D-DNS 10: 202x  
 
  
 
DOMINICA NATIONAL STANDARD  
 
 
 
 
 
 
 
 
 
METHODOLOGIES FOR SAMPLING OF CONSIGNMENTS  
 
D-DNS 10: 202x  
 
 
 
 
©DBOS 202x  
Dominica Bureau of Standards  
National Centre of Testing Excellence  
P.O. Box 1015, Stockfarm, Roseau  
Commonwealth of Dominica, W.I.  
Tel.: 767 -275-5921/3017  
Email: info@dominicastandards.org  
 
 
 
 
 
___________ 202x       Price Group  ______  
 
 
   
COPYRIGHT © 202x  
 
This document contains proprietary information, and should not be published, reproduced, 
copied, disclosed or used for any purpose without the prior written approval of the Dominica 
Bureau of Standards (DBOS).  This does  not preclude quotation for the purposes of review 
or comments. Enquiries relating to copyright may be addressed to the Director, Dominica 
Bureau of Standards  
  
i 
 Draft No.  1 
ISSUED FOR COMMENT ONLY  
DRAFT  
DOMINICA NATIONAL STANDARD  
METHODOLOGIES FOR SAMPLING OF CONSIGNMENTS  
D-DNS 10: 202x  
 
 
 
 
 
Last date for comments …………………………..  
 
 
 
DOMINICA BUREAU OF STANDARDS  
National Centre of Testing Excellence  
Stockfarm  
P.O. Box 1015  
Roseau  
COMMONWEALTH OF DOMINICA  
Email: info@dominicastandards.org   
  This is a draft and should not be regarded or used 
as a Dominica National Standard   
ii 
 GENERAL STATEMENT  
 
The Dominica Bureau of Standards was established under the Standards Act (#4) of 1999 and 
started operations in April 2000. A broad -based 15 -member Standards Council governs the affairs 
of the Bureau.  
 
The Standards Act gives the Bureau the responsibility  to facilitate the development and promotion 
of Standards and Codes of Practice for products and services for the protection of the health and 
safety of consumers and the environment as well as for industrial development in order to promote 
the enhancement  of the economy of Dominica.  
 
The Bureau develops Standards through consultations with relevant interest groups. In accordance 
with the provisions of the Standards Act, public comment is invited on all draft Standards before 
they are declared as Dominica National Standards (DNS).  
 
The Bureau is a correspondent member body of the International Organization for Standardization 
(ISO), an affiliate member of the International Electro -technical Commission (IEC), and a member 
of the Caribbean Regional Organization for Standards and Quality ( CROSQ) and the Pan 
American Standards Commission (COPANT). The Bureau is the local agent for foreign Standard 
Body, the American Standards for Testing and Measurement (ASTM). The Bureau also serves as 
the enquiry point for the World Trade Organization (WTO ) on matters pertaining to the Technical 
Barriers to Trade (TBT) Agreement and is the Contact Point for Codex Alimentarius.  
 
In accordance with good practice for the adoption and application of Standards, Dominica National 
Standards are subject to periodic  review every five years.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
iii 
 AMENDMENTS  
 
 
 
Amendment No.   
Date of Issue   
Text (s) Affected  
   
 
   
iv 
 DOMINICA NATIONAL STANDARD  
METHODOLOGIES FOR SAMPLING OF CONSIGNMENTS  
 
TECHNICAL COMMITTEE – Food Products, Processes and Services (FPPS)  
 
 
ORGANIZATION  REPRESENTIVE (S)  
(Alternate)  
Dominica Association of Industry and Commerce  Alleyna Robin  
Dominica Export Import Agency  Lloyd Pascal  
Sharon Rolle  
Dominica Manufacturers Association  Linvor Ambo  
Dominica State College  Sharon Allicock Joseph  
Valda Joseph  
IICA  Kent Coipel  
Ministry of Agriculture, Food, and Fisheries  Anna Mary Seraphine  
Ministry of Trade, Energy, and Employment  Margaret Roudette  
Jackie Xavier  
TECHNICAL SECRETARY  
Mr. Kyle James  
Technical Officer, DBOS  
 
 
 
 
 
 
 
 
 
 
 
  
1 
 TABLE OF CONTENTS  
Contents  
0.0 FOREWORD  ................................ ................................ ................................ ................................ ... 3 
INTRODUCTION  ................................ ................................ ................................ ................................ ........  4 
Scope  ................................ ................................ ................................ ................................ .........................  4 
References  ................................ ................................ ................................ ................................ .....................  4 
Definitions  ................................ ................................ ................................ ................................ .....................  4 
Outline of Requirement s ................................ ................................ ................................ ...............................  4 
BACKGROUND  ................................ ................................ ................................ ................................ ..........  5 
OBJECTIVES OF SAMPLING OF CONSIGNMENTS  ................................ ................................ .............  5 
REQUIREMENTS  ................................ ................................ ................................ ................................ ........  6 
1. Lot Identification  ................................ ................................ ................................ ................................ .. 6 
2. Sample Un it ................................ ................................ ................................ ................................ ..........  7 
3. Statistical and Non -Statistical Sampling  ................................ ................................ ...............................  7 
3.1. Statistically based sampling  ................................ ................................ ................................ ..........  7 
3.1.1.  Parameters and related concepts  ................................ ................................ ...........................  7 
3.1.1.1.  Acceptance number  ................................ ................................ ................................ ...............  7 
3.1.1.2.  Level of detection ................................ ................................ ................................ ..................  8 
3.1.1.3.  Confidence level  ................................ ................................ ................................ ...................  8 
3.1.1.4.  Efficacy of detection  ................................ ................................ ................................ .............  8 
3.1.1.5.  Sample size  ................................ ................................ ................................ ...........................  9 
3.1.1.6.  Tolerance level  ................................ ................................ ................................ ......................  9 
3.1.2.  Links between the parameters and tolerance level  ................................ ................................  9 
3.1.3.  Statistically based sampling methods ................................ ................................ ........................  9 
3.1.3.1.  Simple random sampling  ................................ ................................ ................................ ...... 9 
3.1.3.2.  Systematic sampling  ................................ ................................ ................................ ...........  10 
3.1.3.3. Stratified sampling  ................................ ................................ ................................ ..............  10 
3.1.3.4.  Sequential sampling  ................................ ................................ ................................ ............  10 
3.1.3.5.  Cluster sampling  ................................ ................................ ................................ .................  11 
3.1.3.6.  Fixed proportion sampling  ................................ ................................ ................................ .. 11 
3.2. Non-statistically based sampling  ................................ ................................ ................................  11 
3.2.1.  Convenience sampling  ................................ ................................ ................................ ........  11 
3.2.2.  Haphazard sampling  ................................ ................................ ................................ ............  11 
3.2.3.  Selective or targeted sampling  ................................ ................................ ............................  11 
4. Selecting a Sampling Method  ................................ ................................ ................................ .............  12  
2 
 5. Sample Size Determination  ................................ ................................ ................................ .................  13 
5.1. Pests distribution unknown in the lot  ................................ ................................ ..........................  13 
5.2. Pest distribution aggregated in the lot  ................................ ................................ .........................  13 
6. Varying Level of Detection ................................ ................................ ................................ .................  14 
7. Outcome of Sampling  ................................ ................................ ................................ .........................  14 
APPENDIX 1: Formulae used in Appendixes 2 –5 ................................ ................................ .....................  15 
APPENDIX 2: Calculating sample sizes for small lots: hypergeometric -based sampling  .........................  16 
(simple random sampling)  ................................ ................................ ................................ .......................  16 
APPENDIX 3: Sampling of large lots: binomial or Poisson based sampling  ................................ .............  20 
APPENDIX 4: Sampling for pests with an aggregated distribution: beta -binomial based sampling  .........  23 
APPENDIX 5: Comparison of hypergeome tric and fixed proportion sampling results  .............................  24 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
3 
  
0.0 FOREWORD  
 
0.1. This Dominica National Standard was adopted by the Bureau of Standards (the 
Bureau) of the Commonwealth of Dominica on  _____________  after the draft was 
finalized by Technical Committee for Food Products, Processes and Services (FPPS) 
and has been approved by the  Minister responsible for the Bureau.  
 
0.2. This Standard b ecame effective as a Compulsory Standard on the date notified by the 
Minister with responsibility for the Bureau of Standards in a Notice published in the 
Commonwealth of Dominica Official Gazette on ________________.  
 
0.3. This standard is an identical adoptio n of International Standards for Phytosanitary 
Measures (ISPM) 31: 201 6 - International Movement of Used Vehicles, Machinery 
and Equipment.  
 
0.4. Acknowledgement is given to International Plant Protection Convention  (IPPC ) for 
providing permission to adopt ISPM 31: 201 6.  
 
0.5. Although the editorial style and layout of the ISPM 31: 201 6 are not in conformity 
with that of Dominica's Standards, the identical adoption has been approved as suitable 
for publication as a Dominica Nati onal Standard.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
4 
 INTRODUCTION   
Scope   
This standard provides guidance to national plant protection organizations (NPPOs) in selecting 
appropriate sampling methodologies for inspection or testing of consignments to verify 
compliance with phytosanitary requirements.   
This standard does not give  guidance on field sampling (for example, as required for surveys).  
References  
The present standard refers to International Standards for Phytosanitary Measures (ISPMs). 
ISPMs are available  on the International Phytosanitary Portal (IPP) at 
https://www.ippc.int/core activities/standards -setting/ispms .  
Cochran, W.G.  1977. Sampling techniques . 3rd edn. New York, John Wiley & Sons. 428 pp.  
Definitions  
Definitions of phytosanitary terms used in the present standard can be found in ISPM 5 ( Glossary 
of phytosanitary terms ).  
Outline of Requirements  
The sampling methodologies used by NPPOs in selecting samples for the inspection of 
consignments of commodities moving in international trade are based on a number of sampling 
concepts. Th ese include parameters such as acceptance level, level of detection, confidence level, 
efficacy of detection and sample size.  
The application of statistically based methods, such as simple random sampling, systematic 
sampling, stratified sampling, sequent ial sampling or cluster sampling, provides results with a 
statistical confidence level. Other sampling methods that are not statistically based, such as 
convenience sampling, haphazard sampling or selective sampling, may provide valid results in 
determinin g the presence or absence of a regulated pest(s) but no statistical inference can be made 
on their basis. Operational limitations will have an effect on the practicality of sampling under one 
or another method.  
In using sampling methodologies, NPPOs accep t some degree of risk that non -conforming lots 
may not be detected. Inspection using statistically based methods can provide results with a certain 
level of confidence only and cannot prove the absence of a pest from a consignment.    
5 
 BACKGROUND  
This standard provides the statistical basis for, and complements, ISPM 20 ( Guidelines for a 
phytosanitary import regulatory system ) and ISPM 23 ( Guidelines for inspection ). Inspection of 
consignments of regulated articles moving in trade is an essential tool for the management of pest 
risks and is the most frequently used phytosanitary procedure worldwide to determin e if pests are 
present and/or the compliance with phytosanitary import requirements.  
It is usually not feasible to inspect entire consignments, so phytosanitary inspection is performed 
mainly on samples obtained from a consignment. It is noted that the sa mpling concepts presented 
in this standard may also apply to other phytosanitary procedures, notably selection of units for 
testing.  
Sampling of plants, plant products and other regulated articles may occur prior to export, at the 
point of import, or othe r points as determined by NPPOs.  
It is important that sampling procedures established and used by NPPOs are documented and 
transparent, and take into account the principle of minimum impact (ISPM 1 ( Phytosanitary 
principles for the protection of plants an d the application of phytosanitary measures in 
international trade )), particularly because inspection based on sampling may lead to the refusal to 
issue a phytosanitary certificate, refusal of entry, or treatment or destruction of a consignment or 
part of a consignment.  
Sampling methodologies used by NPPOs will depend on the sampling objectives (for example, 
sampling for testing) and may be solely statistically based or developed noting particular 
operational constraints. Methodologies developed to achieve  the sampling objectives, within 
operational constraints, may not yield the same statistical confidence levels in the results as fully 
statistically based methods, but such methods may still give valid results depending on the desired 
sampling objective. I f the sole purpose of sampling is to increase the chance of finding a pest, 
selective or targeted sampling is also valid.  
OBJECTIVES OF SAMPLING OF CONSIGNMENTS  
Sampling of consignments is done for inspection and/or testing in order to:  
- detect regulated  pests  
- provide assurance that the number of regulated pests or infested units in a consignment does 
not exceed the specified tolerance level for the pest  
- provide assurance of the general phytosanitary condition of a consignment  
- detect organisms for which a phytosanitary risk has not yet been determined  
- optimize the probability of detecting specific regulated pests  
- maximize the use of available sampling resources   
6 
 - gather other information such as for monitoring of a pathway - verify compliance with 
phytosanitary requirements  
- determine the proportion of the consignment infested.  
It should be noted that inspection and/or testing based on sampling always involves a degree of 
error. The acceptance of some probability that the pests  are present is inherent in the use of 
sampling procedures for inspection and/or testing. Inspection and/or testing using statistically 
based sampling methods can provide a level of confidence that the incidence of a pest is below a 
certain level, but it d oes not prove that a pest is truly absent from a consignment.  
REQUIREMENTS  
1. Lot Identification  
A consignment may consist of one or more lots. Where a consignment comprises more than one 
lot, the inspection to determine compliance may have to consist of s everal separate visual 
examinations, and therefore the lots will have to be sampled separately. In such cases, the samples 
relating to each lot should be segregated and identified in order that the appropriate lot can be 
clearly identified if subsequent in spection or testing reveals non -compliance with phytosanitary 
requirements. Whether or not a lot will be inspected should be determined using factors stated in 
ISPM 23 (section on other considerations for inspection).   
A lot to be sampled should be a number of units of a single commodity identifiable by its 
homogeneity in factors such as:  
- origin  
- grower  
- packing facility  
- species, variety, or degree of maturity  
- exporter  
- area of production  
- regulated pests and their characteristics - treatment at origin  
- type of processing.  
The criteria used by the NPPO to distinguish lots should be consistently applied for similar 
consignments.  
Treating multiple commodities as a single lot for convenience may mean that statistical inferences 
cannot  be drawn from the results of the sampling.   
7 
 2. Sample Unit  
Sampling first involves the identification of the appropriate unit for sampling (for example,  a fruit, 
stem, bunch, unit of weight, bag or carton). The determination of the sample unit is affected by 
issues related to homogeneity in the distribution of pests through the commodity, whether the pests 
are sedentary or mobile, how the consignment is p ackaged, intended use, and operational 
considerations. For example, if determined solely on pest biology, the appropriate sample unit 
might be an individual plant or plant product in the case of a low -mobility pest, whereas in the 
case of mobile pests, a c arton or other commodity container may be the preferred sample unit. 
However, when inspection is to detect more than one type of pest, other considerations (for 
example, practicality of using different sample units) may apply. Sample units should be 
consis tently defined and independent from each other. This will allow NPPOs to simplify the 
process of making inferences from the sample to the lot or consignment from which the sample 
was selected.  
3. Statistical and Non -Statistical Sampling   
The sampling method  is the process approved by the NPPO to select units for inspection and/or 
testing. Sampling for phytosanitary inspection of consignments or lots is done by taking units from 
the consignment or lot without replacement of the units selected1. NPPOs may cho ose either a 
statistically based or non -statistical sampling methodology.  
Sampling based on statistical or targeted methods is designed to facilitate the detection of a 
regulated pest(s) in a consignment and/or lot.  
3.1. Statistically based sampling  
Statisti cally based sampling methods involve the determination of a number of interrelated 
parameters and the selection of the most appropriate statistically based sampling method.  
3.1.1.  Parameters and related concepts  
Statistically based sampling is designed to detect a certain percentage or proportion of infestation 
with a specific confidence level, and thus requires the NPPO to determine the following 
interrelated parameters: acceptance number, level of detection, con fidence level, efficacy of 
detection and sample size. The NPPO may also establish a tolerance level for certain pests (for 
example, regulated nonquarantine pests).  
3.1.1.1.  Acceptance number  
The acceptance number is the number of infested units or the number of i ndividual pests that are 
permissible in a sample of a given size before phytosanitary action is taken. Many NPPOs 
determine this number to be zero for quarantine pests. For example, if the acceptance number is 
zero and an infested unit is detected in the s ample then phytosanitary action will be taken. It is 
important to appreciate that a zero-acceptance  number within a sample does not imply a zero-
 
1 Sampling without replacement is selecting a unit from the consignment or lot without replacing the unit before the 
next units are selected. Sampling without replacement does not mean that a selected item cannot be returned   
8 
 tolerance  level in the consignment as a whole. Even if no pests are detected in the sample there 
remains a prob ability that the pest may be present in the remainder of the consignment, albeit at a 
very low level.  
The acceptance number is linked to the sample. The acceptance number is the number of infested 
units or the number of individual pests that are permissible in the sample whereas the tolerance 
level (see section 3.1.1.6) refers to the status of the entire c onsignment.   
3.1.1.2.  Level of detection  
The level of detection is the minimum percentage or proportion of infestation that the sampling 
methodology will detect at the specified efficacy of detection and level of confidence and which 
the NPPO intends to detect in  a consignment.   
The level of detection may be specified for a pest, a group or category of pests, or for unspecified 
pests. The level of detection may be derived from:  
- a decision based on pest risk analysis to detect a specified level of infestation (th e infestation 
determined to present an unacceptable risk)  
- an evaluation of the effectiveness of phytosanitary measures applied before inspection  
- an operationally based decision that inspection intensity above a certain level is not practical.  
3.1.1.3.  Confidence  level  
The confidence level indicates the probability that a consignment with a degree of infestation 
exceeding the level of detection will be detected. A confidence level of 95% is commonly used. 
The NPPO may choose to require different confidence levels  depending on the intended use of the 
commodity. For example, a higher confidence level for detection may be required for commodities 
for planting than for commodities for consumption, and the confidence level may also vary with 
the strength of the phytosa nitary measures applied and historical evidence of non -compliance. 
Very high confidence level values quickly become difficult to achieve, and lower values become 
less meaningful  
                                                                                                                                                                      
to a consignment (except for destructive sampling); it means only that the inspector should not 
return it before selecting the remainder of the sample.  
for decision -making. A 95% confidence level means that the conclusions drawn from the results 
of sampli ng will detect a non -compliant consignment, on average, 95 times out of 100, and 
therefore, it may be assumed that, on average, 5% of non -compliant consignments will not be 
detected.   
3.1.1.4.  Efficacy of detection  
The efficacy of detection is the probability tha t an inspection or test of an infested unit(s) will 
detect a pest. In general,  the efficacy should not be assumed to be 100%. For example, pests may 
be difficult to detect visually, plants may not express symptoms of disease (latent infection), or 
efficacy  may be reduced as a result of human error. It is possible to include lower efficacy values 
(for instance, an 80% chance of detecting the pest when an infested unit is inspected) in the 
determination of sample size.   
9 
 3.1.1.5.  Sample size  
The sample size is the num ber of units selected from the lot or consignment that will be inspected 
or tested. Guidance on determining the sample size is provided in section 5.  
3.1.1.6.  Tolerance level  
Tolerance level refers to the percentage of infestation in the entire consignment or lot  that is the 
threshold for phytosanitary action.   
Tolerance levels may be established for regulated non -quarantine pests (as described in ISPM 21 ( Pest 
risk analysis for regulated non -quarantine pests )) and may also be established for conditions related t o 
other phytosanitary import requirements (for example, bark on wood or soil on plant roots).  
Most NPPOs have a zero-tolerance  level for all quarantine pests, taking into account probabilities 
of pest presence in the non -sampled units as described in sect ion 3.1.1.1. However, an NPPO may 
determine to establish a tolerance level for a quarantine pest based on pest risk analysis (as 
described in ISPM 11 ( Pest risk analysis for quarantine pests )) and then determine sampling rates 
from this. For example, NPPOs  may determine a tolerance level that is greater than zero because 
small numbers of the quarantine pest may be acceptable if the establishment potential of the pest 
is considered low or if the intended end use of the product (for example, fresh fruit and v egetables 
imported for processing) limits the potential of entry of the pest into endangered areas.  
3.1.2.  Links between the parameters and tolerance level  
The five parameters (acceptance number, level of detection, confidence level, efficacy of detection 
and s ample size) are statistically related. Taking into account the established tolerance level, the 
NPPO should determine the efficacy of the detection method used and decide upon the acceptance 
number in the sample; any two of the remaining three parameters c an also be chosen, and the 
remainder will be determined from the values chosen for the rest.  
If a tolerance level greater than zero has been established, the level of detection chosen should be 
equal to (or less than, if the acceptance number is greater t han zero) the tolerance level to ensure 
that consignments having an infestation level greater than the tolerance level will be detected with 
the specified confidence level.   
If no pests are detected in the sample unit, then the percentage of infestation i n the consignment 
cannot  be stated beyond the fact that it falls below the level of detection at the stated confidence 
level. If the pest is not detected with the appropriate sample size, the confidence level gives a 
probability that the tolerance level is  not exceeded.   
3.1.3.  Statistically based sampling methods  
3.1.3.1.  Simple random sampling  
Simple random sampling results in all sample units having an equal probability of being selected 
from the lot or consignment. Simple random sampling involves drawing the sample units in 
accordance with a tool such as a random numbers table. The use of a pr edetermined randomization 
process is what distinguishes this method from haphazard sampling (described in section 3.2.2).   
10 
 This method is used when little is known about the pest distribution or rate of infestation. Simple 
random sampling can be difficult to apply correctly in operational situations. To use this method, 
each unit should have an equal probability of selection. In cases where a pest is not distributed 
randomly through the lot, this method may not be optimal. Simple random sampling may require  
greater resources than other sampling methods. The application can be dependent on the type 
and/or configuration of the consignment.  
3.1.3.2.  Systematic sampling  
Systematic sampling involves drawing a sample from units in the lot at fixed, predetermined 
interval s. However, the first selection must be made at random through the lot. Biased results are 
possible if pests are distributed in a manner similar to the interval chosen for sampling.  
Two advantages of this method are that the sampling process may be automa ted through machinery 
and that it requires the use of a random process only to select the first unit.  
3.1.3.3.  Stratified sampling  
Stratified sampling involves separating the lot into separate subdivisions (that is, strata) and then 
drawing the sample units from each and every subdivision. Within each subdivision, sample units 
are taken using a particular method (systematic or random). Under some circumstances, different 
numbers of sample units may be taken from each subdivision – for instance, the number of sampl e 
units may be proportional to the size of the subdivision, or based on prior knowledge concerning 
the infestation of the subdivisions.  
If at all feasible, stratified sampling will almost always improve detection accuracy. The smaller 
variation associated  with stratified sampling yields more accurate results. This is especially true 
when infestation levels may vary across a lot depending on packing procedures or storage 
conditions. Stratified sampling is the preferred choice when knowledge about the pest d istribution 
is presumed and operational considerations will allow it.  
3.1.3.4.  Sequential sampling  
Sequential sampling involves drawing a series of sample units using one of the above methods. 
After each sample (or group) is drawn, the data are accumulated and co mpared with predetermined 
ranges to decide whether to accept the consignment, reject the consignment or continue sampling.   
This method can be used when a tolerance level greater than zero is determined and the first set of 
sample units does not provide s ufficient information to allow a decision to be made on whether or 
not the tolerance level is exceeded. This method would not be used if the acceptance number in a 
sample of any size is zero. Sequential sampling may reduce the number of samples required fo r a 
decision to be made or reduce the possibility of rejecting a conforming consignment.   
11 
 3.1.3.5.  Cluster sampling  
Cluster sampling involves selecting groups of units based on a predefined cluster size (for example, 
boxes of fruit, bunches of flowers) to make up the total number of sample units required from the 
lot. Cluster sampling is simpler to evaluate and more reliable if the clusters are of equal size. It is 
useful if  resources available for sampling are limited and works well when the distribution of pests 
is expected to be random.   
Cluster sampling can be stratified, and can use either systematic or random methods for selecting 
the groups. Of the statistically based methods, this method is often the most practical to implement.  
3.1.3.6.  Fixed proportion sampling  
Sampling a fixed proportion of the units in the lot (for example, 2%) results in inconsistent levels 
of detection or confidence levels when lot size varies. As shown in Appendix 5, fixed proportion 
sampling results in changing confidence levels f or a given level of detection, or in changing levels 
of detection for a given confidence level.  
3.2. Non-statistically based sampling  
Other sampling methods that are not statistically based, such as convenience sampling, haphazard 
sampling or selective or tar geted sampling, may provide valid results in determining the presence 
or absence of a regulated pest(s). The following methods may be used based on specific operational 
considerations or when the goal is purely detection of pests.   
3.2.1.  Convenience sampling  
Convenience sampling involves selecting the most convenient (for example, accessible, cheapest, 
fastest) units from the lot, without selecting units in a random or systematic manner.   
3.2.2.  Haphazard sampling  
Haphazard sampling involves selecting arbitrary unit s without using a true randomization process. 
This may often appear to be random because the inspector is not conscious of having any selection 
bias. However, unconscious bias may occur, so that the degree to which the sample is 
representative of the lot i s unknown.  
3.2.3.  Selective or targeted sampling  
Selective sampling involves deliberately selecting samples from parts of the lot most likely to be 
infested, or units that are obviously infested, in order to increase the chance of detecting a specific 
regulated  pest. This method may rely on inspectors who are experienced with the commodity and 
familiar with the pest’s biology. Use of this method may also be triggered through a pathway 
analysis identifying a specific section of the lot with a higher probability o f being infested (for 
example, a wet section of timber may be more likely to harbour nematodes). Because the sample 
is targeted, and hence statistically biased, a probabilistic statement about the infestation level in 
the lot cannot  be made. However, if th e sole purpose of sampling is to increase the chance of 
finding a regulated pest(s), this method is valid. Separate samples of the commodity may be 
required to meet general confidence in detection of other regulated pests. The use of selective or  
12 
 targeted sampling may limit the opportunities to derive information about the overall pest status 
of the lot or consignment, because sampling is focused on where specific regulated pests are likely 
to be found not on the remainder of the lot or consignment.   
4. Selec ting a Sampling Method  
In most cases the selection of an appropriate sampling method is necessarily dependent on 
information available about pest incidence and distribution in the consignment or lot as well as the 
operational parameters associated with the inspection situation i n question. In most phytosanitary 
applications operational limitations will dictate the practicality of sampling under one or another 
method. Subsequently determining the statistical validity of practical methods will narrow the field 
of alternatives.   
The sampling method that is ultimately selected by the NPPO should be operationally feasible and 
be the most appropriate to achieve the objective and be well documented for transparency. 
Operational feasibility is clearly linked to judgements concerning situ ation -specific factors, but 
should be consistently applied.  
If sampling is undertaken to increase the chance of detecting a specific pest targeted sampling 
(described in section 3.2.3) may be the preferred option as long as the inspectors can identify the  
section(s) of the lot with a higher probability of being infested. Without this knowledge, one of 
the statistically based methods will be more appropriate. Non -statistically based sampling methods 
do not result in each unit having an equal probability of being included in the sample and do not 
allow for quantification of a confidence level or level of detection.  
Statistically based methods will be appropriate if sampling is undertaken to provide information 
about the general phytosanitary condition of a c onsignment, to detect multiple quarantine pests or 
to verify compliance with phytosanitary requirements.  
In selecting a statistically based method, consideration may be given to how the consignment has 
been treated in harvesting, sorting and packing, and the likely distribution of the pest(s) in the lot. 
Sampling methods may be combined: for instance, a stratified sample may have either random or 
systematic selection of sample units (or clusters) within strata.   
If sampling is undertaken to determine whet her a specific non -zero tolerance level has been 
exceeded, a sequential sampling method may be appropriate.   
Once a sampling method has been selected and correctly applied, repeating the sampling with the 
aim of achieving a different result is unacceptabl e. Sampling should not be repeated unless 
considered necessary for specific technical reasons (for example, suspected incorrect application 
of sampling methodology).   
13 
 5. Sample Size Determination  
To determine the number of samples to be taken, the NPPO shoul d select a confidence level (for 
example, 95%), a level of detection (for example, 5%) and an acceptance number (for example, 
zero), and determine the efficacy of detection (for example, 80%). From these values and the lot 
size, a sample size can be calcul ated. Appendixes 2 –5 set out the mathematical basis for sample 
size determination. Section 3.1.3 of this standard provides guidance on the most appropriate 
statistical based sampling method when considering the distribution of the pest in the lot.  
5.1. Pests d istribution unknown in the lot  
Because sampling is done without replacement and the population size is finite, the 
hypergeometric distribution should be used to determine the sample size. This distribution gives a 
probability of detecting a certain number  of infested units in a sample of a given size drawn from 
a lot of a given size, when a specific number of infested units exist in the lot (see Appendix 2). 
The number of infested units in the lot is estimated as the level of detection multiplied by the to tal 
number of units in the lot.  
As lot size increases, the sample size required for a specific level of detection and confidence level 
approaches an upper limit. When the sample size is less than 5% of the lot size, the sample size 
can be calculated using  either the binomial or Poisson distribution (see Appendix 3). All three 
distributions (hypergeometric, binomial and Poisson) give almost identical sample sizes for 
specific confidence and detection levels with large lot sizes, but binomial and Poisson dis tributions 
are easier to calculate.  
5.2. Pest distribution aggregated in the lot  
Most pest populations are aggregated to some degree in the field. Because commodities may be 
harvested and packed in the field without being graded or sorted, the distribution of  infested units 
in the lot may be clustered or aggregated. Aggregation of infested units of a commodity will always 
lower the likelihood of finding an infestation. However, phytosanitary inspections are aimed at 
detection of infested units and/or pest(s) a t a low level. The effect of aggregation of the infested 
units on the efficacy of detection of a sample and on the required sample size is small in most 
cases. When NPPOs identify that there is a high likelihood that there will be aggregation of 
infested u nits in the lot a stratified sampling method may help increase the chance of detecting an 
aggregated infestation.   
When pests are aggregated, the calculation of sample size should ideally be performed using a 
betabinomial distribution (see Appendix 4). However, this calculation requires knowledge of the 
degree of aggregation, which is generally not known and therefore this distribution may not be 
practical for general use. One of the other distributions (hypergeometric, binomial or Poisson) can 
be used; however, the confidence level of the sampling will decline as the degree of aggregation 
increases.   
14 
 6. Varying Level of D etection  
The choice of a constant level of detection may result in a varying number of infested units entering 
with imported consignments because lot size varies (for example, a 1% infestation level of 1000 
units corresponds to 10 infested units, while a 1% infesta tion level of 10,000 units corresponds to 
100 infested units). Ideally the selection of a level of detection will reflect in part the number of 
infested units entering on all consignments within a particular period of time. If NPPOs want to 
manage the numb er of infested units entering with each consignment as well, a varying level of 
detection may be used. A tolerance level would be specified in terms of a number of infested items 
per consignment, and the sample size would be set in order to give the desire d confidence and 
detection levels.  
7. Outcome of Sampling  
The outcome of activities and techniques related to sampling may result in phytosanitary action 
being taken (further details can be found in ISPM 23 in relation to inspection outcome).    
15 
  Methodologies for sampling of consignments                               Appendix 1  
This appendix is for reference purposes only and is not a prescriptive part of the standard.  
APPENDIX 1: Formulae used in Appendixes 2 –5 
 
Formula 
No.  Purpose  Appendix 
No.  
1  Probability of detecting i infested units in a sample.  2  
2  Approximation for calculating the probability of finding no infested units.  2  
3  Probability of detecting i infested units in a sample of n units (sample size is less than 5% of the 
lot size).  3  
4  Binomial distribution probability of not observing an infested unit in a sample of n units.  3  
5  Binomial distribution probability of observing at least one infested unit.  3  
6  Binomial distribution formulae 5 and 6 rearranged to determine n.  3  
7  Poisson distribution version of binomial formula 6  3  
8  Poisson distribution probability of finding no infested units (simplified).  3  
9  Poisson distribution probability of finding at least one infested unit (the confidence level).  3  
10  Poisson distribution to determine the sample size for n.  3  
11  Beta-binomial based sampling for aggregated spatial distribution   4  
12  Beta-binomial – probability of not observing an infested unit after inspecting several lots  
(for a single lot)  4  
13  Beta-binomial – probability of observing one or more infested units  4  
14  Beta-binomial formulae 12 and 13 rearranged to determine m.  4  
  
 
 
 
 
 
 
  
16 
 This appendix is for reference purposes only and is not a prescriptive part of the standard  
APPENDIX 2: Calculating sample sizes for small lots: hypergeometric -based sampling  
(simple random sampling)  
The hypergeometric distribution is appropriate to describe the probability of finding a pest in a relatively 
small lot. A lot is considered as small  when the sample size is more than 5% of the lot size. In this case, 
sampling of one unit from the lot affects the probability of finding an infested unit in the next unit selected. 
Hypergeometric -based sampling is based on sampling without replacement.  
It is also assumed that the distribution of the pest in the lot is not aggregated and that random sampling is 
used. This methodology can be extended for other schemes such as stratified sampling (further details can 
be found in Cochran, 1977).   
The probabi lity of detecting i infested units in a sample is given by  
 
 
 
 
Where:   
 
 
 where a!= a(a -1)(a-2)….. 1 and 0!=1  
P(X = i) is the probability of observing i infested units in the sample, where i = 0, …, n.   
The confidence level corresponds to: 1 - P(X = i)  
A = number of infested units in the lot that could be detected if every unit in the lot was inspected or tested, 
given the efficacy of detection (level of  detection × N × efficacy, truncated to an integer) i = number of 
infested units in the sample N = number of units in the lot (size of the lot) n = number of units in the sample 
(sample size)   
In particular the approximation that can be used for the proba bility of finding no infested units is  
 
 
 
where u = (n -1)/2 (from Cochran, 1977).  
Solving the equation to determine n is difficult arithmetically but can be done with approximation or 
through maximum likelihood estimation.   
Tables 1 and 2 show sample s izes calculated for different lot sizes, levels of detection and confidence levels, 
when the acceptance number is 0.  
= 
  
)! 
 ( 
! 
! 
b 
a 
b 
a 
 
 
17 
 Table 1:  Table of minimum sample sizes for 95% and 99% confidence levels at varying levels of detection according to lot size, 
hypergeometric distribution  
Number  
of units in 
lot  
25  P = 95% (confidence level)  
% level of detection × efficacy of detection  P = 99% (confidence level)  
% level of detection × efficacy of detection  
5  2  1  0.5  0.1  5  2  1  0.5  0.1  
24*  –  –  –  –  25*  –  –  –  –  
50  39*  48  –  –  –  45*  50  –  –  –  
100  45  78  95  –  –  59  90  99  –  –  
200  51  105  155  190  –  73  136  180  198  –  
300  54  117  189  285*  –  78  160  235  297*  –  
400  55  124  211  311  –  81  174  273  360  –  
500  56  129  225  388*  –  83  183  300  450*  –  
600  56  132  235  379  –  84  190  321  470  –  
700  57  134  243  442*  –  85  195  336  549*  –  
800  57  136  249  421  –  85  199  349  546  –  
900  57  137  254  474*  –  86  202  359  615*  –  
1 000  57  138  258  450  950  86  204  368  601  990  
2 000  58  143  277  517  1553  88  216  410  737  1800  
3 000  58  145  284  542  1895  89  220  425  792  2353  
4 000  58  146  288  556  2108  89  222  433  821  2735  
5 000  59  147  290  564  2253  89  223  438  840  3009  
6 000  59  147  291  569  2358  90  224  442  852  3214  
7 000  59  147  292  573  2437  90  225  444  861  3373  
8 000  59  147  293  576  2498  90  225  446  868  3500  
9 000  59  148  294  579  2548  90  226  447  874  3604  
10 000  59  148  294  581  2588  90  226  448  878  3689  
20 000  59  148  296  589  2781  90  227  453  898  4112  
30 000  59  148  297  592  2850  90  228  455  905  4268  
40 000  59  149  297  594  2885  90  228  456  909  4348  
50 000  59  149  298  595  2907  90  228  457  911  4398  
60 000  59  149  298  595  2921  90  228  457  912  4431  
70 000  59  149  298  596  2932  90  228  457  913  4455  
80 000  59  149  298  596  2939  90  228  457  914  4473  
90 000  59  149  298  596  2945  90  228  458  915  4488   
18 
 Number  
of units in 
lot  
25  P = 95% (confidence level)  
% level of detection × efficacy of detection  P = 99% (confidence level)  
% level of detection × efficacy of detection  
5  2  1  0.5  0.1  5  2  1  0.5  0.1  
24*  –  –  –  –  25*  –  –  –  –  
100 000  59  149  298  596  2950  90  228  458  915  4499  
200 000+  59  149  298  597  2972  90  228  458  917  4551  
Values in Table 1 marked with an asterisk (*) have been rounded down to a whole number because scenarios resulting in a fract ion 
of a unit being infested (for example, 300 units with 0.5% infestation corresponds to 1.5 infested units in the shipment) are  not 
possible. This means that the sampling intensity increases slightly, and may be greater for a shipment size where the number of 
infested units is rounded down than for a larger shipment where a larger number of infested units are calculated (for example , 
compare results for 700 and 800 units in the lot). It also means that a slightly lower proportion of infested units might be detected 
than the proportion indicated by the table, or that such infestation is more likely to be detected than the confidence l evel shown.   
Values in Table 1 marked with a dash ( –) refer to scenarios presented that are not possible (less than one unit infested).  
 
 
Table 2:  Table of sample sizes for 80% and 90% confidence levels at varying levels of detection according to lot siz e, 
hypergeometric distribution  
Number  
of units in 
lot  
 
100  P = 80% (confidence level)  
% level of detection × efficacy of detection  P = 90% (confidence level)  
% level of detection × efficacy of detection  
5  2  1  0.5  0.1  5  2  1  0.5  0.1  
27  56  80  –  –  37  69  90  –  –  
200  30  66  111  160  –  41  87  137  180  –  
300  30  70  125  240*  –  42  95  161  270*  –  
400  31  73  133  221  –  43  100  175  274  –  
500  31  74  138  277*  –  43  102  184  342*  –  
600  31  75  141  249  –  44  104  191  321  –  
700  31  76  144  291*  –  44  106  196  375*  –  
800  31  76  146  265  –  44  107  200  350  –  
900  31  77  147  298*  –  44  108  203  394*  –  
1 000  31  77  148  275  800  44  108  205  369  900  
2 000  32  79  154  297  1106  45  111  217  411  1368  
3 000  32  79  156  305  1246  45  112  221  426  1607  
4 000  32  79  157  309  1325  45  113  223  434  1750  
5 000  32  80  158  311  1376  45  113  224  439  1845  
6 000  32  80  159  313  1412  45  113  225  443  1912  
7 000  32  80  159  314  1438  45  114  226  445  1962  
8 000  32  80  159  315  1458  45  114  226  447  2000   
19 
 Number  
of units in 
lot  
 
100  P = 80% (confidence level)  
% level of detection × efficacy of detection  P = 90% (confidence level)  
% level of detection × efficacy of detection  
5  2  1  0.5  0.1  5  2  1  0.5  0.1  
27  56  80  –  –  37  69  90  –  –  
9 000  32  80  159  316  1474  45  114  227  448  2031  
10 000  32  80  159  316  1486  45  114  227  449  2056  
20 000  32  80  160  319  1546  45  114  228  455  2114  
30 000  32  80  160  320  1567  45  114  229  456  2216  
40 000  32  80  160  320  1577  45  114  229  457  2237  
50 000  32  80  160  321  1584  45  114  229  458  2250  
60 000  32  80  160  321  1588  45  114  229  458  2258  
70 000  32  80  160  321  1591  45  114  229  458  2265  
80 000  32  80  160  321  1593  45  114  229  459  2269  
90 000  32  80  160  321  1595  45  114  229  459  2273  
100 000  32  80  160  321  1596  45  114  229  459  2276  
200 000  32  80  160  321  1603  45  114  229  459  2289  
Values in Table 2 marked with an asterisk (*) have been rounded down to a whole number because scenarios resulting in a fract ion 
of a unit being infested (for example, 300 units with 0.5% infestation corresponds to 1.5 infested units in the shipment) are  not 
possible. This means that the sampling intensity increases slightly, and may be greater for a shipment size where the number of 
infested units is rounded down than for a larger shipment where a larger number of infested units are calculated (for example , 
compare results for 700 and 800 units in the lot). It also means that a slightly lower proportion of infested units might be detected 
than the proportion indicated by the table, or that such infestation is more likely to be detected than the confidence l evel shown.   
Values in Table 2 marked with a dash ( –) refer to scenarios presented that are not possible (less than one unit infested).  
  
   
20 
 This appendix is for reference purposes only and is not a prescriptive part of the standard.  
APPENDIX 3: Sampling  of large lots: binomial or Poisson based sampling  
For large lots sufficiently mixed, the likelihood of finding an infested unit is approximated by simple 
binomial statistics. The sample size is less than 5% of the lot size. The probability of observing i infested 
units in a sample of n units is given by:  
 
 
 
p is the average proportion of infested units (infestation level) in the lot and 
  represents the percentage 
inspection efficacy divided by 100.  
P(X = i) is the probability of observing i infested units in the sample. The confidence level corresponds to: 
1- P(X = i), i = 0, 1, 2, …, n.  
For phytosanitary purposes, the probability of no t observing a pest specimen or symptom in the sample is 
determined. The probability of not observing an infested unit in a sample of n units is given by  
   
The probability of observing at least one infested unit is then:  
   
This equation can be rearra nged to determine n   
 
 
The sample size n can be determined with this equation when the infestation level (p), efficacy (
  and 
the confidence level (1 - P (X > 0)) are determined by the NPPO.  
The binomial distribution can be approximated with the Poisson distribution. As n increases and p 
decreases, the binomial distribution equation given above tends to the Poisson distributi on equation  
given below,   
 
 
 
where e is the base -value of the natural logarithm.  
The probability of finding no infested units simplifies to  
  
 
The probability of finding at least one infested unit (the confidence level) is calculated as  
  
 
21 
 Solving for n gives the following, which can be used to determine the sample size:  
  
Tables 3 and 4 show sample sizes when the acceptance number is 0, calculated for different levels of 
detection, efficacy and confidence levels with the binomial and Pois son distributions, respectively. A 
comparison of the case for 100% efficacy with the sample sizes in Table 1 (see Appendix 2) shows that the 
binomial and Poisson give very similar results to the hypergeometric distribution when n is large and p is 
small.  
Appendix 3  
Table 3:  Table of sample sizes for 95% and 99% confidence levels at varying levels of detection, according to efficacy values 
where lot size is large and sufficiently mixed, binomial distribution  
%  
efficacy   P = 95% (confidence level)  
% level of detection    P = 99% (confidence level)  
% level of detection   
5  2  1  0.5  0.1  5  2  1  0.5  0.1  
100  59  149  299  598  2995  90  228  459  919  4603  
99  60  150  302  604  3025  91  231  463  929  4650  
95  62  157  314  630  3152  95  241  483  968  4846  
90  66  165  332  665  3328  101  254  510  1022  5115  
85  69  175  351  704  3523  107  269  540  1082  5416  
80  74  186  373  748  3744  113  286  574  1149  5755  
75  79  199  398  798  3993  121  305  612  1226  6138  
50  119  299  598  1197  5990  182  459  919  1840  9209  
25  239  598  1197  2396  11982  367  919  1840  3682  18419  
10  598  1497  2995  5990  29956  919  2301  4603  9209  46050  
 
Table 4:  Table of sample sizes for 95% and 99% confidence levels at varying levels of detection, according to efficacy values 
where lot size is large and sufficiently mixed, Poisson distribution  
%  
efficacy   P = 95% (confidence level)  
% level of detection    P = 99% (confidence level)  
% level of detection   
5  2  1  0.5  0.1  5  2  1  0.5  0.1  
100  60  150  300  600  2996  93  231  461  922  4606  
99  61  152  303  606  3026  94  233  466  931  4652  
95  64  158  316  631  3154  97  243  485  970  4848  
90  67  167  333  666  3329  103  256  512  1024  5117  
85  71  177  353  705  3525  109  271  542  1084  5418  
80  75  188  375  749  3745  116  288  576  1152  5757  
75  80  200  400  799  3995  123  308  615  1229  6141  
 
22 
 %  
efficacy   P = 95% (confidence level)  
% level of detection    P = 99% (confidence level)  
% level of detection   
5  2  1  0.5  0.1  5  2  1  0.5  0.1  
50  120  300  600  1199  5992  185  461  922  1843  9211  
25  240  600  1199  2397  11983  369  922  1843  3685  18421  
10  600  1498  2996  5992  29958  922  2303  4606  9211  46052  
  
 Methodologies for sampling of consignments  Appendix 
4 
This appendix is for reference purposes only and is not a prescriptive part of the standard.  
   
23 
 APPENDIX 4: Sampling for pests with an aggregated distribution: beta -binomial based 
sampling  
In the case of aggregated spatial distribution, sampling can be adjusted to compensate for aggregation. For 
this adjustment to apply, it should be assumed that the commodity is sampled in clusters (for example, 
boxes) and that each unit in a chosen cluster  is examined (cluster sampling). In such cases, the proportion 
of infested units, f, is no longer constant across all clusters but will follow a beta density function.   
 
 
 
  
 
f is the average proportion of infested units (infestation level) in the lot.  
P(X = i) is the probability of observing i infested units in a lot.  n = 
number of units in a lot.  
 is the product function.  
 provides a measure of aggregation for the jth lot where 
  is 0<
 <1.  
Phytosanitary sampling is often more concerned with the probability of not observing an infested unit after  
 
 
 
inspecting several batches. For a single batch, the probability that X>0 is  
and the probability that each of several lots  has no infested unit equals P(X=0)m, where m is the number of 
lots. When f is low, equation 1 can be estimated by   
  
 
The probability of observing one or more infested units is given by 1 - Pr (X=0).  
This equation can be rearranged to determine m   
 
 
Stratified sampling 
offers a way of 
reducing the impact of aggregation. Strata should be chosen so that the degree of aggr egation within the 
strata is minimized.  
When the degree of aggregation and the confidence level are fixed, the size of the sample can be determined. 
Without the degree of aggregation, the sample size cannot be determined.  
Efficacy (
  values of less than 100% can be included by substituting 
 f for f in the equations.  
Appendix 5  
This appendix is for reference purposes only and is not a prescriptive part of the standard.  
 
24 
 APPENDIX 5: Comparison of hypergeometric and fixed proportion sampling results  
Table 5:  Confidence in the results of different sampling schemes for a 10% level of detection  
  Hypergeometric -based sampling (random 
sampling)  Fixed proportion sampling (2%)  
Lot size  sample size  confidence level  sample size  confidence level  
10  10  1  1  0.100  
50  22  0.954  1  0.100  
100  25  0.952  2  0.191  
200  27  0.953  4  0.346  
300  28  0.955  6  0.472  
400  28  0.953  8  0.573  
500  28  0.952  10  0.655  
1 000  28  0.950  20  0.881  
1 500  29  0.954  30  0.959  
3 000  29  0.954  60  0.998  
 
 
Table 6:  Minimum levels that can be detected with 95% confidence using different sampling schemes  
  Hypergeometric -based sampling (random 
sampling)  Fixed proportion sampling (2%)  
Lot size  sample size  minimum level of 
detection  sample size  minimum level of 
detection  
10  10  0.10  1  1.00  
50  22  0.10  1  0.96  
100  25  0.10  2  0.78  
200  27  0.10  4  0.53  
300  28  0.10  6  0.39  
400  28  0.10  8  0.31  
500  28  0.10  10  0.26  
1 000  28  0.10  20  0.14  
1 500  29  0.10  30  0.09  
3 000  29  0.10  60  0.05  
  
   
25 
  
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