Uji hipotesis bootstrap satu-sampel

Seekor katak juvenil lain diteliti, Katak C, dan Anda ingin melihat apakah Katak B dan Katak C memiliki gaya tumbukan yang serupa. Sayangnya, Anda tidak memiliki data gaya tumbukan Katak C, tetapi Anda mengetahui rataan gaya tumbukannya sebesar 0,55 N. Karena Anda tidak memiliki data asli, Anda tidak dapat melakukan uji permutasi, dan Anda tidak dapat menilai hipotesis bahwa gaya dari Katak B dan Katak C berasal dari sebaran yang sama. Oleh karena itu, Anda akan menguji hipotesis lain yang kurang ketat: Rataan gaya pukulan Katak B sama dengan rataan gaya pukulan Katak C.

Untuk menyiapkan uji hipotesis bootstrap, Anda akan menggunakan rataan sebagai statistik uji. Ingat, tujuan Anda adalah menghitung probabilitas memperoleh rataan gaya tumbukan yang kurang dari atau sama dengan yang teramati untuk Katak B jika hipotesis bahwa rataan sebenarnya dari gaya tumbukan Katak B sama dengan rataan Katak C adalah benar. Pertama, Anda mentranslasi seluruh data Katak B sehingga rataan menjadi 0,55 N. Ini dilakukan dengan menambahkan rataan gaya Katak C dan mengurangkan rataan gaya Katak B dari setiap pengukuran Katak B. Cara ini mempertahankan properti lain dari sebaran Katak B, seperti varians, agar tetap tidak berubah.

Latihan ini adalah bagian dari kursus

Pemikiran Statistik dengan Python (Bagian 2)

Petunjuk latihan

Translasi gaya tumbukan Katak B sehingga rataan (mean)‑nya menjadi 0,55 N.
Gunakan fungsi draw_bs_reps() Anda untuk mengambil 10.000 replikasi bootstrap dari rataan gaya yang sudah ditranslasi.
Hitung p-value dengan mencari fraksi replikasi bootstrap yang lebih kecil daripada rataan gaya tumbukan teramati milik Katak B. Perhatikan bahwa variabel yang digunakan di sini adalah force_b.
Cetak p-value Anda.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Make an array of translated impact forces: translated_force_b
translated_force_b = ____

# Take bootstrap replicates of Frog B's translated impact forces: bs_replicates
bs_replicates = draw_bs_reps(____, ____, 10000)

# Compute fraction of replicates that are less than the observed Frog B force: p
p = np.sum(____ <= np.mean(____)) / 10000

# Print the p-value
print('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: Merumuskan dan mensimulasikan sebuah hipotesis Exercise 2: Membuat sampel permutasi Exercise 3: Memvisualisasikan pengambilan sampel permutasi Exercise 4: Statistik uji dan p-value Exercise 5: Statistik uji Exercise 6: Apa itu p-value?Exercise 7: Membuat replika permutasi Exercise 8: Berhati-hatilah sebelum melompat: EDA sebelum pengujian hipotesis Exercise 9: Uji permutasi pada data katak Exercise 10: Uji hipotesis dengan bootstrap Exercise 11: Uji hipotesis bootstrap satu-sampel

Latihan Saat Ini

Exercise 12: Uji hipotesis bootstrap dua-sampel untuk selisih rata-rata

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