Citation needed! Let’s study Bernoulli trial statistics! (USA 2014 retrospective edition)


manga_probability_distribution
For purposes of the present argument, I will make a few assumptions that do NOT hold in most arguments:
1. In this argument, the USA BJS is allowed to conflate rape and sexual assault.
2. In this argument, the data collection methods of the USA BJS are not questioned.
3. In this argument, we consider a hypothetical lifetime from 12 to 82 years of age.
4. In this argument, the random chances for a single individual are independent from year to year. (This is dictated by the limited information; obviously common sense suggests that a 21-year-old is more likely to be assaulted than a 75-year-old. The BJS should have summarized the data in smaller sets to avoid this problem. Notes on refinement are below the main calculation.)
5. In this argument, we assume our hypothetical lifetime has zero sexual experience at age 12.

(That last two are huge vague spots necessitated by the limits of statistics. The random chances involved are obviously not independent from year to year for one individual; individuals in vulnerable social situations have above-average chances to be assaulted. Because the USA BJS starts collecting data at 12, all their conclusions can be selectively attacked – but that is for a different argument.)

The USA BJS claims that in 2014 there were 1.1 rapes (including sexual assaults) per 1000 persons 12 or older.

http://www.bjs.gov/content/pub/pdf/cv14.pdf

https://en.wikipedia.org/wiki/Bernoulli_trial

A little bit of arithmetic:

1.1 per 1000 per year equals .0011 per year.

Thus the basic chance per year is p = .0011

and q = 1-p = .9989

A lifetime from 12 to 82 includes 70 random chances.

The probability of exactly k events over all 70 years is:

“n choose k” * [p^k] * [q^(70-k)]

A little bit of software magic:

The spreadsheet formula for “n choose k” is “=COMBIN(n,k)“. (You can use a free software spreadsheet such as LibreCalc.)

We can draw up a spreadsheet from 0 to 70. The first few lines are:
bernouliiTrials

Therefore – according to the USA BJS – the chance that our hypothetical USA person will go from ages 12 to 82 without reporting even one sexual assault to the USA BJS is more than 92%. About 74 out of 1000 hypothetical respondents would report one or more sexual assaults in a lifetime.

Of course that sounds ridiculously low. Investigations of reports of rape are complicated by false negatives and false positives – i.e., there are incidents that should have been reported, that never get reported – and there are reports alleging incidents when no such incident has occurred.

The above statistical calculation can and should be refined. However, it is not likely that the original USA BJS study contains enough information for an adequate refinement. There is a huge proof gap. We have actionable evidence regarding a certain set of claims of rapes. Within that set, some portion is entirely false, a different portion is based on partial truths, and the remainder is based on unambiguous truths. We know that the original set of allegations leaves out the huge class of unreported rapes, but we have no rational way of measuring that problem.


Why am I bothering to debunk what so many others have already debunked?

Ian Welsh usually writes well, but he recently wrote a bad post that relied on statistics that are widely disbelieved; further he didn’t bother to argue his claim. Ian Welsh’s claim was:

The stats on rape or attempted rate for women are somewhere between one in four and one in six.

wikipedian_protester
In the first place, he didn’t cite a specific document (this is somewhat forgiveable, because a quick search can provide sources to which Welsh would agree). In the second place he didn’t address numerous points of evidence that similar accusations are often false. In the third place, he didn’t address the problem of false confessions.
However the comments to his post are better than Welsh’s post:


June 10, 2016

There is sort of a prisoner’s dilemma here. In an ethnically diverse country, each ethnic group would find it easier to ally with capital to extract resources from other groups than fight against capital.

An ethnic group fighting a class warfare would then have to fight other groups and the ruling elites. However, since they are fighting a class war, even their victories benefit other ethnic groups. So it’s a losing game.


bruce wilder permalink

Some of the commenters are writing as if the penchant of human nature for tribalism is some terrible defect marring the surface of the Platonic Ideal of Rational, Ethical Political Man. That is not even silly.

If there is a problem with tribalism implicated in identity politics it is that tribalism of this kind is so superficial, so easily manipulated by symbolic communications. Identity politics is bad because it is so superficial.

Say what you will about the ethnic balkanization and sexist caste system of pre-1960 America, but it was not superficial. It had roots in the real investment of time and personal energy. People went to union meetings, to church, to the Lodge meeting, to the Chamber of Commerce luncheon, to the Women’s Club. They listened and read.

And, here is the thing that matters: the investment was sometimes sufficient — not always, but often enough — to create a leadership and bind that leadership to the identity and welfare of the group. A Samuel Gompers or WEB DuBois or Brandeis — however capable — was bound to the section of the Commons that made him.

The problem we have in our politics is that we have a steep technocratic hierarchy. And that is new to civilization. It has existed outside militaries for only 150 years, maybe a bit more, if you count railroads. And, we have gained and apparently lost the ability of the commons to discipline elites in those few generations.

Identity politics is a degeneracy of tribalism, where so little energy is invested and the binding is loose enough that it becomes nothing more than a means by which elites manipulate the rubes. A War on Women is the product of a few hours of brainstorming clever PR. If you saw the NYT magazine article on the White House foreign policy PR effort, you know this is how the country is governed.

A key aspect of it is the emergence of corporate business management as the elite’s social and economic class, with a tiny dominating CEO super elite as the kleptocrats in charge. They are invested in their class identity, having gone to specialized schools, attending all kinds of corporate and trade and professional meetings. But, by its nature, this is an elite set at odds against the commons, especially at the C-suite level and among financial managers. And, increasingly, it is all we have.

Identity politics is the window dressing for rule by the corporate executive class. It is Clinton’s feminism of “lean-in”. It is the social justice of no ceilings, a social justice of no floors either. It is a black Congressional Caucus worried that inheritance taxes will inhibit capital accumulation.


 

BlizzardOfOz permalink
June 10, 2016

@tony, good comment. I read De Tocqueville’s Democracy in America recently, and he could have easily predicted the dilemma you mention.

One fact of democracy that seems to have been lost to our public discourse, is that it tends to tyranny because there is nothing to restrain the will of the majority. In his evaluation of American democracy, he cited two factors mitigating that risk: its decentralized administration, and the ethnic, linguistic, and racial homogeneity of the country. We can see that the first is long gone, and the second is going fast.

Liberals seem to be betting on a secular/national identity subsuming tribal and religious ones. And yet, we can see that such an identity is weak, and already cracking under the strain. And further the mass media complex is actively hostile to assimilation to a shared national identity. The western multi-racial nations seem destined for breakup or civil war within a few generations. White liberals are so far unable to see this, and still think they are in class solidarity with the racial and religious minorities they acquiesce to importing in large numbers.


All emphases above were not in the originals.

 

Advertisements
This entry was posted in natural science. Bookmark the permalink.