Een analogie met tijd op de website

Het blijkt dat je al een hypothesetoets hebt gedaan die lijkt op een A/B-test waarin je wilt weten hoeveel tijd er op de website wordt doorgebracht vóór en na een advertentiecampagne. De kikker-tongkracht (een continue grootheid, net als tijd op de website) is een analogie. "Voor" = Kikker A en "na" = Kikker B. Laten we dit opnieuw oefenen met iets dat echt een voor/na-situatie is.

We keren terug naar de no-hittergegevensset. In 1920 voerde Major League Baseball belangrijke regelwijzigingen door die een einde maakten aan het zogeheten dead ball-tijdperk. Belangrijk was dat de werper de bal niet langer mocht bespugen of krassen, iets dat werpers sterk bevoordeelde. In dit probleem voer je een A/B-test uit om te bepalen of deze regelwijzigingen hebben geleid tot een lagere frequentie van no-hitters (dus een langere gemiddelde tijd tussen no-hitters), waarbij je het verschil in gemiddelde inter-no-hittertijd als teststatistiek gebruikt. De inter-no-hittertijden voor de respectievelijke tijdperken staan in de arrays nht_dead en nht_live, waarbij "nht" staat voor "no-hitter time".

Omdat je in deze oefening je functie draw_perm_reps() gebruikt, is het handig om jezelf nog even te herinneren aan de aanroep: draw_perm_reps(d1, d2, func, size=1) of zelfs terug te kijken naar de oefening uit hoofdstuk 3 waarin je deze hebt gedefinieerd.

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Statistical Thinking in Python (deel 2)

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Oefeninstructies

Bereken het geobserveerde verschil in gemiddelde inter-nohittertijd met diff_of_means().
Genereer 10.000 permutatiereplicaties van het verschil van gemiddelden met draw_perm_reps().
Bereken en print de p-waarde.

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Compute the observed difference in mean inter-no-hitter times: nht_diff_obs
nht_diff_obs = ____

# Acquire 10,000 permutation replicates of difference in mean no-hitter time: perm_replicates
perm_replicates = ____


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

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Deze oefening maakt deel uit van de cursus

Statistical Thinking in Python (deel 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-testen Exercise 2: De stemming over de Civil Rights Act in 1964 Exercise 3: Wat is equivalent?Exercise 4: Een analogie met tijd op de website

Huidige oefening

Exercise 5: Wat had je eerst moeten doen?Exercise 6: Toets op correlatie Exercise 7: Een nulhypothese over correlatie simuleren Exercise 8: Hypothesetoets op Pearson-correlatie Exercise 9: Hebben neonicotinoïde insecticiden onbedoelde gevolgen?Exercise 10: Bootstrap-hypothesetoets op spermatelling bij bijen

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