CourseTrain the student in the use of basic statistical techniques for exploratory data analysis. Present problems involving the use of statistical data analysis in decisions.For the student:- BUSSAB, Wilton de O.; MORETTIN, Pedro A. Basic Statistics. Saraiva, 2017.- Attendance will be required;- There will be a test and an exam.StatisticsAs a reminder, statistics aims at the collection, reduction, analysis, and modeling of data. From now on, we will focus heavily on data modeling. A statistical model is a simplified representation of reality.As the saying goes:“Essentially, all models are wrong, but some are useful”- George E. P. BoxWhen we say that a coin, when tossed, has a 50% chance of being heads and a 50% chance of being tails, we are creating a mathematical/statistical model that helps us understand this phenomenon, assisting us in decision-making. If you stop to think about it, perhaps the coin lands on its edge (or perhaps it does not even fall); these n possibilities are discarded in order to have a useful and understandable model.A model widely used in biology to estimate the population size of a species is the Lincoln-Petersen estimator. In this model, you have to follow a few steps: capture some individuals, mark them, wait a while, capture some individuals again. In the end, we have the following rule of three: First capture -------- Total population Marked found in the second capture -------- Second capture The animals captured first are marked. Soon afterward, there is a second capture and it is checked how many of those captured have the marks; the number found is proportional to the total population. Given that we know how many we captured the first and second time, we can use a rule of three to know the total population. Done, a model has been described.The Lincoln-Petersen estimator has several caveats (it is left as an exercise to think about what they are), but it is in fact useful and the final result almost always is close to the true result!The problem here lies in the use of almost always; since one expects information that is assimilated equally by everyone, these terms can generate doubt.- What is almost always to you?- Is the chance of being close to the result the same in every situation?- What is close to the result?For there to be uniformity in the scientific method, models are not characterized using abstract words, but rather probability! Changing the statement to:>The model predicts a significance of 1%or:>the model predicts that in 99% of cases there will be an error of less than 5%ProbabilityThe study of probability began with humans' desire to predict the future, from the Romans carrying out battle formations to questions about whether astrology really had any meaning. Cicero, upon seeing the Roman army at Cannae being slaughtered by Hannibal's smaller army, remarked ironically: "did all the Romans who fell at Cannae, by chance, have the same horoscope?" Cicero created the term probabilis, which eventually gave rise to the word probability. [2]The Romans also created the Digest, a section of the Roman code of laws compiled by Emperor Justinian in the 6th century, the first document in which probability appears as a legal concept. Previously, legal conflicts were resolved by force, choosing a man to fight in one's place. When they replaced this old method, the concept of evidence and witnesses was used; in the end, they were concerned with the probability that the truth was being told being the greatest. [2]But why, before the Romans, were there no studies in the field of probability?> Why didn't the Greeks develop a theory of probability? One answer is that many Greeks believed that the future unfolded according to the will of the gods. If the result of a game of astragali meant “marry the stocky Spartan woman who pinned you in that fight behind the barracks,” a Greek youth would not see the game as a product of luck (or misfortune) in a random process; he would see it as the will of the gods. With this worldview, an understanding of randomness would be irrelevant. Therefore, the mathematical prediction of randomness would have seemed impossible. [2]The will of the gods is not the only plausible explanation. The lack of interest in the study of probability can also be explained by the heuristic biases we deal with daily.The availability heuristic, related to the individual's tendency to resort to their most recent memories or experiences, easily retrieved from memory. This occurs because when we reconstruct the past, we give unjustified importance to the most vivid memories. For example, how many 6-letter words have ç as the 4th letter? And how many 6-letter words end with ção? If you believe there are more words ending in ção than words that have ç as the 4th letter, you have fallen for the availability heuristic. [1]Let's take another example. Imagine the following woman: "Joana studied law and has always been in favor of animals and against nuclear programs. She has always stood up for herself and believes that the world can improve." Which is more likely? (1) Joana is a banker; (2) Joana is a banker and a feminist. If you answered 2, you are part of the majority. Many people forget that being a banker and a feminist is within the set of being just a banker.Let's go to another example: "Diego is a shy young man who loves stories and reading books." Which is more likely? (1) Diego is a librarian; (2) Diego is a farmer. If you answered 1, you are part of the majority that forgot that the population of farmers is larger than the population of librarians, so the probability of being a farmer should end up being greater than being a librarian.The representativeness heuristic is based on the use of reference mental models (stereotypes) as the basis for decision-making. Cases of prejudice, racism, or "uncomfortable situations," such as that of the Brazilian Jean Charles de Menezes, killed in 2005 after being mistaken for a terrorist, are clear examples of how this heuristic can affect our decisions. [1]The anchoring heuristic is a cognitive bias that describes the common human tendency to "anchor" oneself to a characteristic or part of the information received. To prove the anchoring effect, there is a simulation in which people write the last two numbers of their CPF on a piece of paper. Soon after, the instructor creates a scenario in which the person must give a cigar as a gift to someone else and write the amount they would pay for it next to the CPF numbers. The result proves that: the higher the person's CPF number, the greater the tendency for the value assigned to the cigar to be higher. The explanation lies in the simple fact that many people do not have the anchoring of a cigar in their life experience, and even so, unconsciously, the brain searches through an anchor for the answer to the price of the cigar. Since the CPF number is the only anchor given to the brain, it bases itself on it to give the answer. [3]The table below demonstrates the heuristics we experience daily.HeuristicBiasAvailabilityEase of recall Presupposed associations RetrievabilityRepresentativenessInsensitivity to base rates Misinterpretation of chance Regression to the mean misinterpretation of chance conjunction fallacyAnchoring and adjustmentOverconfidence Confirmation trap Curse of knowledgeThe Monty Hall ProblemThe game, from 1970, consists of the following: Monty Hall (the host) presented three doors to the contestants, knowing that behind one of them there is a car (a good prize) and that the others have prizes of little value; one imagines a goat behind each of the other doors. [4]- In the 1st stage, the contestant chooses one of the three doors (which is not yet opened);- In the 2nd stage, Monty opens one of the other two doors that the contestant did not choose, revealing that the car is not behind that door;- In the 3rd stage, Monty asks the contestant whether they want to decide to stay with the door they chose at the beginning of the game and open it, or whether they switch to the other door that is still closed and then open it. Now, with only two doors to choose from — since one of them was already seen, in the 2nd stage, not to have the prize — and knowing that the car is behind one of the two, the contestant has to make the decision.Choose the other door or stay with the same one? The Monty Hall paradox is less than 50 years old, but it was one of the most discussed cases in the field of statistics. Inspired by the program Let's Make a Deal from the same period, it became extremely famous in the USA, and the person who answered it was Marilyn vos Savant, famous for having been cited for many years in the Guinness Book of Records Hall of Fame as the person with the highest IQ ever recorded on the planet (228). Marilyn stated that it is advantageous to choose another door, which generated an avalanche of letters in which more than 92% of the American public said she was wrong!Marilyn is right, which led to the phrase:> Our brain was not very well designed to solve probability problemsWork to Think About- Has any bias ever influenced your opinions?- Think about models we can create for situations that occur in our lives.ConclusionThe course aims to present models and situations of probability from our real life. Pay close attention to the flaws in the models, to the flaws that people have simply because they are people, which may occur in the collection, analysis, and inference of data. Remember that from now on we are in the field of science, and for that reason the language changes. Do not use abstract terms; use universal terms!References[1] JUNIOR, Willian Gatti; NASCIMENTO, Paulo Tromboni de Souza. Heuristics and biases applied to supplier relationship management: A contribution to the theory of behavioral operations. XVIII SIMPEP–Production Engineering Symposium. Bauru–SP: Nov, 2011.[2] MLODINOW, Leonard. The Drunkard's Walk. Zahar, 2009.[3] Aronson, E. et al. (2003). Social Psychology. Pearson Studium. ISBN 3827370841[4] https://pt.wikipedia.org/wiki/Problema_de_Monty_Hall
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