Always, humans struggle to live with uncertainty And they seek ways to predict the future. If in the past they wondered the oracles, today we rely on more scientific tools: the chance and the statistics. These two disciplines, often confused, try to quantify the uncertainty of events from two different but complementary points of view.
There chance starts from a a priori theoretical model And try to predict what is possible that a certain event really happens. There statisticson the other hand, observes, collects and interpret the data On a phenomenon that has already happened and tries to understand what the process that generated it was.
In other words, the chance va From theory to datawhile the statistics va From data to theory. These two approaches, however, are closely linked to each other and the boundaries on where the probabilistic approach ends and where the statistical one began are often nuanced. In this article we see what are the differences between these two disciplines and what their applications are.
The probability starts from a model and provides what will happen
There chance It is the branch of mathematics that measures the degree of uncertainty of an event a priori. In simple words, it helps us to understand how much it is possible that something happens before it really happens.
Let’s imagine launching a nut Don’t make up: we already know that every face has the same possibility to go out, so the probability of obtaining a 5 is 1 in 6 (about 16.7%). We did not need to actually launch the dice hundreds of times to get to this conclusion: we just need to know how the nut is made (he has six faces and is not made up) for create our model And calculate the chance theoretical of each launch. This is precisely what is probability: it builds and studies a theoretical model and uses it to predict what could happen in the future.
The statistics starts from the data and tries to reconstruct the model that generated them
If the probability starts from a model to make predictions, the statistics The reverse path follows: collects, analyzes and interprets the real data For understand the model that generated them.
Let’s resume the example of the nut: if we launch it 100 times and come out 50 times the face with one and only 10 times each of the other faces, we can suspect that the nut is make -up. Observing the data available to us, we could say that the face with the 1 is heavier and we could therefore predict that, at the next launch, the number 1 has a 50% probability of going out, while each of the other faces has a 10% probability.
This is what statistics do: observe a phenomenon, it describes it and tries to understand why it happened. If we just observe and describe the data, then let’s talk about Descriptive statistics. We can, however, push us a little further and try to predict what will happen in the future generalizing what we learned from the data. In this case, we talk about inferential statistics.
Statistics and probability help us make decisions in many different areas
Without realizing it, we both use these tools every day. When we say “Heaven with sheep, water in Catinelle“we are making an inference, that is, a generalization and statistical prediction, based on the observation of past events. If instead we evaluate If it is better to bring the umbrella Based on the probability of rain provided by the weatherwe are applying a probabilistic reasoning.
Statistics and probability are everywhere
There are several areas where statistics and probability are fundamental:
- in the politics, where the electoral polls help to predict the result of the elections;
- in the medicine, where they are used to study the effects of drugs on groups of patients;
- in sport, where the performance of athletes are analyzed to optimize game strategies;
- in the finance, where probabilistic models are used to evaluate the risk of an investment and statistics to analyze market trends;
- In the gambling, where the shares are decided based on the probability of a certain event or according to the statistics of the players and teams;
- in the’artificial intelligence, where they are used to generate phrases and likely images.
In Italy, the main institutions that deal with data collection and statistical analysis are theIstat (National Statistics Institute), which collects demographic and economic data, and theISS (Higher Institute of Health), which studies epidemiological and health data. Collecting the data, studying them and trying to understand the causes is essential to make informed decisions.
