Chapter 5 - Basic Math and Statistics

Segment 6 - Delving into non-parametric methods using pandas and scipy

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt
import seaborn as sb
from pylab import rcParams

import scipy
from scipy.stats import spearmanr

%matplotlib inline
rcParams['figure.figsize'] = 14, 7
plt.style.use('seaborn-whitegrid')

The Spearman Rank Correlation

address = '~/Data/mtcars.csv'

cars = pd.read_csv(address)
cars.columns = ['car_names','mpg','cyl','disp', 'hp', 'drat', 'wt', 'qsec', 'vs', 'am', 'gear', 'carb']

cars.head()

	car_names	mpg	cyl	disp	hp	drat	wt	qsec	vs	am	gear	carb
0	Mazda RX4	21.0	6	160.0	110	3.90	2.620	16.46	0	1	4	4
1	Mazda RX4 Wag	21.0	6	160.0	110	3.90	2.875	17.02	0	1	4	4
2	Datsun 710	22.8	4	108.0	93	3.85	2.320	18.61	1	1	4	1
3	Hornet 4 Drive	21.4	6	258.0	110	3.08	3.215	19.44	1	0	3	1
4	Hornet Sportabout	18.7	8	360.0	175	3.15	3.440	17.02	0	0	3	2

sb.pairplot(cars)

<seaborn.axisgrid.PairGrid at 0x7f1891238e80>

X = cars[['cyl','vs','am','gear']]
sb.pairplot(X)

<seaborn.axisgrid.PairGrid at 0x7f188b9b8ba8>

cyl = cars['cyl']
vs = cars['vs']
am = cars['am']
gear = cars['gear']

spearmanr_coefficient, p_value = spearmanr(cyl,vs)

print('Spearman Rank Correlation Coefficient %0.3f' % (spearmanr_coefficient))

Spearman Rank Correlation Coefficient -0.814

spearmanr_coefficient, p_value = spearmanr(cyl,am)

print('Spearman Rank Correlation Coefficient %0.3f' % (spearmanr_coefficient))

Spearman Rank Correlation Coefficient -0.522

spearmanr_coefficient, p_value = spearmanr(cyl,gear)

print('Spearman Rank Correlation Coefficient %0.3f' % (spearmanr_coefficient))

Spearman Rank Correlation Coefficient -0.564

Chi-square test for independence

table = pd.crosstab(cyl, am)

from scipy.stats import chi2_contingency
chi2, p, dof, expected = chi2_contingency(table.values)
print('Chi-square statistic %0.3f p_value %0.3f' % (chi2,p))

Chi-square statistic 8.741 p_value 0.013

table = pd.crosstab(cyl, vs)

from scipy.stats import chi2_contingency
chi2, p, dof, expected = chi2_contingency(table.values)
print('Chi-square statistic %0.3f p_value %0.3f' % (chi2,p))

Chi-square statistic 21.340 p_value 0.000

table = pd.crosstab(cyl, gear)

from scipy.stats import chi2_contingency
chi2, p, dof, expected = chi2_contingency(table.values)
print('Chi-square statistic %0.3f p_value %0.3f' % (chi2,p))

Chi-square statistic 18.036 p_value 0.001