Bootstrap secara manual

Untuk membantu Anda mendapatkan intuisi tentang cara kerja bootstrapping, bayangkan Anda memiliki himpunan data yang hanya berisi tiga titik, [-1, 0, 1]. Berapa banyak sampel bootstrap unik yang dapat diambil (misalnya, [-1, 0, 1] dan [1, 0, -1] adalah unik), dan berapakah ratarata maksimum yang dapat Anda peroleh dari sebuah sampel bootstrap? Akan bermanfaat jika Anda menuliskan sampel-sampelnya di selembar kertas.

(Data ini terlalu sedikit untuk menghasilkan hasil yang bermakna dari prosedur bootstrap, tetapi contoh ini berguna untuk membangun intuisi.)

Latihan ini adalah bagian dari kursus

Pemikiran Statistik dengan Python (Bagian 2)

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Latihan ini adalah bagian dari kursus

Pemikiran Statistik dengan Python (Bagian 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: Membuat replikasi bootstrap Exercise 2: Memantapkan istilah kunci Exercise 3: Bootstrap secara manual

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Exercise 4: Memvisualisasikan sampel bootstrap Exercise 5: Interval kepercayaan bootstrap Exercise 6: Menghasilkan banyak replikasi bootstrap Exercise 7: Replikasi bootstrap dari rata-rata dan SEM Exercise 8: Interval kepercayaan untuk data curah hujan Exercise 9: Replikasi bootstrap untuk statistik lain Exercise 10: Interval kepercayaan untuk laju no-hitter Exercise 11: Bootstrap berpasangan Exercise 12: Fungsi untuk melakukan pairs bootstrap Exercise 13: Pairs bootstrap pada data melek huruf/kelahiran Exercise 14: Memplot regresi bootstrap

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: Finch beaks and the need for statistics Exercise 2: EDA of beak depths of Darwin's finches Exercise 3: ECDFs of beak depths Exercise 4: Parameter estimates of beak depths Exercise 5: Hypothesis test: Are beaks deeper in 2012?Exercise 6: Variation in beak shapes Exercise 7: EDA of beak length and depth Exercise 8: Linear regressions Exercise 9: Displaying the linear regression results Exercise 10: Beak length to depth ratio Exercise 11: How different is the ratio?Exercise 12: Calculation of heritability Exercise 13: EDA of heritability Exercise 14: Correlation of offspring and parental data Exercise 15: Pearson correlation of offspring and parental data Exercise 16: Measuring heritability Exercise 17: Is beak depth heritable at all in G. scandens?Exercise 18: Final thoughts