To test a hypothesis using various statistical methods (like t-tests, ANOVA, Chi-Square, and regression analysis) in Python, you can follow these step

Step 1: Set Up the Environment

First, ensure you have the required Python libraries installed:

pip install numpy scipy matplotlib seaborn statsmodels pandas        

Then, import the necessary libraries in your code:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats
from statsmodels.formula.api import ols        

Step 2: Data Setup

Generate or import sample data for testing each hypothesis.

Example Data:

# Generate example data
group1 = np.random.normal(60, 10, 100)  # Group 1: Mean=60, SD=10
group2 = np.random.normal(65, 10, 100)  # Group 2: Mean=65, SD=10
group3 = np.random.normal(70, 10, 100)  # Group 3: Mean=70, SD=10

# Combine into a dataframe for analysis
df = pd.DataFrame({
    'Group1': group1,
    'Group2': group2,
    'Group3': group3
})        

Step 3: t-test (Comparing Two Groups)

A t-test compares the means of two groups. For example, comparing group1 and group2.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats
from statsmodels.formula.api import ols        

Interpretation:

• If the p-value is less than 0.05, you reject the null hypothesis, meaning there's a statistically significant difference between the two groups.
• The box plot will help visualize the distribution of the groups.

Step 4: ANOVA (Comparing Multiple Groups)

ANOVA is used when comparing more than two groups. Here, we’ll compare group1, group2, and group3.

# Perform t-test
t_stat, p_value = stats.ttest_ind(group1, group2)
print(f"T-statistic: {t_stat}, P-value: {p_value}")

# Visualization: Box Plot
plt.boxplot([group1, group2], labels=["Group 1", "Group 2"])
plt.title('T-Test: Group 1 vs Group 2')
plt.ylabel('Values')
plt.show()        

Interpretation:

• The ANOVA table will provide an F-statistic and p-value. If the p-value is less than 0.05, there is a significant difference between at least one pair of groups.
• The box plot shows the distribution for each group.

Step 5: Chi-Square Test (Categorical Data)

The Chi-Square test compares categorical data to see if distributions of categorical variables differ from each other.

# Combine groups into a single dataset
data = pd.melt(df.reset_index(), id_vars=['index'], value_vars=['Group1', 'Group2', 'Group3'])
data.columns = ['index', 'group', 'value']

# Perform ANOVA
anova_result = ols('value ~ C(group)', data=data).fit()
anova_table = statsmodels.stats.anova.anova_lm(anova_result)
print(anova_table)

# Visualization: Box Plot for all groups
sns.boxplot(x='group', y='value', data=data)
plt.title('ANOVA: Comparison of Groups')
plt.ylabel('Values')
plt.show()        

Interpretation:

• If the p-value is below 0.05, there is a significant association between the categorical variables.
• The heatmap visualizes the contingency table.

Step 6: Regression Analysis (Testing Relationships Between Variables)

Regression analysis determines if there is a relationship between two or more variables. Let’s test if group1 values are influenced by some independent variable x.

# Generate some example independent variable data
x = np.random.normal(50, 10, 100)

# Perform regression analysis
slope, intercept, r_value, p_value, std_err = stats.linregress(x, group1)
print(f"Slope: {slope}, Intercept: {intercept}, P-value: {p_value}")

# Visualization: Scatter plot with regression line
plt.scatter(x, group1, label='Data points')
plt.plot(x, intercept + slope * x, 'r', label='Fitted line')
plt.title('Regression Analysis: X vs Group 1')
plt.xlabel('X')
plt.ylabel('Group 1 Values')
plt.legend()
plt.show()        

Interpretation:

• The p-value will indicate whether the independent variable (x) significantly predicts the dependent variable (group1).
• The scatter plot visualizes the relationship, with the regression line indicating the trend.

Step 7: Conclusion and Interpretation

• For each test, interpret the p-value: a p-value < 0.05 suggests a significant result, meaning you can reject the null hypothesis.
• Use visualizations like box plots, heatmaps, and scatter plots to help explain and showcase the data and results clearly.

This step-by-step guide provides a full workflow for testing different types of hypotheses (t-test, ANOVA, Chi-Square, and regression) using Python with appropriate visualizations.