import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
plt.switch_backend('Agg')

# Sample data
method1 = [75, 80, 85, 90, 95, 70, 80, 85]
method2 = [80, 85, 90, 95, 100, 75, 85, 90]
method3 = [70, 75, 80, 85, 90, 65, 75, 80]

# Perform one-way ANOVA
f_statistic, p_value = stats.f_oneway(method1, method2, method3)

print("One-Way ANOVA Results:")
print(f"F-statistic: {f_statistic:.4f}")
print(f"p-value: {p_value:.4f}")

# Visualize the data
plt.figure(figsize=(10, 6))
plt.boxplot([method1, method2, method3], labels=['Method 1', 'Method 2', 'Method 3'])
plt.title('Boxplot of Test Scores by Teaching Method')
plt.ylabel('Test Scores')
plt.show()
print("Plot created successfully.")

# Interpret results
alpha = 0.05
if p_value < alpha:
    print("Reject the null hypothesis. There are significant differences between teaching methods.")
else:
    print("Fail to reject the null hypothesis. There are no significant differences between teaching methods.")

interpretation = f"""
Interpretation:
Based on the p-value of {p_value:.4f}, which is {'less' if p_value < alpha else 'greater'} than our significance level of {alpha},
we {'reject' if p_value < alpha else 'fail to reject'} the null hypothesis.

This suggests that there {'are' if p_value < alpha else 'are not'} significant differences in the effectiveness of the three teaching methods.
{'Further post-hoc tests may be needed to determine which specific methods differ from each other.' if p_value < alpha else ''}

The box plot provides a visual representation of the score distributions for each method, 
showing {'differences' if p_value < alpha else 'similarities'} in median scores and score ranges across the methods.
"""
print(interpretation)
                

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
plt.switch_backend('Agg')

# Contingency table: rows are age groups, columns are social media platforms
observed = np.array([
    [50, 30, 20],  # 18-25 age group
    [40, 35, 25],  # 26-35 age group
    [30, 40, 30]   # 36-45 age group
])

# Perform chi-square test
chi2, p_value, dof, expected = stats.chi2_contingency(observed)

print("Chi-Square Test of Independence Results:")
print(f"Chi-square statistic: {chi2:.4f}")
print(f"p-value: {p_value:.4f}")
print(f"Degrees of freedom: {dof}")

# Visualize the data
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))

ax1.imshow(observed, cmap='Blues')
ax1.set_title('Observed Frequencies')
ax1.set_xlabel('Social Media Platforms')
ax1.set_ylabel('Age Groups')

for i in range(observed.shape[0]):
    for j in range(observed.shape[1]):
        ax1.text(j, i, observed[i, j], ha='center', va='center')

ax2.imshow(expected, cmap='Blues')
ax2.set_title('Expected Frequencies')
ax2.set_xlabel('Social Media Platforms')
ax2.set_ylabel('Age Groups')

for i in range(expected.shape[0]):
    for j in range(expected.shape[1]):
        ax2.text(j, i, f'{expected[i, j]:.1f}', ha='center', va='center')

plt.tight_layout()
plt.show()
print("Plot created successfully.")

# Interpret results
alpha = 0.05
if p_value < alpha:
    print("Reject the null hypothesis. There is a significant relationship between age group and social media preference.")
else:
    print("Fail to reject the null hypothesis. There is no significant relationship between age group and social media preference.")

interpretation = f"""
Interpretation:
Based on the p-value of {p_value:.4f}, which is {'less' if p_value < alpha else 'greater'} than our significance level of {alpha},
we {'reject' if p_value < alpha else 'fail to reject'} the null hypothesis.

This suggests that there {'is' if p_value < alpha else 'is not'} a significant relationship between age group and social media platform preference.
{'The observed frequencies differ significantly from what would be expected if there were no relationship between these variables.' if p_value < alpha else 'The observed frequencies are not significantly different from what would be expected if there were no relationship between these variables.'}

The visualizations show the observed frequencies and the expected frequencies if there were no relationship.
{'Notable differences between these two plots indicate where the relationship is strongest.' if p_value < alpha else 'The similarity between these two plots supports the lack of a significant relationship.'}
"""
print(interpretation)