Tag: Statistics

Thinking Statistically

Thinking Statistically

Posted on by jabittan
In Thinking Fast and Slow, Daniel Kahneman personifies two modes of thought as System 1 and System 2. System 1 is fast. It takes in information, processes it rapidly, and doesn’t always make us cognizant of the information we took in. It reacts to the world around us on an intuitive level, isn’t good at math, but is great at positioning us for catching a football.

 

System 2 is slow. Its is deliberate, calculating, and uses a lot of energy to maintain. Because it requires so much energy, we don’t actually active it very often, not unless we really need to. What is worse, System 2 can only operate on the information (unless we have a lot of time to pause specifically for information intake) that System 1 takes in, meaning, it processes incomplete information.

 

System 1 and System 2 are important to keep in mind when we start to to think statistically, something our minds are not good at. When we think back to the 2016 US Presidential election, we can see how hard statistical thinking is. Clinton was favored to win, but there was a statistical chance that Trump would win, as happened. The chance was small, but that didn’t mean the models were all wrong when he did win, it just means that the most likely event forecasted didn’t materialize. We had trouble thinking statistically about win percentages going into the election, and had trouble understanding an unlikely outcome after it happened.

 

“Why is it so difficult for us to think statistically?” Kahneman asks in his book, “We easily think associatively, wee think metaphorically, we think causally, but statistics requires thinking about many things at once, which is something that System 1 is not designed to do.”

 

System 1 operates quickly and cheaply. It takes less energy and effort to run on System 1, but because it is subject to bias and because it makes judgments on incomplete information, it is not reliable for important decisions and calculations based on nuance. We have to engage System 2 to be great at thinking statistically, but statistical thinking still trips up System 2 because it is hard to think about multiple competing outcomes at the same time and weight them appropriately. In Risk Savvy, Gerd Gigerenzer shows that statistical thinking can be substantially improved and that we really can think statistically, but that we need some help from visual aids and tools so that our minds can grasp statistical concepts better. We have to help System 1 so that it can set up System 2 for success if we want to be good at thinking statistically.

 

From the framework that Kahneman lays out, a quick reacting System 1 running on power save mode with limited informational processing power and System 2 operating on incomplete information aggregated by System 1, statistical thinking is nearly impossible. System 1 can’t bring in enough information for System 2 to analyze appropriately. As a result, we fall back on biases or maybe substitute an easier question over the challenging statistical question. Gigerenzer argues that we can think statistically, but that we need the appropriate framing and cues for System 1, so that System 2 can understand the number crunching and leg work that is needed. In the end, statistical thinking doesn’t happen quickly, and requires an ability to hold competing and conflicting information in the mind at the same time, making it hard for us to think statistically rather than anecdotally or metaphorically.

The Trouble of Probability

Posted on by jabittan
“Most people, it should be noted, are terrible at offhandedly understanding, or even estimating, probability,” Colin Wright writes in his book Becoming Who We Need To Be. Without specific training, human beings generally seem to be pretty bad at statistics and statistical thinking, as Wright states. Our ability to estimate how frequently something should occur or the relative risk of something is not as good as one would think considering the power of our brain to recognize patterns and help us evolve to the point where we are as a species.

 

We really didn’t evolve to be good at numbers. Humans evolved in small tribes that likely numbered 150 people or less. As hunters and gatherers we likely just didn’t deal with numbers that were so large that we needed complex statistics to understand them. The largest numbers we probably really focused on were 10 or 20 and we have enough fingers and toes to help us there. As our societies began to take shape and grow, numbers and statistics still were not the deciding things that determined whether ones genes were passed on or not. Story telling has always had a much greater influence on the human mind than statistics.

 

For most of us, the fact that we are bad at statistics probably doesn’t matter too much. We can invest in mutual funds or index funds, have someone else tell us how much money should be taken from our paycheck automatically, and we will be fine. But if we want to engage with public policy, if we want to do the most good we can do, and if we want to approach the world rationally and leave it better than we found it, we must not only understand a base level of statistics, we must be able to understand how little statistical grounding most people have for their decisions. Convincing someone to make donations to help indigent people is much easier if you can focus on a single individual with a compassionate story who needs help. Overwhelming a person with statistics regarding the number of people who need aid will not convince anyone that their action is necessary. Giving your neighbor or uncle a dizzying array of data points around climate change and global warming is probably less effective than focusing on a single whale that washes up with plastic bags in its stomach, less effective than a story about coral bleaching along the Great Barrier Reef, and less valuable than a visual story of storms destroying the house of someone who looks like your neighbor or uncle. We must work to understand science and statistics ourselves, and we must take what we learn in dry numerically dense academic papers and craft a story that shows people exactly what they will lose if they do not act, or how they can be a hero if they do take the action we encourage.