ASTM D5791-23

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Designation: D5791 − 95 (Reapproved 2017) D5791 − 23
Standard Guide for
Using Probability Sampling Methods in Studies of Indoor Air
Quality in Buildings
This standard is issued under the fixed designation D5791; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This guide covers criteria for determining when probability sampling methods should be used to select locations for placement
of environmental monitoring equipment in a building or to select a sample of building occupants for questionnaire administration
for a study of indoor air quality. Some of the basic probability sampling methods that are applicable for these types of studies are
introduced.
1.2 Probability sampling refers to statistical sampling methods that select units for observation with known probabilities (including
probabilities equal to one for a census) so that statistically defensible inferences are supported from the sample to the entire
population of units that had a positive probability of being selected into the sample.
1.3 This guide describes those situations in which probability sampling methods are needed for a scientific study of the indoor air
quality in a building. For those situations for which probability sampling methods are recommended, guidance is provided on how
to implement probability sampling methods, including obstacles that may arise. Examples of their application are provided for
selected situations. Because some indoor air quality investigations may require application of complex, multistage, survey
sampling procedures and because this standard is a guide rather than a practice, the references in Appendix X1 are recommended
for guidance on appropriate probability sampling methods, rather than including expositions of such methods in this guide.
1.4 This standard does not address non-probability sampling approaches. Non-probability sampling approaches may be needed,
such as worst-case sampling, range finding sampling, and screening sampling as inputs to help guide and inform probability
sampling methods.
1.5 Units—The values stated in SI units are to be regarded as standard. No other units of measurement are included in this
standard.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
This guide is under the jurisdiction of ASTM Committee D22 on Air Quality and is the direct responsibility of Subcommittee D22.05 on Indoor Air.
Current edition approved Oct. 1, 2017Sept. 1, 2023. Published October 2017September 2023. Originally approved in 1995. Last previous edition approved in 20122017
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as D5791 – 95 (2012)(2017). . DOI: 10.1520/D5791-95R17.10.1520/D5791-23.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5791 − 23
D1356 Terminology Relating to Sampling and Analysis of Atmospheres
3. Terminology
3.1 Definitions—For definitions of terms used in this guide, refer to Terminology D1356.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 census, n—survey of all elements of the target population.
3.2.2 cluster sample, n—a sample in which the sampling frame is partitioned into disjoint subsets called clusters and a sample of
the clusters is selected.
3.2.2.1 Discussion—
Data may be collected for all units in each sample cluster or, when a multistage sample is being selected, the units within the
sampled clusters may be further subsampled.
3.2.3 compositing samples, v—physically combining the material collected in two or more environmental samples.
3.2.4 expected value, n—the average value of a sample statistic over all possible samples that could be selected using a specified
sample selection procedure.
3.2.5 multistage sample, n—a sample selected in stages such that larger units are selected at the first stage, and smaller units are
selected at each subsequent stage from within the units selected at the previous stage of sampling.
3.2.5.1 Discussion—
For assessing the indoor air quality in a population of office buildings, individual buildings might be selected at the first stage of
sampling, floors selected within sample buildings at the second stage, and monitoring locations (for example, rooms or grid points)
selected on sampled floors at the third stage.
3.2.6 population parameter, n—a characteristic based on or calculated from all units in the target population.
3.2.6.1 Discussion—
The purpose of selecting a sample is usually to estimate population parameters. Population parameters cannot actually be
calculated unless data are available for all units in the population.
3.2.7 probability sample, n—a sample for which every unit on the sampling frame has a known, positive probability of being
selected into the sample.
3.2.7.1 Discussion—
The terms probability sampling and random sampling are sometimes used interchangeably.
3.2.8 sampling frame, n—a list from which a sample is selected.
3.2.8.1 Discussion—
An ideal sampling frame contains each member of the target population exactly once and contains no units that are not members
of the target population. In practice, the sampling frame may miss some members of the target population (for example, new
employees in a building) and include some individuals who are not members of the target population (for example, individuals who
no longer work in the building). However, no member of the population should be listed more than once on the sampling frame.
3.2.9 simple random sample, n—a sample of n elements selected from the sampling frame in such a way that all possible samples
of n elements have the same chance of being selected.
3.2.10 statistic, n—a sample-based estimate of a population parameter.
3.2.11 stratified sample, n—a sample in which the sampling frame is partitioned into disjoint subsets called strata, and sample units
are selected independently from each stratum, possibly at different sampling rates.
3.2.12 systematic sample, n—a sample selected by choosing one of the first k elements on the sampling frame at random and then
including every kth element thereafter.
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3.2.13 target population, n—the set of units or elements (for example, people or locations in space and time) about which a sample
is designed to provide inferences.
3.2.13.1 Discussion—
The target population is sometimes referred to as the population or universe of interest.
3.2.14 unbiased estimator, n—a statistic whose expected value is equal to the population parameter that it is intended to estimate.
4. Summary of Guide
4.1 When the objectives of an investigation of indoor air quality include extending inferences from a sample of units to the larger
population from which those units were selected, probability sampling methods must be used to select the sample units to be
observed and measured. Examples include:
4.1.1 Estimating the distributions of health and comfort symptoms experienced by the employees in a particular building during
a specific week.
4.1.2 Estimating the distribution of hourly average concentrations of specific substances in the breathing zone air in a particular
building during the working hours of a specific week.
4.1.3 Estimating the relationship between measures of environmental conditions in a building and the health or comfort symptoms
experienced by the occupants.
4.1.4 Thus, the study objectives are always a key consideration for determining if probability sampling methods are necessary.
Potential objectives for indoor air studies that would require probability sampling methods are discussed explicitly in Section 6.
4.2 Guidance is provided regarding the appropriate probability sampling methods to address these and other goals that require
extending inferences from a sample to a specific population. Those sampling methods require construction of a sampling frame
from which population elements can be selected. Examples include:
4.2.1 A list of all offices or work stations in a building,
4.2.2 A grid of potential monitoring locations that effectively covers the entire population of interest, and
4.2.3 A list of all persons who work in a specific building.
4.3 Since environmental concentrations usually vary continuously in time, spatial frame units like those listed in 4.2 often must
be crossed with temporal units, such as seasons, weeks, days, or hours, to form sampling frame units (for example,
building-seasons, office-weeks, or person-days). Specific issues that must be considered when constructing these types of sampling
frames are discussed in Section 7.
4.4 In addition to constructing sampling frames, a randomization procedure is necessary so that units can be selected from the
frame with known probabilities. Some basic considerations for and methods of selecting probability samples for studies of indoor
air quality are presented in Section 8.
4.5 Finally, Section 9 discusses considerations for statistical analysis and reporting that are peculiar to data collected using
probability sampling designs. Special statistical analysis methods are necessary when the sampling design includes stratification,
clustering, multistage sampling, or unequal probabilities of selection.
5. Significance and Use
5.1 Studies of indoor air problems are often iterative in nature. A thorough engineering evaluation of a building (1-4) is
sometimes sufficient to identify likely causes of indoor air problems. When these investigations and subsequent remedial measures
are not sufficient to solve a problem, more intensive investigations may be necessary.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
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5.2 This guide provides the basis for determining when probability sampling methods are needed to achieve statistically defensible
inferences regarding the goals of a study of indoor air quality. The need for probability sampling methods in a study of indoor air
quality depends on the specific objectives of the study. Such methods may be needed to select a sample of people to be asked
questions, examined medically, or monitored for personal exposures. They may also be needed to select a sample of locations in
space and time to be monitored for environmental contaminants.
5.3 This guide identifies several potential obstacles to proper implementation of probability sampling methods in studies of indoor
air quality in buildings and presents procedures that overcome those obstacles or at least minimize their impact.
5.4 Although this guide specifically addresses sampling people or locations across time within a building, it also provides
important guidance for studying populations of buildings. The guidance in this document is fully applicable to sampling locations
to determine environmental quality or sampling people to determine environmental effects within each building in the sample
selected from a larger population of buildings.
6. Study Objectives That Require Probability Sampling Methods
6.1 Inferences beyond the units actually observed in a sample are not rigorously defensible unless the units observed are a
probability sample selected from the population to which inferences will be extended. Thus, probability sampling methods are
needed whenever inferences will be extended from the units observed in a sample to a larger population. The need for such
inferences depends directly on the objectives of the study. The study objectives may include characterizing a building’s occupants
using a survey, or characterizing a building’s air quality using environmental monitoring, or a combination of both.
6.2 Occupant Survey:
6.2.1 A sample of building occupants may be asked to complete a questionnaire or to submit to a physical examination. If the
intention is to make inferences from the sample regarding the health and comfort symptoms of all the employees of the building,
a census of all building occupants or a probability sample selected from them is required. The occupants would typically be asked
about their health and comfort symptoms for a specific time period of time (for example, the day that the survey is administered,
the previous week, month, or year, and so forth). Developing a valid and reliable questionnaire is a complex process and is not
directly addressed by this guide (5).
6.2.2 Specific study objectives that require inferences to a population of building occupants include the following:
6.2.2.1 Estimate the distribution of health and comfort symptoms in a building either before beginning air quality measurements,
after implementing remedial measures, or as a measure of the magnitude of a potential indoor air problem.
6.2.2.2 Estimate the distribution of health and comfort symptoms in a building with reported problems and in another building
studied for comparison purposes.
6.2.2.3 Estimate the relationship of health and comfort symptoms with worker characteristics, such as age, sex, work location, or
type of work performed.
6.2.3 When inferences regarding the occupants of a building are needed, a census of all the building occupants may be necessary.
For example, a census of building occupants may be needed to establish statistical differences in occupant comfort or health
symptoms between different work areas (for example, floors) within a building. In other cases (for example, estimating the relative
frequency of complaints in a building with a large number of workers), a probability sample may provide sufficient precision at
less cost.
6.2.4 If the characteristics measured in a questionnaire are temporally dependent (for example, comfort and health symptoms on
the day of questionnaire administration), a sample of people and time periods may be needed (for example, a sample of person-days
within a given week). Moreover, the survey may need to be replicated across time (that is, repeated in different seasons).
6.2.5 A successful occupant survey requires that a large portion of the sample subjects complete the survey. For example, the
United States Office of Management and Budget usually requires 75 % or more for federally funded surveys. Thus, the success
of a survey may depend upon the burden it imposes, pre-survey publicity (for example, newsletters or union endorsements), and
follow-up of nonrespondents. The survey should be conducted in such a manner that people are sufficiently motivated to participate
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but not unduly alarmed about a potential air quality problem. Finally, residual nonresponse is inevitable, and survey data analysis
procedures that utilize weighting or imputation to compensate for nonresponse are recommended.
6.3 Environmental Monitoring:
6.3.1 Since air quality characteristics generally exhibit both spatial and temporal variability, each air quality measurement (for
example, temperature, humidity, or concentrations of specific substances) is generally representative of a specific location and time
(or period of time). If the objective is to infer information about the distribution of the measured characteristics (for example, the
mean or the range) for a target population of times and places, then probability sampling of both locations and times is required
to justify that inference.
6.3.2 Specific study objectives that require inferences to a population of units defined in time and space include the following:
6.3.2.1 Estimate the distribution of hourly average concentrations of specific substances in a building during a specified time frame
either before or after implementing remedial measures, or as a measure of the magnitude of a potential indoor air problem.
6.3.2.2 Estimate the distribution of hourly average concentrations of specific substances in a building with suspected problems and
in another building studied for comparison purposes. In each case, the target population would be defined as a specific set of
building locations crossed with a specific set of time points. Inferences to the population would require that data be collected for
a probability sample of the population units.
6.3.3 Temporal variations in air quality must always be considered when designing a survey of a building’s air quality. Periodic
variations, such as diurnal, weekday/weekend, and seasonal effects can be important. Periodic effects may be caused by periodic
variation in activity patterns within the building or environmental factors that affect source strength or ventilation rate. These
temporal variations will affect such sampling design characteristics as the definition of the population units and the definition of
sample selection strata.
6.3.4 For example, if diurnal effects must be estimated, the temporal dimension of the population units to be measured cannot be
greater than 12 h, and the sampling plan must include both daytime and nighttime measurements. If estimating other temporal
differences is important (for example, weekday/weekend, high/low wind, before/during/after second-shift), population units must
be defined and sampled for each temporal period. The precision for estimates of differences between time periods can be increased
by monitoring a single sample of locations during multiple time periods. If concurrent surveys of building occupants and air quality
characteristics are required to establish relationships, a separate sample of building occupants may be needed for each time period.
6.3.5 Likewise, the survey may need to be replicated across time to characterize building conditions during multiple seasons.
Similarly, if certain air quality problems are perceived to be worse on weekday mornings, surveys conducted on a weekday
morning, a weekday evening, and a weekend day may be useful for estimating temporal differences.
6.3.6 Whenever environmental monitoring is being conducted indoors and the outdoor air is a potential source of the substances
being monitored, indoor and outdoor air should be monitored concurrently. Constructing a sampling frame for selecting a
probability sample of outdoor monitoring locations may not be feasible. Instead, each indoor monitoring location may be matched
to one of a small number of outdoor monitoring sites (for example, one to four) that best represents the outdoor air source for the
monitored indoor site.
6.4 Combining an Occupant Survey with Environmental Monitoring:
6.4.1 Air quality characteristics and people’s perceptions of the air quality may be measured simultaneously. If the objective is
to infer a relationship between the two sets of measurements for a larger population of people, places, and times, then a probability
sample of people, places, and times is necessary.
6.4.2 When a survey objective is to estimate the relationship between data collected for building occupants and indoor air
monitoring data (for example, between the occurrence of specific symptoms and the concentrations of specific substances), a
probability sample of locations and times (for the air quality monitoring and symptom measurement) plus associated people (for
example, the people who work primarily at the locations and times being monitored) is needed to support those inferences. In this
case, recording symptoms for the same temporal reference periods over which air quality samples are collected is important. See
Ref (6) for an example of such an investigation.
6.4.3 A specific survey objective that would require a probability sample of times, locations, and people is the following:
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6.4.3.1 Estimate the relationship of health and comfort symptoms with concentrations of specific substances measured in the same
times and places as the health and comfort symptoms.
6.4.4 While one may be able to approximate a relationship based on a non-probability sample (for example, locations that
approximate the range of health and comfort symptoms or the range of environmental measurements), a population sample is
needed if the relationship is to be representative of the entire population. Moreover, if other population characteristics (for example,
the distribution of health and comfort symptoms or the mean air concentration) are to be estimated from the same database, a
population sample is required.
7. Defining Population Units
7.1 The identification of population units depends on measurement procedures and study objectives. The units in the target
population are those units for which measurements will be obtained and which in their aggregate represent the entire universe to
which inferences will be extended. For environmental studies, these units usually need to be defined in time and space (7).
7.2 Occupant Survey:
7.2.1 When a survey of the occupants of an office building is needed, defining the population of interest is relatively
straightforward. Nevertheless, temporal and spatial effects need to be considered. Questions to be answered regarding the
inclusiveness of the population include the following:
7.2.1.1 Does the population include both part-time and full-time workers?
7.2.1.2 Does the population include both temporary and permanent staff?
7.2.1.3 Does the population include all work shifts?
7.2.1.4 Does the population include custodial staff?
7.2.1.5 Does the population include workers in all of the building or only specific areas of the building?
7.2.2 If the data to be collected are time dependent (for example, health and comfort symptoms on a particular day or during the
previous week), then the population units have a temporal component, also. Thus, the population units to be sampled may be
person-days or person-weeks. The set of days or other time units to be represented by the survey must be explicitly defined. If only
one temporal unit is to be represented (for example, one day or one week), no sampling in time is required. Otherwise, sampling
in time is necessary to represent the desired population of people and times.
7.3 Environmental Monitoring:
7.3.1 The population units for environmental monitoring usually must be defined in time and space because environmental
conditions usually change continuously. A population unit is essentially the unit of time and space that is characterized by a single
measurement from a monitoring instrument. Thus, different monitoring instruments may produce measurements for different
population units (for example, one provides average concentrations for 6 to 12-h6 h to 12 h periods while another provides
continuous measurements for up to 24 h).
7.3.2 The spatial dimension of a population unit for an air monitoring device may be an envelope of specified volume (for
example, 1000 m ) centered at the monitoring device. However, the reliability with which the monitoring device can characterize
the air quality in an envelope surrounding itself depends directly on air mixing in the immediate vicinity of the device. Therefore,
definition of the spatial population units generally depends on locations of physical boundaries (for example, walls) and on
characteristics of the heating, ventilating, and air conditioning (HVAC) system (for example, air handling zones).
7.3.3 The space characterized by a monitoring instrument will not usually have fixed boundaries. Thus, the spatial dimension of
a population unit may be somewhat arbitrary. Nevertheless, the spatial population units can be defined by first reviewing the floor
plan and the HVAC system of a building to construct a grid of points that, in their entirety, would effectively characterize the entire
breathing-zone space of the building if they were all monitored. The spatial population units are then disjoint envelopes centered
at the grid points (potential monitoring locations). If the envelopes are of different sizes, statistical analyses must account for these
differences.
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