The numbers

Some years ago, I had a statistics class where our teacher used a very telling example:

'If I survey 3 dentists, and 2 of them recommend a specific toothpaste or dental hygiene tool, can I go ahead and make the statement: 2 out of 3 dentists recommend such a toothpaste?"

An argument consists of a conclusion that makes a claim of some sort and one or more premises intended to provide support for that conclusion. There are 2 different ways such support can be offered, depending on whether the premises aim at guaranteeing the truth of the conclusion or at simply providing some reasons for it. We can say that a conclusive relation between certain premises and a claim is a mark of a deductive argument, and a nonconclusive relation to that of an inductive argument. All arguments exemplify either one or the other of these two relations.

Why do I mention the above?

Let's talk about "black on black crimes" for a minute. I was inspired by a recent thread on Twitter by Michael Harriot, a senior writer at The Roots. I wanted to dive in what he says and write my own version of it with my own calculations.

As a numbers person myself, I always remember that a lot of arguments rest on fallacies. Such as in our above example where a hasty generalization affects the enumerative induction that 67% of dentists will recommend a specific toothpaste while only 3 have been interviewed. See where I'm going? A representative number of dentists was not observed to draw this conclusion. This is a mistake of trying to draw a conclusion about all things of a certain kind having a certain feature on the basis of one having it, or a sample that is neither comprehensive nor randomly selected like a serious study will.

Let's get back to the numbers. By looking at the FBI website, we can find data about arrests, do remember that crimes were committed by the same person (room for duplication). We can use an assumption here, let's say that each crime (murder) was committed by a different black person. The results show 53% (5,025) were committed by black or African American.

https://ucr.fbi.gov/crime-in-the-u.s/2017/crime-in-the-u.s.-2017/topic-pages/tables/table-43

The latest census tells us that there are 47 million black people in the US. Following the assumption we made earlier that each crime was committed by a different person, that means a ratio of 5025/47 million will yield that 99.989497% of black people not committing murders. By the same math, that also suggests that 99.994923% of white people did not commit murder.

The black population represents more or less 13% of the total US population, using the actual numbers it means 0.10% of black people committed murders and 0.005% of white did the same. In other words, as Michael Harriot beautifully stated:" I will need to meet 10,000 different people before I meet a murderer". We can do the same calculations using all the other crimes, but I think my point is becoming clearer here. The robustness of methodology provides more reliable statistics that can be use in arguments. This argument about: "there are more black on black" crimes is basically not what it seems to be.

Let's dive into another aspect, we know that generally without context and history, it is easy to use statistical syllogism. This is basically an inductive argument whereby a certain feature is ascribed to some case or cases on the basis of their being subsumed within a larger class of things, some of which, sometimes many, have the ascribed feature. In our example, we see that the underneath calculation yielded a different result than what is generally heard.

We know that crimes have a context, any crime has some kind of sociological aspect associated with it. We know that sociologists describe crime as a whole as being an economic phenomenon so this suggests that the people with less will commit more crime, in other words people who are poor are more likely to commit crime. We will dive in this reality in another post as it is a little more complicated than this even though we know there is a correlation between crimes and inequality in society.

So to come back to that anecdote from the beginning, we see that we can make the numbers tell any story if we do not have to prove anything. The definition of statistics includes "large quantities" when we want to make inferences and this matters when anyone wants to use "stats" to justify a point or an argument. Always look for the underlying truth in anything that uses numbers, the same statistics could tell a different story

Until next time.

Feel free to share your thoughts in the comments below!

Oscar the talkative Platypus.