Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions based on data. It allows us to determine whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis.

2.1 Definitions

• Null Hypothesis (H0): A statement that there is no effect or no difference, which we aim to test against.
• Alternative Hypothesis (H1): A statement that indicates the presence of an effect or difference.
• p-value: The probability of observing the test results under the null hypothesis. A small p-value indicates strong evidence against H0.
• Significance Level (α): A threshold set to determine whether to reject H0, commonly 0.05.

1. Define the null (H0) and alternative (H1) hypotheses.
2. Select the significance level (α).
3. Collect data and calculate the test statistic.
4. Calculate the p-value.
5. Compare the p-value to α:
• If p-value ≤ α, reject H0.
• If p-value > α, do not reject H0.
6. Draw conclusions based on the results.

Here’s a simple example using Python's SciPy library to perform a t-test:

import numpy as np
from scipy import stats

# Sample data
data1 = np.array([23, 21, 18, 30, 27])
data2 = np.array([29, 32, 27, 22, 24])

# Perform t-test
t_stat, p_value = stats.ttest_ind(data1, data2)
alpha = 0.05

# Output results
print(f'T-statistic: {t_stat}, P-value: {p_value}')
if p_value < alpha:
    print("Reject the null hypothesis (H0)")
else:
    print("Do not reject the null hypothesis (H0)")