from __future__ import print_function, division

import numpy
import scipy.stats

import matplotlib.pyplot as pyplot

from ipywidgets import interact, interactive, fixed
import ipywidgets as widgets

import first

# seed the random number generator so we all get the same results
numpy.random.seed(19)

# some nicer colors from http://colorbrewer2.org/
COLOR1 = '#7fc97f'
COLOR2 = '#beaed4'
COLOR3 = '#fdc086'
COLOR4 = '#ffff99'
COLOR5 = '#386cb0'

%matplotlib inline

"""
Explanation: Hypothesis Testing
Copyright 2016 Allen Downey
License: Creative Commons Attribution 4.0 International
End of explanation
"""


live, firsts, others = first.MakeFrames()

"""
Explanation: Part One
Suppose you observe an apparent difference between two groups and you want to check whether it might be due to chance.
As an example, we'll look at differences between first babies and others.  The first module provides code to read data from the National Survey of Family Growth (NSFG).
End of explanation
"""


def TestStatistic(data):
    group1, group2 = data
    test_stat = abs(group1.mean() - group2.mean())
    return test_stat

"""
Explanation: We'll look at a couple of variables, including pregnancy length and birth weight.  The effect size we'll consider is the difference in the means.
Other examples might include a correlation between variables or a coefficient in a linear regression.  The number that quantifies the size of the effect is called the "test statistic".
End of explanation
"""


group1 = firsts.prglngth
group2 = others.prglngth

"""
Explanation: For the first example, I extract the pregnancy length for first babies and others.  The results are pandas Series objects.
End of explanation
"""


actual = TestStatistic((group1, group2))
actual

"""
Explanation: The actual difference in the means is 0.078 weeks, which is only 13 hours.
End of explanation
"""


n, m = len(group1), len(group2)
pool = numpy.hstack((group1, group2))

"""
Explanation: The null hypothesis is that there is no difference between the groups.  We can model that by forming a pooled sample that includes first babies and others.
End of explanation
"""


def RunModel():
    numpy.random.shuffle(pool)
    data = pool[:n], pool[n:]
    return data

"""
Explanation: Then we can simulate the null hypothesis by shuffling the pool and dividing it into two groups, using the same sizes as the actual sample.
End of explanation
"""


RunModel()

"""
Explanation: The result of running the model is two NumPy arrays with the shuffled pregnancy lengths:
End of explanation
"""


TestStatistic(RunModel())

"""
Explanation: Then we compute the same test statistic using the simulated data:
End of explanation
"""


test_stats = numpy.array([TestStatistic(RunModel()) for i in range(1000)])
test_stats.shape

"""
Explanation: If we run the model 1000 times and compute the test statistic, we can see how much the test statistic varies under the null hypothesis.
End of explanation
"""


pyplot.vlines(actual, 0, 300, linewidth=3, color='0.8')
pyplot.hist(test_stats, color=COLOR5)
pyplot.xlabel('difference in means')
pyplot.ylabel('count')
None

"""
Explanation: Here's the sampling distribution of the test statistic under the null hypothesis, with the actual difference in means indicated by a gray line.
End of explanation
"""


pvalue = sum(test_stats >= actual) / len(test_stats)
pvalue

"""
Explanation: The p-value is the probability that the test statistic under the null hypothesis exceeds the actual value.
End of explanation
"""


class HypothesisTest(object):
    """Represents a hypothesis test."""

    def __init__(self, data):
        """Initializes.

        data: data in whatever form is relevant
        """
        self.data = data
        self.MakeModel()
        self.actual = self.TestStatistic(data)
        self.test_stats = None

    def PValue(self, iters=1000):
        """Computes the distribution of the test statistic and p-value.

        iters: number of iterations

        returns: float p-value
        """
        self.test_stats = numpy.array([self.TestStatistic(self.RunModel()) 
                                       for _ in range(iters)])

        count = sum(self.test_stats >= self.actual)
        return count / iters

    def MaxTestStat(self):
        """Returns the largest test statistic seen during simulations.
        """
        return max(self.test_stats)

    def PlotHist(self, label=None):
        """Draws a Cdf with vertical lines at the observed test stat.
        """
        ys, xs, patches = pyplot.hist(ht.test_stats, color=COLOR4)
        pyplot.vlines(self.actual, 0, max(ys), linewidth=3, color='0.8')
        pyplot.xlabel('test statistic')
        pyplot.ylabel('count')

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

        data: data in whatever form is relevant        
        """
        raise UnimplementedMethodException()

    def MakeModel(self):
        """Build a model of the null hypothesis.
        """
        pass

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

        returns: simulated data
        """
        raise UnimplementedMethodException()


"""
Explanation: In this case the result is about 15%, which means that even if there is no difference between the groups, it is plausible that we could see a sample difference as big as 0.078 weeks.
We conclude that the apparent effect might be due to chance, so we are not confident that it would appear in the general population, or in another sample from the same population.
STOP HERE
Part Two
We can take the pieces from the previous section and organize them in a class that represents the structure of a hypothesis test.
End of explanation
"""


class DiffMeansPermute(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 = numpy.hstack((group1, group2))

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

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

"""
Explanation: HypothesisTest is an abstract parent class that encodes the template.  Child classes fill in the missing methods.  For example, here's the test from the previous section.
End of explanation
"""


data = (firsts.prglngth, others.prglngth)
ht = DiffMeansPermute(data)
p_value = ht.PValue(iters=1000)
print('\nmeans permute pregnancy length')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())

"""
Explanation: Now we can run the test by instantiating a DiffMeansPermute object:
End of explanation
"""


ht.PlotHist()

"""
Explanation: And we can plot the sampling distribution of the test statistic under the null hypothesis.
End of explanation
"""


# Solution goes here

class DiffStdPermute(DiffMeansPermute):
    """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.std() - group2.std())
        return test_stat

"""
Explanation: Difference in standard deviation
Exercize 1: Write a class named DiffStdPermute that extends DiffMeansPermute and overrides TestStatistic to compute the difference in standard deviations.  Is the difference in standard deviations statistically significant?
End of explanation
"""


data = (firsts.prglngth, others.prglngth)
ht = DiffStdPermute(data)
p_value = ht.PValue(iters=1000)
print('\nstd permute pregnancy length')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())

"""
Explanation: Here's the code to test your solution to the previous exercise.
End of explanation
"""


data = (firsts.totalwgt_lb.dropna(), others.totalwgt_lb.dropna())
ht = DiffMeansPermute(data)
p_value = ht.PValue(iters=1000)
print('\nmeans permute birthweight')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())

"""
Explanation: Difference in birth weights
Now let's run DiffMeansPermute again to see if there is a difference in birth weight between first babies and others.
End of explanation
"""


