Study guide
5.4 Sampling Strategy: Sample Size, Power, and Worker Selection
CIH Certified Industrial Hygienist Exam
Track your progress as you read
Finished sections get a check mark.
1 Chapter 1: The CIH Exam and How to Use This Guide
1.1 CIH Exam Format, Scoring, and Test-Day Logistics 1.2 Eligibility, Application Windows, Fees, and Certification Maintenance 1.3 The BGC Blueprint, Subject Areas, and a Calculation-First Study Plan
2 Chapter 2: Basic Science & Calculations
2.1 Gas Laws and Vapor Calculations 2.2 Unit Conversions: ppm, mg/m³, and Standard Temperature/Pressure 2.3 Fluid Mechanics and Airflow Fundamentals
3 Chapter 3: Air Sampling & Instrumentation
3.1 Active and Passive Air Sampling Strategies 3.2 Particulate and Aerosol Sampling 3.3 Direct-Reading Instruments and Calibration
4 Chapter 4: Analytical Chemistry & Lab Methods
4.1 Gas Chromatography and Mass Spectrometry 4.2 High-Performance Liquid Chromatography and Ion Chromatography 4.3 Spectroscopy and Elemental Analysis 4.4 Gravimetric, Microscopy, and Wet Chemical Methods 4.5 Laboratory Quality Assurance, Chain of Custody, and Desorption Efficiency
5 Chapter 5: Biostatistics & Epidemiology
5.1 Lognormal Distributions and Exposure Data Statistics 5.2 Upper Confidence Limits (UCL95) and Compliance Decision Rules 5.3 Epidemiological Study Designs and Measures of Association 5.4 Sampling Strategy: Sample Size, Power, and Worker Selection
6 Chapter 6: Toxicology & Biological Monitoring
6.1 Dose-Response Relationships and Points of Departure 6.2 Toxicokinetics: Absorption, Distribution, Metabolism, and Elimination 6.3 Aerosol Deposition, Clearance, and Respiratory Tract Dosimetry 6.4 Hepatic, Renal, Neurologic, and Hematologic Target Organ Toxicity 6.5 Pulmonary Toxicology, Carcinogenicity, and Reproductive Hazards 6.6 OEL Frameworks, Classifications, and Excursion Limits 6.7 Chemical Mixtures and Extended Work-Shift OEL Adjustments 6.8 Biological Exposure Indices (BEIs) and Biomonitoring
7 Chapter 7: Biohazards & Indoor Environmental Quality
7.1 Mold, Fungi, and Microbial Contaminants 7.2 Infectious Agents, Bloodborne Pathogens, and Biosafety Levels 7.3 Indoor Environmental Quality (IEQ) Investigations 7.4 Sanitation, Potable Water, and Personal Hygiene Programs
8 Chapter 8: Community Exposure & Environmental Health
8.1 Clean Air Act Framework, NAAQS, and New Source Review 8.2 Hazardous Air Pollutants, CEMS, and EPA Reference Methods 8.3 Atmospheric Stability, Lapse Rates, and Plume Morphology 8.4 Gaussian Plume Modeling, Plume Rise, and Environmental Fate 8.5 HAZWOPER Scope, Mandates, and Training Tiers 8.6 Protection Levels, Site Zoning, Incident Command, and Decontamination 8.7 Water Pollution, Hazardous Waste, and Community Right-to-Know
9 Chapter 9: Health Risk Analysis & Hazard Communication
9.1 GHS Hazard Classification: Health and Physical Hazard Criteria 9.2 GHS Labels, Safety Data Sheets, and Trade Secret Rules 9.3 The AIHA Exposure Assessment Strategy and Similar Exposure Groups 9.4 Qualitative Exposure Profiling and the AIHA Risk Matrix 9.5 Quantitative Health Risk Characterization: HQ, HI, and ELCR 9.6 NIOSH Occupational Exposure Banding 9.7 Risk Communication and Reporting to Affected Parties
10 Chapter 10: Industrial Ventilation Principles & LEV Design
10.1 Elimination, Substitution, Isolation, Containment, and Process Change 10.2 LEV Hood Taxonomy and Capture Velocity Selection 10.3 Hood Airflow Equations, Entry Losses, and Hood Static Pressure 10.4 Particulate Transport Aerodynamics and Duct Sizing 10.5 Duct Friction, Fitting Losses, and System Balancing 10.6 Fan Categories and Pressure Dynamics Across the Fan 10.7 System Curves, the Fan Laws, and Density Corrections
11 Chapter 11: General Ventilation, Air Cleaning & Diagnostics
11.1 Dilution Ventilation Principles and Steady-State Modeling 11.2 Transient Purging and Air Distribution Geometry 11.3 Particulate Air Cleaning: Cyclones, Baghouses, Scrubbers, and ESPs 11.4 Gaseous Emission Control and Air Cleaner Selection 11.5 Ventilation System Troubleshooting and Testing
12 Chapter 12: Noise Measurement & Hearing Conservation
12.1 Acoustic Physics and Decibel Mathematics 12.2 Sound Propagation, Octave Bands, and Frequency Weighting 12.3 Noise Dose Metrics and OSHA versus ACGIH Criteria 12.4 Exchange Rates, Extended Shifts, and Dosimetry Field Protocols 12.5 Engineering Noise Controls and Hearing Protector Attenuation 12.6 Hearing Conservation Programs and Standard Threshold Shifts 12.7 Hand-Arm and Whole-Body Vibration
13 Chapter 13: Thermal Stress Assessment & Control
13.1 Wet Bulb Globe Temperature (WBGT) and Heat Stress Indices 13.2 Heat-Related Disorders, Acclimatization, and Work/Rest Regimens 13.3 Cold Stress Evaluation and Wind Chill
14 Chapter 14: Ionizing Radiation Protection
14.1 Ionizing Radiation Physics and Radioactive Decay Kinetics 14.2 Radiation Units, Radiobiology, and Health Effects 14.3 ALARA, Stay-Time, and the Inverse Square Law 14.4 Shielding Physics, Material Selection, and Gamma Constants 14.5 Radiation Detection Instruments and Spectrometry 14.6 Personnel Dosimetry, Dose Limits, and Contamination Surveys
15 Chapter 15: Non-Ionizing Radiation & Laser Safety
15.1 The Non-Ionizing Spectrum and Static/ELF Field Exposures 15.2 Radiofrequency and Microwave Exposure: SAR, Standards, and Surveys 15.3 Ultraviolet, Visible, and Infrared Radiation Hazards 15.4 Laser Safety Classifications and Optical Density Calculations 15.5 Illumination, Lighting Design, and Visual Performance
16 Chapter 16: Non-Engineering Controls & Personal Protective Equipment
16.1 Respiratory Protection Programs and Assigned Protection Factors 16.2 Maximum Use Concentration, Oxygen Deficiency, and Breathing Air 16.3 Particulate Filters, Sorbent Cartridges, and Change Schedules 16.4 Respirator Fit Testing Protocols 16.5 Chemical Protective Clothing and Dermal Exposure Control
17 Chapter 17: Ergonomics & Workstation Design
17.1 Soft-Tissue Biomechanics and WMSD Pathophysiology 17.2 Ergonomic Risk Factors and Their Interaction Effects 17.3 The Revised NIOSH Lifting Equation 17.4 RULA, REBA, the Strain Index, and the ACGIH HAL TLV 17.5 Anthropometry and Workstation Geometry 17.6 VDT Workstations, Hand Tool Design, and Administrative Ergonomics
18 Chapter 18: Work Environments & Industrial Processes
18.1 Welding Fume Emissions, Metal Fume Fever, and Cr(VI)/Manganese Toxicology 18.2 Foundry Operations and Hot Work Fire Prevention 18.3 Vapor Degreasing, Pickling, Electroplating, and Cyanide Baths 18.4 Spray Coatings, Isocyanates, and Semiconductor Manufacturing 18.5 Confined Spaces and High-Hazard Industrial Operations 18.6 Asbestos, Lead, and Silica: Regulated Substance Programs 18.7 Abrasive Blasting and Surface Preparation
19 Chapter 19: IH Program Management & Professional Ethics
19.1 The BGC Code of Ethics: Canons and Enforcement 19.2 Professional Liability, Standard of Care, and Expert Testimony 19.3 Occupational Health & Safety Management Systems (ISO 45001, ANSI Z10) 19.4 Exposure Records Access and Medical Surveillance 19.5 OSHA Injury and Illness Recordkeeping and Enforcement
5.4 Sampling Strategy: Sample Size, Power, and Worker Selection
Key Takeaways Explain This Topic AI
To be C confident of sampling at least one worker from the top p fraction of a large group, the required random sample size is n = ln(1 − C) / ln(1 − p), giving 22 workers for 90% confidence of reaching the top 10%.
NIOSH tabulated the finite-population (hypergeometric) version of that calculation, which requires far fewer samples from small groups than the large-group formula.
The maximum-risk-employee approach substitutes professional judgement for random selection and is efficient but cannot support a statistical statement about the group.
AIHA guidance treats roughly 6 to 10 samples per similar exposure group as the practical minimum for a statistically defensible exposure profile.
Precision of the geometric mean improves only with the square root of sample size, so halving the confidence interval width requires roughly four times as many samples.
Last updated: August 2026
Sampling Strategy: Sample Size, Power, and Worker Selection
"How many samples do I need?" is the most frequently asked and least frequently answered question in exposure assessment. Two distinct statistical questions hide inside it, and they have different answers:
Whom do I sample so that I do not miss the most exposed workers?
How many samples do I need to characterise the exposure distribution of a group with acceptable precision?
1. Whom to Sample: The Top-Fraction Problem
Suppose a similar exposure group contains many workers and you can only sample a few. You want reasonable confidence that at least one of the workers you pick is among the most exposed.
For random selection from a large group , if the fraction of interest is p (say the top 10%, p = 0.10) and you want confidence C (say 0.90), the probability that a sample of n workers contains none of the top fraction is (1 − p)ⁿ. Setting the complement equal to C: 1 − ( 1 − p ) n = C ⟹ n = ln ( 1 − C ) ln ( 1 − p ) 1 - (1-p)^n = C \quad \Longrightarrow \quad n = \frac{\ln(1-C)}{\ln(1-p)} 1 − ( 1 − p ) n = C ⟹ n = ln ( 1 − p ) ln ( 1 − C )
Worked example. For 90% confidence of including at least one worker from the top 10%:
n = ln(0.10) / ln(0.90) = (−2.3026) / (−0.10536) = 21.85 → 22 workers
The numbers are unforgiving and worth memorising in outline:
- Confidence Top 10% Top 20%
- 90% 22 11
- 95% 29 14
- The finite-population correction
Real similar exposure groups are small, and sampling without replacement from a small group is far more efficient than the large-group formula implies. If a group has 10 workers, the "top 10%" is a single worker, and sampling 9 of the 10 gives 90% confidence directly. This is a hypergeometric rather than binomial problem, and it is exactly what the NIOSH Occupational Exposure Sampling Strategy Manual tabulated: partial-sampling tables that give the required number of workers as a function of group size.
The practical rule that follows: for groups of six or fewer, sample everyone. The tabulated saving only becomes meaningful for larger groups.
The maximum-risk-employee alternative
Instead of random selection, the industrial hygienist can identify the maximum-risk employee — the worker judged, from process knowledge, proximity to the source, task duration, and work practices, to have the highest exposure — and sample that person.
- Random selection Maximum-risk employee
- Samples required Many Few
- Supports a statistical statement about the group Yes No
- Depends on the hygienist's judgement being correct No Completely
- Compliance usefulness Characterises the distribution If the worst case is compliant, the group probably is
The two are complementary. Maximum-risk sampling is an efficient screening strategy; only random sampling supports a defensible statement about the exposure distribution of the group as a whole.
2. How Many Samples: Characterising the Distribution
Once the group is defined, the number of samples determines how precisely you know its geometric mean and geometric standard deviation.
AIHA guidance treats roughly 6 to 10 samples per similar exposure group as the practical minimum for a defensible exposure profile. Fewer than about six makes any estimate of the GSD nearly worthless, and the GSD is what drives the 95th percentile estimate on which the acceptability judgement rests.
Two consequences follow from the mathematics of the lognormal distribution:
Precision improves only as the square root of n. The standard error of the mean of the log-transformed data is s_y / √n. Halving the width of a confidence interval therefore requires roughly four times as many samples. There is no cheap route to precision.
A high GSD demands more samples. A homogeneous group (GSD near 1.5) can be characterised with far fewer samples than a heterogeneous one (GSD above 3). A high GSD is usually a symptom of a badly constructed SEG, and the correct response is to split the group , not to keep sampling it. +---------------------------------------------------------------+
- | SAMPLES NEEDED vs GSD (to reach a given precision on X95) |
- | |
- | GSD 1.5 |#### few samples |
- | GSD 2.0 |######## |
- | GSD 3.0 |################ |
- | GSD 4.0 |############################ split the SEG |
- +---------------------------------------------------------------+
- 3. Statistical Power and the Two Ways to Be Wrong
Exposure decisions carry two error types, and industrial hygiene cares far more about one of them:
- Error Statistical name What it means here Who is harmed
- Type I (α) False positive Concluding overexposure that does not exist Employer: unnecessary control cost
- Type II (β) False negative Failing to detect a real overexposure Worker: continued exposure
Power = 1 − β is the probability of detecting an overexposure that is genuinely present. Under-sampling is not a neutral economy: it directly reduces power and therefore directly increases the probability of leaving an overexposed group unprotected. This asymmetry is why a hygienist should be far more reluctant to declare "acceptable" on three samples than to declare "unacceptable."
Power rises with:
- larger sample size,
- lower variability (a tighter, better-defined SEG),
a larger true difference between the actual exposure and the OEL.
The last term explains a common field observation: an exposure at 95% of the OEL is very hard to distinguish statistically from one at 105%, while an exposure at 300% of the OEL is obvious from two samples.
4. Practical Rules
Define the SEG first. Sample size questions are unanswerable until the group is defined, and a bad group cannot be rescued by more samples.
Sample everyone in groups of six or fewer.
Plan 6 to 10 samples per SEG as a baseline, more if the GSD proves high.
Use maximum-risk sampling to screen and random sampling to characterise; document which you did, because the inference you may draw differs.
Treat a GSD above about 3 as evidence of a heterogeneous group and split it.
Never report an "acceptable" judgement from an under-powered data set without stating the uncertainty.