Uji hipotesis pada korelasi Pearson

Korelasi yang teramati antara buta huruf perempuan dan fertilitas bisa saja terjadi karena kebetulan; fertilitas suatu negara bisa jadi sepenuhnya independen dari tingkat buta hurufnya. Anda akan menguji hipotesis ini. Untuk melakukannya, permutasikan nilai buta huruf tetapi biarkan nilai fertilitas tetap. Ini mensimulasikan hipotesis bahwa keduanya benar-benar independen satu sama lain. Untuk setiap permutasi, hitung koefisien korelasi Pearson dan nilai berapa banyak replikasi permutasi Anda yang memiliki koefisien korelasi Pearson lebih besar daripada yang teramati.

Fungsi pearson_r() yang Anda tulis di bagian awal kursus ini untuk menghitung koefisien korelasi Pearson sudah tersedia untuk Anda.

Latihan ini adalah bagian dari kursus

Pemikiran Statistik dengan Python (Bagian 2)

Petunjuk latihan

Hitung korelasi Pearson teramati antara illiteracy dan fertility.
Inisialisasi sebuah array untuk menyimpan replikasi permutasi Anda.
Tulis for loop untuk menggambar 10.000 replikasi:
- Permutasikan pengukuran illiteracy menggunakan np.random.permutation().
- Hitung korelasi Pearson antara array buta huruf yang dipermutasi, illiteracy_permuted, dan fertility.
Hitung dan cetak nilai p dari replikasi tersebut.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Compute observed correlation: r_obs
r_obs = ____

# Initialize permutation replicates: perm_replicates
perm_replicates = np.empty(10000)

# Draw replicates
for ____ in ____:
    # Permute illiteracy measurments: illiteracy_permuted
    illiteracy_permuted = ____

    # Compute Pearson correlation
    perm_replicates[i] = ____

# Compute p-value: p
p = ____
print('p-val =', p)

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: Pengujian A/B Exercise 2: Pemungutan suara untuk Civil Rights Act tahun 1964 Exercise 3: Mana yang setara?Exercise 4: Analogi waktu di situs web Exercise 5: Apa yang seharusnya Anda lakukan terlebih dahulu?Exercise 6: Uji korelasi Exercise 7: Mensimulasikan hipotesis nol terkait korelasi Exercise 8: Uji hipotesis pada korelasi Pearson

Latihan Saat Ini

Exercise 9: Apakah insektisida neonicotinoid memiliki konsekuensi yang tidak diinginkan?Exercise 10: Uji hipotesis bootstrap pada jumlah sperma lebah

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