Korelasi data anak dan induk

Untuk mengkuantifikasi korelasi antara kedalaman paruh anak dan induknya, kita ingin menghitung statistik seperti koefisien korelasi Pearson antara induk dan anak. Untuk mendapatkan interval kepercayaan, kita perlu melakukan pairs bootstrap.

Anda telah menulis sebuah fungsi untuk melakukan pairs bootstrap guna memperoleh taksiran parameter dari regresi linear. Tugas Anda dalam latihan ini adalah membuat fungsi baru dengan tanda panggilan draw_bs_pairs(x, y, func, size=1) yang melakukan pairs bootstrap dan menghitung satu statistik pada pasangan sampel yang didefinisikan. Statistik yang diminati dihitung dengan memanggil func(bs_x, bs_y). Pada latihan berikutnya, Anda akan menggunakan pearson_r sebagai func.

Latihan ini adalah bagian dari kursus

Pemikiran Statistik dengan Python (Bagian 2)

Petunjuk latihan

Siapkan sebuah array indeks sebagai sumber pengambilan sampel. (Ingat, saat melakukan pairs bootstrap, kita memilih indeks secara acak dan menggunakannya untuk mendapatkan pasangan.)
Inisialisasi array replikasi bootstrap. Ini harus berupa array satu dimensi dengan panjang size.
Tulis loop for untuk menggambar sampel.
Pilih indeks secara acak dari array indeks yang telah Anda siapkan sebelumnya.
Ekstrak nilai x dan nilai y dari array masukan menggunakan indeks yang baru Anda pilih untuk menghasilkan sampel bootstrap.
Gunakan func untuk menghitung statistik yang diminati dari sampel bootstrap x dan y, lalu simpan ke dalam array replikasi bootstrap Anda.
Kembalikan array replikasi bootstrap tersebut.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

def draw_bs_pairs(x, y, func, size=1):
    """Perform pairs bootstrap for a single statistic."""

    # Set up array of indices to sample from: inds
    inds = ____

    # Initialize replicates: bs_replicates
    bs_replicates = ____

    # Generate replicates
    for i in range(size):
        bs_inds = ____
        bs_x, bs_y = ____
        bs_replicates[i] = ____

    return bs_replicates

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Pemikiran Statistik dengan Python (Bagian 2)

SkillTag.level.intermediateSkillTag.label

4.8+

Mulai Kursus Gratis

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: Paruh burung Finch dan pentingnya statistika Exercise 2: EDA kedalaman paruh burung finch Darwin Exercise 3: ECDF kedalaman paruh Exercise 4: Estimasi parameter kedalaman paruh Exercise 5: Uji hipotesis: Apakah paruh lebih dalam pada 2012?Exercise 6: Variasi bentuk paruh Exercise 7: EDA panjang dan kedalaman paruh Exercise 8: Regresi linear Exercise 9: Menampilkan hasil regresi linear Exercise 10: Rasio panjang terhadap kedalaman paruh Exercise 11: Seberapa berbeda rasionya?Exercise 12: Perhitungan heritabilitas Exercise 13: EDA tentang heritabilitas Exercise 14: Korelasi data anak dan induk

Latihan Saat Ini

Exercise 15: Korelasi Pearson antara data anak dan induk Exercise 16: Mengukur heritabilitas Exercise 17: Apakah kedalaman paruh diwariskan pada G. scandens?Exercise 18: Pemikiran akhir