not a particularly useful way of thinking. In the first place, most of us have trouble translating these figures into useful totals, because we don’t have a good sense of how many minutes there are in a year. Knowing that there are roughly half a million – 525,600 – minutes in a year is potentially useful – a good number to add to our list of benchmarks. Thus, you might say to yourself, “Hmm. Every 13 minutes would be roughly half a million divided by 13, say, around 40,000. That seems like an awful lot of suicides by young people.”

Moreover, we should not compare minutes-between-events figures from one year to the next. For instance, below the headline quoted above, the flyer continued: “Thirty years ago the suicide rate in the same group was every 26 minutes. Why the epidemic increase?” The problem here is that the population rises each year, but the number of minutes per year doesn’t change. Even if young people continue to commit suicide at the same rate (about 9.9 suicides per 100,000 young people in 2002), as the number of young people increases, their number of suicides will also rise, and the number of minutes between those suicides will fall. While we intuitively assume that a declining number of minutes between events must mean that the problem is getting worse, that decline might simply reflect the growing population. The actual rate at which the problem is occurring might be unchanged – or even declining.