Introduction and Context

• Josh Stormer presenting StatQuest from UNC Chapel Hill Genetics Department
• Topic: sample size vs effective sample size
• Builds on previous StatQuest about technical and biological replicates

Basic Sample Size Concepts

• Simple example: gene expression testing in "blue dudes" (representing mouse strains or tree types)
• Basic sampling: 3 separate blue dudes = N=3 sample size
• Population specificity: blue dudes N=3, blue ladies N=0
• Technical replicates: measuring same individual twice
  • Don't increase sample size for population inferences
  • Only count when describing method accuracy, not population differences
  • Example: 2 measurements per blue dude still N=3 for population inference
  • For method accuracy description: N=4 (counting technical replicates)

Expanded Population Studies

• Testing hypothesis about "dudes in general" (not just blue dudes)
• Requires diverse sampling: blue, orange, green dudes
• Sample size remains N=3 (one of each type)

Effective Sample Size with Correlated Samples

• Problem: adding twin to blue dude group
• Question: sample size 3 or 4?
• Answer: somewhere between due to correlation

Twin Correlation Analysis

• Twins share genomes → highly correlated gene expression
• Effective sample size formula: N / (1 + (N-1) × correlation)

High Correlation Example (r=0.7)

• Formula: 2 / (1 + (2-1) × 0.7)
• Calculation: 2 / (1 + 0.7) = 2 / 1.7 = 1.18
• Interpretation: twins count as 1.18 people instead of 2

Low Correlation Example (r=0.1)

• Formula: 2 / (1 + (2-1) × 0.1)
• Calculation: 2 / (1 + 0.1) = 2 / 1.1 = 1.82
• Interpretation: twins count as 1.82 people (nearly 2)

Summary Guidelines

• Method accuracy reporting: count technical replicates (N=3)
• Specific population (blue dudes): count biological replicates (N=3)
• General population with correlations: use effective sample size
  • High correlation (0.7): effective N = 3.18
  • Low correlation (0.1): effective N = 3.82
• Key principle: highly correlated samples don't count as individual samples