BP101T • Unit 5Topic 2 of 3⏱ 5 Min Read

2. Statistical Hypothesis Testing: Student's t-test for Batch Comparison

💡 Core Concept & Clinical Context:

When changing raw material suppliers or modifying tableting machine speeds, quality control departments must prove that the new formulation batch exhibits identical drug content compared to reference standards. The two-sample independent Student's t-test evaluates whether the difference in mean assay between two batches is statistically significant or merely due to random experimental variance.

Pharmaceutical Code & Calculation Examples:

1Two-Batch Assay Statistical Comparison Script

Using SciPy to execute an independent two-sample t-test at 95% confidence level (alpha = 0.05).

example_1.py

from scipy import stats
import numpy as np

# Assay percentages across 10 sample tablets from Supplier A and Supplier B
supplier_a = np.array([99.4, 98.8, 100.2, 99.1, 99.8, 100.5, 98.9, 99.6, 100.1, 99.3])
supplier_b = np.array([98.9, 99.2, 99.0, 98.7, 99.5, 99.1, 98.8, 99.3, 99.0, 98.9])

t_stat, p_val = stats.ttest_ind(supplier_a, supplier_b)

print(f"Supplier A Mean: {np.mean(supplier_a):.2f}% | Supplier B Mean: {np.mean(supplier_b):.2f}%")
print(f"Calculated t-statistic: {t_stat:.4f}")
print(f"Two-tailed p-value: {p_val:.4f}")

if p_val > 0.05:
    print("Conclusion: No statistically significant difference between suppliers (p > 0.05). Both are interchangeable.")
else:
    print("Conclusion: Statistically significant difference observed (p <= 0.05).")

📋Key Takeaways & Exam Highlights

Null Hypothesis ($H_0$): Mean drug content of Batch A is identical to Batch B ($\mu_A = \mu_B$).
Alternative Hypothesis ($H_1$): Mean drug content differs significantly ($\mu_A \ne \mu_B$).
Significance Threshold ($p < 0.05$): If p-value is less than 0.05, reject null hypothesis.

🇮🇳 हिन्दी व्याख्या (2. Statistical Hypothesis Testing: Student's t-test for Batch Comparison)

Student's t-test से यह साबित किया जाता है कि नए सप्लायर या नई मशीन से बनी दवाओं की गुणवत्ता में कोई सांख्यिकीय अंतर (Significant Difference) नहीं है।