Quanto è diverso il rapporto?

Nell’esercizio precedente, hai calcolato il rapporto medio tra lunghezza e profondità del becco con intervalli di confidenza al 99% per il 1975 e per il 2012. I risultati di quel calcolo sono mostrati graficamente nel grafico che accompagna questo problema. Oltre a questi risultati, cosa diresti del rapporto tra lunghezza e profondità del becco?

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Pensiero statistico in Python (Parte 2)

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Pensiero statistico in Python (Parte 2)

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When doing statistical inference, we speak the language of probability. A probability distribution that describes your data has parameters. So, a major goal of statistical inference is to estimate the values of these parameters, which allows us to concisely and unambiguously describe our data and draw conclusions from it. In this chapter, you will learn how to find the optimal parameters, those that best describe your data.

Exercise 1: Optimal parameters Exercise 2: How often do we get no-hitters?Exercise 3: Do the data follow our story?Exercise 4: How is this parameter optimal?Exercise 5: Linear regression by least squares Exercise 6: EDA of literacy/fertility data Exercise 7: Linear regression Exercise 8: How is it optimal?Exercise 9: The importance of EDA: Anscombe's quartet Exercise 10: The importance of EDA Exercise 11: Linear regression on appropriate Anscombe data Exercise 12: Linear regression on all Anscombe data

To "pull yourself up by your bootstraps" is a classic idiom meaning that you achieve a difficult task by yourself with no help at all. In statistical inference, you want to know what would happen if you could repeat your data acquisition an infinite number of times. This task is impossible, but can we use only the data we actually have to get close to the same result as an infinitude of experiments? The answer is yes! The technique to do it is aptly called bootstrapping. This chapter will introduce you to this extraordinarily powerful tool.

Exercise 1: Generating bootstrap replicates Exercise 2: Getting the terminology down Exercise 3: Bootstrapping by hand Exercise 4: Visualizing bootstrap samples Exercise 5: Bootstrap confidence intervals Exercise 6: Generating many bootstrap replicates Exercise 7: Bootstrap replicates of the mean and the SEM Exercise 8: Confidence intervals of rainfall data Exercise 9: Bootstrap replicates of other statistics Exercise 10: Confidence interval on the rate of no-hitters Exercise 11: Pairs bootstrap Exercise 12: A function to do pairs bootstrap Exercise 13: Pairs bootstrap of literacy/fertility data Exercise 14: Plotting bootstrap regressions

You now know how to define and estimate parameters given a model. But the question remains: how reasonable is it to observe your data if a model is true? This question is addressed by hypothesis tests. They are the icing on the inference cake. After completing this chapter, you will be able to carefully construct and test hypotheses using hacker statistics.

Exercise 1: Formulating and simulating a hypothesis Exercise 2: Generating a permutation sample Exercise 3: Visualizing permutation sampling Exercise 4: Test statistics and p-values Exercise 5: Test statistics Exercise 6: What is a p-value?Exercise 7: Generating permutation replicates Exercise 8: Look before you leap: EDA before hypothesis testing Exercise 9: Permutation test on frog data Exercise 10: Bootstrap hypothesis tests Exercise 11: A one-sample bootstrap hypothesis test Exercise 12: A two-sample bootstrap hypothesis test for difference of means

As you saw from the last chapter, hypothesis testing can be a bit tricky. You need to define the null hypothesis, figure out how to simulate it, and define clearly what it means to be "more extreme" in order to compute the p-value. Like any skill, practice makes perfect, and this chapter gives you some good practice with hypothesis tests.

Exercise 1: A/B testing Exercise 2: The vote for the Civil Rights Act in 1964 Exercise 3: What is equivalent?Exercise 4: A time-on-website analog Exercise 5: What should you have done first?Exercise 6: Test of correlation Exercise 7: Simulating a null hypothesis concerning correlation Exercise 8: Hypothesis test on Pearson correlation Exercise 9: Do neonicotinoid insecticides have unintended consequences?Exercise 10: Bootstrap hypothesis test on bee sperm counts

Every year for the past 40-plus years, Peter and Rosemary Grant have gone to the Galápagos island of Daphne Major and collected data on Darwin's finches. Using your skills in statistical inference, you will spend this chapter with their data, and witness first hand, through data, evolution in action. It's an exhilarating way to end the course!

Exercise 1: I becchi dei fringuelli e il bisogno della statistica Exercise 2: EDA sulle profondità del becco dei fringuelli di Darwin Exercise 3: ECDF delle profondità del becco Exercise 4: Stime dei parametri delle profondità del becco Exercise 5: Test d'ipotesi: i becchi sono più profondi nel 2012?Exercise 6: Variazione nelle forme del becco Exercise 7: EDA di lunghezza e profondità del becco Exercise 8: Regressioni lineari Exercise 9: Visualizzare i risultati della regressione lineare Exercise 10: Rapporto lunghezza/profondità del becco Exercise 11: Quanto è diverso il rapporto?

Esercizio in corso

Exercise 12: Calcolo dell'ereditarietà Exercise 13: EDA dell'ereditarietà Exercise 14: Correlazione tra discendenti e genitori Exercise 15: Correlazione di Pearson tra dati di prole e genitori Exercise 16: Misurare l’ereditarietà Exercise 17: La profondità del becco è ereditaria in G. scandens?Exercise 18: Considerazioni finali