Exercise from Think Stats, 2nd Edition (thinkstats2.com)
Allen Downey



In [2]:

    
from __future__ import print_function, division

import thinkstats2
import thinkplot

import first
import hypothesis

%matplotlib inline

Read the data:



In [3]:

    
live, firsts, others = first.MakeFrames()

This is a copy of the class defined in hypothesis.py:



In [4]:

    
class DiffMeansPermute(thinkstats2.HypothesisTest):
    """Tests a difference in means by permutation."""

    def TestStatistic(self, data):
        """Computes the test statistic.

        data: data in whatever form is relevant        
        """
        group1, group2 = data
        test_stat = abs(group1.mean() - group2.mean())
        return test_stat

    def MakeModel(self):
        """Build a model of the null hypothesis.
        """
        group1, group2 = self.data
        self.n, self.m = len(group1), len(group2)
        self.pool = np.hstack((group1, group2))

    def RunModel(self):
        """Run the model of the null hypothesis.

        returns: simulated data
        """
        np.random.shuffle(self.pool)
        data = self.pool[:self.n], self.pool[self.n:]
        return data

Compute the p-value of the difference in weights between first babies and others:



In [5]:

    
data = (firsts.totalwgt_lb.dropna().values,
            others.totalwgt_lb.dropna().values)
    ht = hypothesis.DiffMeansPermute(data)
    p_value = ht.PValue(iters=10000)
    print('\nmeans permute birthweight')
    print('p-value =', p_value)
    print('actual =', ht.actual)
    print('ts max =', ht.MaxTestStat())









    



means permute birthweight
p-value = 0.0
actual = 0.124761184535
ts max = 0.110304921919

Plot the CDF of the test statistic under the null hypothesis:



In [6]:

    
ht.PlotCdf()

Exercise 9.2: In Section 9.3, we simulated the null hypothesis by permutation; that is, we treated the observed values as if they represented the entire population, and randomly assigned the members of the population to the two groups.

An alternative is to use the sample to estimate the distribution for the population, then draw a random sample from that distribution. This process is called resampling. There are several ways to implement resampling, but one of the simplest is to draw a sample with replacement from the observed values, as in Section 9.10.

Write a class named DiffMeansResample that inherits from DiffMeansPermute and overrides RunModel to implement resampling, rather than permutation.

Use this model to test the differences in pregnancy length and birth weight. How much does the model affect the results?



In [ ]:

Here's some code to test your implementation of DiffMeansResample.



In [ ]:

    
data = firsts.prglngth.values, others.prglngth.values
    ht = DiffMeansResample(data)
    p_value = ht.PValue(iters=10000)
    print('\nmeans permute preglength')
    print('p-value =', p_value)
    print('actual =', ht.actual)
    print('ts max =', ht.MaxTestStat())