Sample Size Determination
Plan effective studies with proper sample size calculations and understand the factors that influence how many participants you need.
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Introduction
Sample size determination is the process of calculating how many observations or participants you need in a study. Too small a sample may miss important effects; too large wastes resources.
Why Sample Size Matters
Too Small
- • Low statistical power
- • May miss real effects
- • Wide confidence intervals
- • Unreliable conclusions
Too Large
- • Wastes resources
- • Takes more time
- • May detect trivial effects
- • Ethical concerns (unnecessary participants)
Key Concepts
Margin of Error (E)
How much error you're willing to accept. Smaller margin = larger sample needed.
Confidence Level
How confident you want to be (typically 95%). Higher confidence = larger sample.
Population Variability (σ)
How spread out your population is. More variability = larger sample needed.
Sample Size Formula
For Estimating a Mean
Where: n = sample size, z = z-score for confidence level, σ = population standard deviation, E = margin of error
For Estimating a Proportion
Where: p = estimated proportion (use 0.5 if unknown)
Power Analysis
Statistical power is the probability of detecting an effect if one exists. Typically aim for 80% power.
The Power-Sample Size Relationship
- • Larger sample = Higher power
- • Larger effect size = Higher power (fewer participants needed)
- • Stricter significance level = Lower power
Applications
📊 Surveys
Political polls, market research, customer satisfaction studies.
🔬 Clinical Trials
Testing new treatments with enough participants to detect effects.
🏭 Quality Control
Determining inspection sample sizes for manufacturing.
🧪 A/B Testing
Website experiments to detect conversion rate differences.
Summary
Key Takeaways
- 1.Sample size balances precision with resource constraints.
- 2.Key factors: margin of error, confidence level, variability.
- 3.Power analysis ensures you can detect meaningful effects.
- 4.Always calculate sample size before collecting data.