Note
- X, Explantory: Categorical
- Y, Response: Categorical
- Type: Non-Parametric
print 'chi-square statistic, p-value, expected counts'
print ss.chi2_contingency(ct1)
chi-square statistic, p-value, expected counts
(1263.6306705804054, 2.554837585615145e-272, 4, array([[ 7.74251477e+03, 1.71950205e+03, 3.69930718e+02,
4.25495413e+01, 2.50291420e+00],
[ 7.72448523e+03, 1.71549795e+03, 3.69069282e+02,
4.24504587e+01, 2.49708580e+00]]))Note
- Type: Parametric
Note
- Type: Parametric
Analysis of Variance (ANOVA). X, or independent variable can be continuous or categorical. Can input mutiple factors (x).
Categorical Independent Variable
#### IMPORT MOUDLES ####
import numpy as np
import pandas as pd
import statsmodels.formula.api as smf
import statsmodels.stats.multicomp as multi
#### FIT MODEL ####
# response~explanatory OR x~y, 'C' refers to categorical variable
# ANOVA for multiple factors
model = smf.ols(formula='diameter ~ C(layers)', data=df3)
results = model.fit()
>>> print results.summary()
OLS Regression Results
==============================================================================
Dep. Variable: diameter R-squared: 0.219
Model: OLS Adj. R-squared: 0.219
Method: Least Squares F-statistic: 1383.
Date: Tue, 02 Aug 2016 Prob (F-statistic): 0.00
Time: 17:04:57 Log-Likelihood: -60976.
No. Observations: 19731 AIC: 1.220e+05
Df Residuals: 19726 BIC: 1.220e+05
Df Model: 4
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [95.0% Conf. Int.]
----------------------------------------------------------------------------------
Intercept 6.7217 0.043 157.125 0.000 6.638 6.806
C(layers)[T.2] 3.3941 0.100 33.822 0.000 3.197 3.591
C(layers)[T.3] 12.2841 0.200 61.319 0.000 11.891 12.677
C(layers)[T.4] 18.3139 0.579 31.649 0.000 17.180 19.448
C(layers)[T.5] 21.8123 2.380 9.166 0.000 17.148 26.477
==============================================================================
Omnibus: 14916.319 Durbin-Watson: 0.529
Prob(Omnibus): 0.000 Jarque-Bera (JB): 577157.627
Skew: 3.262 Prob(JB): 0.00
Kurtosis: 28.680 Cond. No. 64.0
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
#### POST-HOC TEST ####
mc = multi.MultiComparison(df3['diameter'],df3['layers'])
result1 = mc.tukeyhsd()
print result1
Multiple Comparison of Means - Tukey HSD,FWER=0.05
=============================================
group1 group2 meandiff lower upper reject
---------------------------------------------
1 2 3.3941 3.1204 3.6679 True
1 3 12.2841 11.7376 12.8306 True
1 4 18.3139 16.7353 19.8925 True
1 5 21.8123 15.3204 28.3041 True
2 3 8.89 8.3015 9.4785 True
2 4 14.9198 13.3262 16.5134 True
2 5 18.4181 11.9226 24.9137 True
3 4 6.0298 4.3675 7.6921 True
3 5 9.5281 3.0154 16.0409 True
4 5 3.4984 -3.1806 10.1773 False
---------------------------------------------Multiple Factors
reg2 = smf.ols('depth~diameter_new+layers+lat+long',data=df3).fit()
print reg2.summary()
OLS Regression Results
==============================================================================
Dep. Variable: depth R-squared: 0.518
Model: OLS Adj. R-squared: 0.518
Method: Least Squares F-statistic: 4856.
Date: Wed, 03 Aug 2016 Prob (F-statistic): 0.00
Time: 17:58:20 Log-Likelihood: -1393.4
No. Observations: 18067 AIC: 2797.
Df Residuals: 18062 BIC: 2836.
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [95.0% Conf. Int.]
--------------------------------------------------------------------------------
Intercept 0.5112 0.005 94.795 0.000 0.501 0.522
diameter_new 0.0438 0.000 122.136 0.000 0.043 0.045
layers 0.0061 0.004 1.555 0.120 -0.002 0.014
lat -0.0007 5.3e-05 -13.557 0.000 -0.001 -0.001
long 0.0001 1.93e-05 7.131 0.000 9.97e-05 0.000
==============================================================================
Omnibus: 598.651 Durbin-Watson: 1.078
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1210.720
Skew: -0.234 Prob(JB): 1.25e-263
Kurtosis: 4.179 Cond. No. 342.
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.