Session 2: Hypothesis Testing Laboratory | Statistical Data Treatment in Formulation Development

Master Statistical Inference for Pharmaceutical Decision-Making

Learn to test hypotheses, analyze bioequivalence, and make evidence-based conclusions with step-by-step reasoning

Learning Objectives

Construct and test hypotheses for pharmaceutical quality control scenarios
Apply parametric tests (t-tests, ANOVA) with step-by-step reasoning
Perform bioequivalence analysis using 90% confidence intervals and TOST
Interpret p-values and confidence intervals in regulatory contexts
Select appropriate statistical tests based on data characteristics
Handle multiple comparisons with proper error rate control

Session Components

🧪 Part 1: Hypothesis Construction Workshop

Duration: 30 minutes

Master the foundations of hypothesis testing with pharmaceutical examples and error analysis.

Research Question → Statistical Hypothesis
Type I & Type II Error Analysis
Power Analysis & Sample Size
Confidence Intervals & Standard Error

Start Workshop Download Data

📊 Part 2: Parametric Test Suite

Duration: 45 minutes

Apply t-tests and ANOVA to pharmaceutical data with complete step-by-step calculations.

One-Sample t-Test (Label Claim Testing)
Two-Sample t-Test (Formulation Comparison)
ANOVA Workshop (Multi-Batch Analysis)
Paired t-Test (Crossover Studies)

Practice Tests ANOVA Lab

⚖️ Part 3: Bioequivalence Testing Suite

Duration: 45 minutes

Master bioequivalence analysis with 2×2 crossover design and regulatory requirements.

2×2 Crossover Study Design
Log Transformation & ANOVA Model
90% Confidence Intervals
Two One-Sided Tests (TOST)

BE Practice Sample Study

🎯 Part 4: Advanced Testing Methods

Duration: 30 minutes

Learn when and how to use non-parametric tests and control multiple comparison errors.

Test Selection Decision Tree
Mann-Whitney & Wilcoxon Tests
Bonferroni Correction
False Discovery Rate Control

Explore Methods Test Selector

💊 Part 5: Dissolution Profile Comparison

Duration: 30 minutes

Apply f2 similarity factor and model-independent methods for dissolution testing.

f2 Similarity Factor Calculation
Dissolution Profile Modeling
USP Guidelines Compliance
Quality Control Applications

Start Analysis Sample Data

✅ Part 6: Session Assessment

Duration: 20 minutes

Test your understanding with comprehensive exercises covering all hypothesis testing concepts.

Multiple Choice Questions (15)
Calculation Problems (5)
Interpretation Exercises (3)
Mini Case Study (1)

Take Assessment View Solutions

Step-by-Step Example: Testing Tablet Weight Specifications

Scenario: A pharmaceutical company wants to test if their 500 mg tablets meet label claim specifications.

1

Define Research Question

Question: "Do our tablets meet the 500 mg label claim?"

Let's think step-by-step: We need to determine if the average weight significantly differs from 500 mg.

2

Set Up Hypotheses

Null Hypothesis (H₀): μ = 500 mg (tablets meet specification)

Alternative Hypothesis (H₁): μ ≠ 500 mg (tablets don't meet specification)

Reasoning: We use a two-tailed test because we want to detect both over-weight and under-weight tablets.

3

Set Significance Level

α = 0.05 (5% risk of rejecting a good batch)

Industry Standard: FDA typically uses α = 0.05 for pharmaceutical testing.

4

Collect Data & Calculate Test Statistic

Sample Data: n = 20 tablets, x̄ = 498.5 mg, s = 3.2 mg

t = (x̄ - μ₀) / (s / √n)

Step-by-step calculation:

1. Standard Error (SE) = s / √n = 3.2 / √20 = 3.2 / 4.472 = 0.716

2. t-statistic = (498.5 - 500) / 0.716 = -1.5 / 0.716 = -2.095

3. Degrees of freedom = n - 1 = 20 - 1 = 19

5

Find Critical Value & Make Decision

Critical t-value: t₀.₀₂₅,₁₉ = ±2.093 (two-tailed test)

Decision Rule: Reject H₀ if |t| > 2.093

Our result: |t| = 2.095 > 2.093

Conclusion: Reject H₀ (p < 0.05)

Interpretation: The tablet weights significantly differ from 500 mg specification.

6

Pharmaceutical Decision

Quality Control Action: Investigate manufacturing process for weight variation

Regulatory Consideration: This batch may not meet USP specifications for weight uniformity

Next Steps: Analyze individual tablet weights and adjust manufacturing parameters

Quick Start Guide

Ready to begin? Choose your starting point based on your comfort level:

New to Hypothesis Testing?

Start with Part 1: Hypothesis Construction to build your foundation

Begin Here

Have Basic Knowledge?

Jump to Part 2: Parametric Tests for hands-on practice

Skip to Practice

Ready for Advanced Topics?

Go directly to Part 3: Bioequivalence Testing

Advanced Start

Want to Test Your Skills?

Try the assessment to identify knowledge gaps

Take Assessment