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Inference: p-value here is 0.0021 and it is <= 0.05. So we can reject NULL Hypothesis and say that there is some association between Property_area and loan_status

Post Hoc Testing

We have three combinations here: 'Rural - Semiurban', 'Rural - Urban' and 'Semiurban - Rural'. So le tus create three dataframes and start performing chi-square tests for each of the pair

Apply Bonferroni correction and considering adjusted significance level - 0.05/3 = 0.0167

Here p-value is 0.00107 and it is <= 0.016 (new significance level). So Loan_Status does have an association with Property_Area Rural and Semiurban

Here p-value is 0.43373 and it is > 0.016 (new significance level). So Loan_Status does not have an association with Property_Area - Rural and Urban

Importing required libraries

import os as os import pandas as pd import numpy as np import statsmodels.formula.api as smf import statsmodels.stats.multicomp as multi

Importing Data

df = pd.read_csv('Housing_Data.csv')

The dataset is on loan prediction having customer attributes and the loan outcome

ANOVA problem statement - Checking if Loan Amount is related to Education Qualification

So here Loan Amount is the continuous variable and Education Qualification is Categorical Variable. Education Qualification has only two levels

df_anova_test = df_anova[['Education', 'LoanAmount']]

using ols function for calculating the F-statistic and associated p value

model1 = smf.ols(formula='LoanAmount ~ C(Education)', data=df_anova_test) results1 = model1.fit() print (results1.summary())

So here the p value is 0.000142 and it is < 0.05 (Significance Level). So we can say that Loan Amount does vary with Education Qualification and there is some association between Education Qualification and Loan Amount. So we reject Null Hypothesis

Comparing Means

df_anova_test.groupby('Education').mean()

So we can the difference  of 34 in the means of the two Education levels

ANOVA POST Hoc Testing

Here we will consider categorical variable that has more than two levels. So here the categorical variable would be Property_Area which has three levels and Loan Amount would be the continuous variable

Let us run the ANOVA test first

df_anova_test1 = df_anova[['Property_Area', 'LoanAmount']]

Using ols function for calculating the F-statistic and associated p value

model1 = smf.ols(formula='LoanAmount ~ C(Property_Area)',                   data=df_anova_test1)

results1 = model1.fit() print (results1.summary())

So here p-value < 0.05 and we can say that there is some association between Property Area and Loan Amount. So we reject NULL Hypothesis

Let us perform Post Hoc Test and check on Type I error. So let us perform this by using Tukey HSD test

mc1 = multi.MultiComparison(df_anova_test1['LoanAmount'], df_anova_test1['Property_Area'])

res1 = mc1.tukeyhsd() print(res1.summary())