What is Null Hypothesis, with Examples in Python Pandas

In statistics, the null hypothesis is a statement that there is no significant difference between a set of variables or samples. The purpose of a hypothesis test is to either reject or fail to reject the null hypothesis based on the results of the test. In other words, the null hypothesis is the default assumption that we make until we have evidence to the contrary.

In Python Pandas, we can perform hypothesis tests using various statistical tests from the SciPy library, including t-tests, ANOVA, chi-square tests, and others. Here are a few examples of null hypotheses in Python Pandas:

1. T-test: We can use a t-test to determine whether two groups of data have different means. The null hypothesis in this case is that the two groups have the same mean. For example:

import pandas as pd
from scipy.stats import ttest_ind

data = pd.read_csv('data.csv')

group1 = data[data['Group'] == 'A']['Value']
group2 = data[data['Group'] == 'B']['Value']

t, p = ttest_ind(group1, group2)

if p < 0.05:
    print('Reject null hypothesis: the means are different')
else:
    print('Fail to reject null hypothesis: the means are the same')

2. Chi-square test: We can use a chi-square test to determine whether two categorical variables are independent. The null hypothesis in this case is that the two variables are independent. For example:

python

import pandas as pd
from scipy.stats import chi2_contingency

data = pd.read_csv('data.csv')

observed = pd.crosstab(data['Variable1'], data['Variable2'])

chi2, p, dof, expected = chi2_contingency(observed)

if p < 0.05:
    print('Reject null hypothesis: the variables are dependent')
else:
    print('Fail to reject null hypothesis: the variables are independent')

3. ANOVA: We can use ANOVA to determine whether the means of three or more groups are significantly different. The null hypothesis in this case is that all of the group means are the same. For example:

python

import pandas as pd
from scipy.stats import f_oneway

data = pd.read_csv('data.csv')

group1 = data[data['Group'] == 'A']['Value']
group2 = data[data['Group'] == 'B']['Value']
group3 = data[data['Group'] == 'C']['Value']

f, p = f_oneway(group1, group2, group3)

if p < 0.05:
    print('Reject null hypothesis: at least one group mean is different')
else:
    print('Fail to reject null hypothesis: all group means are the same')

In each of these examples, the null hypothesis is the starting point for the hypothesis test. Based on the results of the test, we either reject the null hypothesis and conclude that there is evidence of a difference or we fail to reject the null hypothesis and conclude that there is not enough evidence to support a difference.