Lost Between the Plus and the Minus

All statistics are a form of the truth.

Give that a moment to settle in. Let that thought marinate on your conscious mind; play with it, look at it from all sides. All statistics are a form of the truth. All statistics are a form of truth. All statistics are a form of truth.

Here is the definition that I intend to use as the basis for this discussion: all statistics have a truth, but it is a truth that is formed and the formation of that truth is more important than the final result. In other words, what requires that we define a “plus” and a “minus”.

For those of you who remember your basic statistics, the plus or minus refer to the amount of ‘sampling error’ that is present in all statistics. Let that sit for a moment: there is no perfect sample set, there is no perfect statistic. It presents a likely version of a quantitative truth, but it lacks the clear guarantee that 1 + 1 = 2.

But, for the slightly more advanced statistical neophyte, a quick question comes to mind: “But, what about the level of confidence assigned?” Oh, yes, that matters – the degree you need a certain amount of confidence, based on the population size, it helps designate a minimum sample requirement, but that doesn’t solve for the intrinsic issue of the statistic itself: the definition of it.

Let’s choose a live example – let’s choose something present in many a person in our current year: it’s 2012, and in the United States of America, come fall, this country needs to vote a new person into the highest office of the land or vote the same man another 4 years in that office. Nothing provides more examples of the ebb and flow of statistics than political polling in a presidential election year.

Easy first choice: Obama’s Approval Rating. Now, this is conducted by professionals: they do their best to account for types of questions, or order of the questions, or who they ask, where they ask, how they ask, when they ask—

But the fact is he (or which group) designates what is asked has already had a bias in shaping the result. Furthermore, there is a translation, very often, from qualitative concerns (is he effective at moving decisions forward in the legislature, how much you agree with his position on the same-sex marriage debate, do you see him to be a good speaker, etc.) and making the degrees of those answers into numbers that must now become meaningful.

What does a result of 58% mean? That 58% of people approve of his policies, his appearance, his thoughts (as you have shaped and structured them) or that 42% of people don’t approve of your structured opinion of who and what he is?

This is as much a mathematical question as it is a philosophical one. The nature of a statistic is the creation of a truth – very much like history is written by the winner (this survey is written by the winner of the bid to create and distribute it or to access a large enough sample set). There are histories of the world, as there are truths to be found in statistics. The truth can be visualized as such:

It lies somewhere in the middle of a variety of opinions – and even then, it’s hard to estimate, because what’s the relation between Pepé Le Pew (and his Fifth Republic  leanings matched with the Brain’s plan for world domination) versus Winnie’s honeypot-plots versus Pinky’s empty adorations?

Exaggerations, of course, in the name of hyper-visualization of the fallacy of the reliance on one statistic because it presents only one point of view – and we live in a 3-D world (we are 3-D people), and no single number can give all sides of that triangle.

Therefore, in reality, a statistic is just a model. It’s an approximation of a whole truth, and it takes particular factors, or pieces of it, interprets it, as best it can, and spits out a value, of certain, yet limited, meaningfulness.

Ah, so now we’re to models, and what’s my favourite thing about models? We already know they are an approximation of reality (yes, a truth), but what are all models made up of? You know this, assumptions.

So, have you caught it now? The real meaning of that plus or minus is the value of the assumptions which have been plugged into the formation of this statistic. It’s an attempt to account for the limited reality that a single statistic presents.

It’s the shades of grey.

Friends, let’s not get lost in the beauty of 58%+/- 4.7%. The plus or minus 4.7% may be where we find a little more truth; it’s fuzzy, yes, it’s grey, but reality is rarely black or white. While we don’t expect the very floors to evaporate underneath our feet, we don’t live in The Truman Show – it’s not a set, it’s not a controlled environment, and the weatherman gives the appearance of being wrong nearly 50% of the time (plus or minus 25%, because the reality is despite years of modelling, weather is still mildly unpredictable – all of the factors of butterfly wings, sea currents, and winds can never be accounted for).

Get lost in the plus or minus. Get lost in the assumptions – challenge them, accept them, discard them, make them, destroy them. Get lost in the tangible things we can touch and get lost the intangible things which we can only sense because of the force they exert (for absence has a presence, we know that).

Get lost because that’s the only place where you can even begin to find or divine even the most simplest of a single truth.

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