Chi Squared Test¶

Define Null and Alternate Hypothesis
State Alpha
Calculate Degree of Freedom
State Decision rule
Calculate the chi-square test statistic
Calculate the critical value
State Results and conclusion

import scipy.stats as stats
import pandas as pd 
import numpy as np

df = pd.read_csv("Placement.csv")

df.head()

1. Define Null and Alternate hypothesis¶

Null Hypothesis (H0) = There is no relationship between the 2 categorical variables

Alternate Hypothesis (H1) = There is a relationship between the 2 categorical variables

df_crosstab = pd.crosstab(df['specialisation'],df['status'])

df_crosstab

df_crosstab.values

array([[25, 95],
       [42, 53]], dtype=int64)

observed_values = df_crosstab.values
print("Observed values: ",observed_values)

Observed values:  [[25 95]
 [42 53]]

test_dependence = stats.chi2_contingency(observed_values)

test_dependence

(12.440229009203623,
 0.00042018425858864284,
 1,
 array([[37.39534884, 82.60465116],
        [29.60465116, 65.39534884]]))

Expected_value = test_dependence[3]

print("Expected value: ",Expected_value)

Expected value:  [[37.39534884 82.60465116]
 [29.60465116 65.39534884]]

2. State Alpha¶

alpha = 0.05

3. State the degree of freedom¶

rows = len(df_crosstab.iloc[0:2,0])
columns = len(df_crosstab.iloc[0,0:2])
degree_of_freedom = (rows-1)*(columns-1)
print("Degree of Freedom: ",degree_of_freedom)

Degree of Freedom:  1

4. State the decision rule¶

If the chi-square statistic is greater than or equal to the critical value, then reject the null hypothesis.
If the P-value is less than or equal to alpha, reject the null hypothesis

5. Calculate the Chi-square test statistic¶

from scipy.stats import chi2
test_statistic = sum([(O-E)**2/E for O,E in zip(observed_values,Expected_value)])
chi_Square_test_statistic = test_statistic[0]+test_statistic[1]

print("The value of chi-squared test statistic: ",chi_Square_test_statistic)

The value of chi-squared test statistic:  13.508014470676486

6. Calculate the critical value¶

critical_value = stats.chi2.ppf(q = 1-alpha,df = degree_of_freedom)
print("critical value: ",critical_value)

critical value:  3.841458820694124

Alternate Method using p-value¶

p_value = 1- stats.chi2.cdf(chi_Square_test_statistic,1)
print("P Value: ",p_value)
print("significance level: ",alpha)

P Value:  0.0002375467465819403
significance level:  0.05

7. State the results and conclusion¶

if chi_Square_test_statistic>=critical_value:
    print("Reject the Null hypothesis H0, as there is relationship between the 2 categorical variables")
else:
    print("Retain the Null hypothesis H0, as there is no relationship between the 2 categorical variables")
if p_value<=alpha:
    print("Reject the Null hypothesis H0, as there is relationship between the 2 categorical variables")
else:
    print("Retain the Null hypothesis H0, as there is no relationship between the 2 categorical variables")

Reject the Null hypothesis H0, as there is relationship between the 2 categorical variables
Reject the Null hypothesis H0, as there is relationship between the 2 categorical variables

	sl_no	gender	ssc_p	ssc_b	hsc_p	hsc_b	hsc_s	degree_p	degree_t	workex	etest_p	specialisation	mba_p	status	salary
0	1	M	67.00	Others	91.00	Others	Commerce	58.00	Sci&Tech	No	55.0	Mkt&HR	58.80	Placed	270000.0
1	2	M	79.33	Central	78.33	Others	Science	77.48	Sci&Tech	Yes	86.5	Mkt&Fin	66.28	Placed	200000.0
2	3	M	65.00	Central	68.00	Central	Arts	64.00	Comm&Mgmt	No	75.0	Mkt&Fin	57.80	Placed	250000.0
3	4	M	56.00	Central	52.00	Central	Science	52.00	Sci&Tech	No	66.0	Mkt&HR	59.43	Not Placed	NaN
4	5	M	85.80	Central	73.60	Central	Commerce	73.30	Comm&Mgmt	No	96.8	Mkt&Fin	55.50	Placed	425000.0