Module 2: Descriptive Statistics Playground
45-Minute Guided Practical SessionStructured approach to complete all analyses efficiently
Realistic tablet manufacturing data for comprehensive analysis
3 production batches (A, B, C)
30 tablets per batch
Total: 90 tablets
Individual tablet weights
Target: 250 mg Β± 5%
USP <905> compliance required
Crushing strength
Range: 40-80 N
Friability correlation analysis
% Dissolved at timepoints
15, 30, 45, 60 minutes
Q-value compliance testing
6-month trending
Potency % remaining
Shelf-life prediction
Distribution analysis
D10, D50, D90 values
Polydispersity assessment
| Batch | Tablet ID | Weight (mg) | Hardness (N) | Dissolution 30min (%) | Particle Size D50 (ΞΌm) |
|---|---|---|---|---|---|
| A | A-01 | 248.7 | 52.3 | 78.2 | 45.7 |
| A | A-02 | 251.2 | 49.8 | 82.1 | 42.3 |
| A | A-03 | 250.1 | 54.7 | 79.5 | 46.8 |
| A | A-04 | 249.3 | 51.2 | 81.3 | 44.2 |
| A | A-05 | 252.8 | 48.9 | 83.7 | 41.9 |
| B | B-01 | 247.9 | 47.6 | 85.3 | 38.4 |
| B | B-02 | 253.4 | 45.2 | 87.8 | 39.7 |
| B | B-03 | 250.7 | 48.8 | 84.2 | 40.1 |
| B | B-04 | 249.6 | 46.3 | 86.9 | 37.8 |
| B | B-05 | 251.9 | 47.9 | 85.7 | 38.9 |
| C | C-01 | 252.3 | 59.7 | 72.4 | 52.1 |
| C | C-02 | 248.1 | 61.2 | 69.8 | 54.3 |
| C | C-03 | 250.9 | 58.4 | 71.9 | 51.7 |
| C | C-04 | 249.7 | 60.8 | 70.3 | 53.2 |
| C | C-05 | 251.6 | 57.9 | 73.1 | 50.8 |
Comprehensive analysis with pharmaceutical interpretation
1. Understanding: "We need to see how our data is distributed to understand the pattern of variation in our manufacturing process."
2. Method Selection: "For continuous data like weight and hardness, we'll create histograms with appropriate bin sizes."
3. Bin Determination: "Using Sturges' Rule: k = 1 + 3.322 Γ logββ(30) β 6 bins per batch"
Weight Distribution: Should follow normal distribution around 250 mg target
Hardness Pattern: Look for bimodal distributions indicating process variation
Dissolution Profiles: Check for consistent release patterns across batches
1. Central Tendency: "We calculate mean, median, and mode to understand the 'typical' tablet in each batch."
2. Dispersion: "Standard deviation and CV% tell us about manufacturing consistency."
3. Shape: "Skewness and kurtosis reveal distribution characteristics."
Weight Variation CV%: Should be β€ 6% for good manufacturing control
Content Uniformity: Individual tablets: 85-115% of label claim
Hardness Consistency: CV% typically β€ 20% for acceptable variation
1. Visual Assessment: "Histograms should look bell-shaped for normal data."
2. Q-Q Plots: "Points should follow a straight line for normal distribution."
3. Statistical Tests: "Shapiro-Wilk test for formal normality testing (nβ€50)."
Normal Data: Can use parametric tests, process control charts
Non-Normal Data: May need transformation or non-parametric methods
Regulatory Consideration: FDA expects normality assessment for BE studies
1. Multiple Methods: "We'll use 3-sigma rule, IQR method, and statistical tests."
2. Pharmaceutical Context: "Outliers might indicate manufacturing problems or analytical errors."
3. Decision Framework: "Document reasons for retention or exclusion per ICH guidelines."
OOS Investigation: Values outside specifications require full investigation
Statistical Outliers: Document scientific justification for any exclusions
Retention Criteria: Prefer retention unless clear analytical error identified
1. Weight Variation: "Apply USP <905> criteria based on tablet weight range."
2. Content Uniformity: "Calculate Acceptance Value (AV) using USP methodology."
3. Dissolution: "Evaluate Q-value compliance at each stage."
| Tablet Weight | Percentage Deviation | Our Batch (250 mg) | Acceptable Range |
|---|---|---|---|
| 130 mg or less | Β±10% | N/A | - |
| More than 130 mg but less than 324 mg | Β±7.5% | β Applies | 231.25 - 268.75 mg |
| 324 mg or more | Β±5% | N/A | - |
1. Descriptive Comparison: "Compare means, SDs, and ranges across batches."
2. Visual Analysis: "Side-by-side box plots reveal distribution differences."
3. Variation Assessment: "CV% comparison shows which batch has better control."
Consistent Batches: Similar means and SDs indicate good process control
Batch Differences: May require process investigation and adjustment
Regulatory Filing: Between-batch variation data required for submissions
1. Linear Regression: "Fit trend line to predict shelf-life."
2. Confidence Intervals: "Calculate 95% CI for regulatory acceptance."
3. Specification Limits: "Determine when product falls below 90% potency."
1. Assessment Need: "If data is significantly non-normal, consider transformation."
2. Log Transformation: "Most common for positively skewed pharmaceutical data."
3. Back-transformation: "Report geometric means for log-transformed data."
Professional outputs for pharmaceutical quality assessment
Evaluation criteria for comprehensive learning assessment
Correct application of statistical formulas, Excel functions, and numerical precision
Choosing correct statistical methods based on data characteristics and assumptions
Professional graphs with proper labeling, scaling, and pharmaceutical context
Clear explanation of statistical results with pharmaceutical and regulatory implications
Report organization, formatting, and adherence to pharmaceutical documentation standards
Download the complete Excel template and dataset to start your pharmaceutical statistical journey
Download Excel Template & Dataset Start Guided Analysis