Why is statistics that difficult? How to make it easier?

Since I have dealt with statistics, one of the phrases that I heard most often is: “I’ve never understood anything about statistics”. Someone even exaggerated: “I hated statistics at University “. And these words are pronounced by researchers, PhD students, doctors, biologists and so on.

I’d like to go through this statement in detail in order to understand this presumed difficulty and to give some suggestion on how to understand it with less trouble.

Premise: everything you will read here is my personal consideration based on my own experience, and on the opinions of my colleagues.

Do we have problems with the concept of probability? Then we can use frequencies

In generale, we use the cause-effect mechanism to understand some phenomenon. We need clear causes and concrete facts. We need certainty: if the etiopathogenetic agent is present then you will have the disease. You can be sure, man!

Statistics on the other hand is an acausal subject. The paradigm that statistics uses is not the cause-effect but the probability. And the human being has problems dealing with probabilities. The study published in the ‘Frontiers in Psychology’ by researchers from the University of Regensburg, Germany, explored carefully this concept. In essence, people have much less difficulty solving problems expressed in frequencies than the same identical problem presented as the probability.

In practice, if the data is presented as “1 to 40”, the question becomes easier to understand than if it is expressed in percent (2.5%).

Facts, not probabilities. This is what we understand as human beings.
Ironically, it has also been observed that, as the statistical literature and university lectures usually use the percentages rather than frequencies, students tend to turn frequencies into probabilities in solving a problem. This is something which is called “Einstellung Effect”, the process by which, faced with a problem we do not use the simplest mental pattern but what is most commonly used by our colleagues, friends, etc.

But let’s go ahead.

Good statistics teachers are rare: let’s use emotions and the “non-democratic” nature of statistics

There are very few good teachers, that you would like to listen to four hours without getting tired. And there are even fewer good statistics teachers. IMHO, a teacher should talk about statistics in terms of faith, trust, love and philosophy. Not just numbers. When we deal with a statistical problem we must always be involved on the emotional way to understand its meaning.

One professor of medical statistics explained me the Positive Predictive Value (PPV) in these terms:

“You went to a party last week and you were drunk. The next day you woke up in the bed of a girl who wasn’t exactly Saint Teresa of Calcutta. Today they gave you the result of the test to see if you caught a sexually transmitted disease (let’s say HIV) and the doctor tells you that the PPV of the test is 55%. Translated: out of 100 positive tests only 55 have actually the disease. What would you say? Is it worth to do this test?”

You will remember what the Predictive Value of a test is for a long time. I don’t know why: probably the story in between, the joke, the point about drunkenness. But we all remember that phrase, that example.

The problem is always to perceive the information emotionally or at least in terms of impact on the existence of human being, when you use a ‘statistical’ language.

You can use the “non-democratic” nature of probability.
Let’s take a sentence that you might find in some statistical lecture: “Exposition to that work environment increases the probability to have a certain disease by 29%”.
This 29% has a meaning that depends on different factors that has a subject which reads it: on its beliefs, self-esteem, religious beliefs, courage, etc. There are those who interpret 29% as: “More than two thirds of a full glass”, and those who interpret it as “Damn, I am doomed”. The Statistics is like this: if we perceive it as a technique and calculation, it could become meaningless. If we add a little bit of emotion, then things get easier.

Hold on and look for a mentor

I was desperate during my first year of the Medical Statistics course. I didn’t understand anything on lectures I attended. A groupmate of mine, who was more trained told me: “Don’t be hurry; wait until the point where you will make a “jump”.”

Statistics being an abstractive subject but with practical applications is not immediate. I spent a year or more of a graduate school to make this “leap”. From the groping in the dark and the mechanical use of formulas to real understanding of what I was doing.

At the beginning you probably understand little; once you will make the “jump” you will understand that statistics is not more difficult than other subjects, and that statistical techniques are tools to address a scientific problem like those of a plumber to repair a tap. To make the “jump” and make a friendship with statistics you have to exercise, exercise, and exercise.

Wait. And, if possible, find a mentor who has done your path before you.

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