ISO 14461-1:2005

Milk and milk products - Quality control in microbiological laboratories - Part 1: Analyst performance assessment for colony counts

ISO 14461-1|IDF 169-1:2005 describes a procedure for testing the performance of the colony-count technique within a laboratory by establishing the within-laboratory variability of its technique and identifying those steps that are associated with excessive variability. The procedure is also suitable for checking the proper observance of Good Laboratory Practice (GLP), which may be a prerequisite for participation in interlaboratory tests of colony-count methods.

Lait et produits laitiers — Contrôle de qualité en laboratoires microbiologiques — Partie 1: Évaluation de la performance des analystes effectuant les comptages de colonies

General Information

• Status: Published
• Publication Date: 19-May-2005
• ICS: 07.100.30 - Food microbiology
• Technical Committee: ISO/TC 34/SC 5 - Milk and milk products
• Drafting Committee: ISO/TC 34/SC 5 - Milk and milk products
• Current Stage: 9093 - International Standard confirmed
• Start Date: 17-Jun-2025
• Completion Date: 30-Oct-2025

Overview

ISO 14461-1:2005 (IDF 169-1:2005) sets out a standardized procedure for assessing analyst performance in performing colony counts on milk and milk products. The standard helps laboratories quantify within‑laboratory variability of the plate‑count (colony‑count) technique, identify steps that contribute to excessive variability, and verify adherence to Good Laboratory Practice (GLP)-useful before participating in interlaboratory comparisons or proficiency tests.

Key topics and requirements

• Principle: Homogenize a test sample and prepare a working suspension (e.g., 500–10 000 CFU/ml).
• Dilution design: From the working suspension prepare four dilution series, each with 12 binary (two‑fold) dilution steps (binary dilutions are used to increase the number of countable plates).
• Plating: Pour three parallel plates from each dilution level.
• Incubation, randomization and counting: Incubate plates, randomize plate sequence, then count colonies on each plate.
• Statistical evaluation: Test for statistical homogeneity of counts; if heterogeneity is found, perform ANOVA to identify contributing factors (dilution series, dilution levels, plating). Annexes provide guidance on weighted means, homogeneity testing and example BASIC code for likelihood ratio index calculations.
• Materials and reagents: Specifies culture medium (tryptone‑glucose‑yeast extract agar with added skimmed milk powder), diluents (peptone/salt solution or quarter‑strength Ringer’s) and GLP‑level apparatus/dispensing practices.
• Sample types: Applicable to raw milk, pasteurized milk and dried milk (examples noted in the standard).

Practical applications

• Internal quality control for dairy microbiology labs to monitor and improve plate‑count consistency.
• Verification of analyst technique and laboratory procedures prior to joining interlaboratory studies or accreditation assessments.
• Troubleshooting: isolates whether variability arises from sampling/homogenization, dilution accuracy, plating technique or colony counting.
• Training and competency assessment for laboratory analysts performing colony counts.

Who should use this standard

• Microbiologists and laboratory managers in dairy and food testing labs
• Quality assurance teams and accreditation bodies assessing GLP compliance
• Proficiency testing organizers and method validation teams

Related standards

• ISO 14461-2: Determination of reliability of colony counts (parallel plates and dilution steps)
• ISO 7218, ISO 8261 and glassware standards referenced for general microbiological procedures and equipment

Keywords: ISO 14461-1, colony counts, milk and milk products, microbiological laboratories, analyst performance assessment, plate count, binary dilution, within‑laboratory variability, GLP.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 14461-1
IDF
169-1
First edition
2005-05-01
Milk and milk products — Quality control
in microbiological laboratories —
Part 1:
Analyst performance assessment for
colony counts
Lait et produits laitiers — Contrôle de qualité en laboratoires
microbiologiques —
Partie 1: Évaluation de la performance des analystes effectuant les
comptages de colonies
Reference numbers
IDF 169-1:2005(E)
©
ISO and IDF 2005
IDF 169-1:2005(E)
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ii © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
Contents Page
Foreword. iv
Introduction . vi
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 1
4 Principle (see Figure 1). 2
5 Diluent, culture media and reagents . 3
6 Apparatus and glassware. 5
7 Sampling . 5
8 Preparation of test sample. 6
8.1 Milk . 6
8.2 Dried milk. 6
9 Procedure. 6
9.1 General. 6
9.2 Number of decimal dilution steps . 6
9.3 Preparation of first decimal dilution . 6
9.4 Preparation of further decimal dilutions. 7
9.5 Melting the medium . 7
9.6 Preparation of binary dilutions and inoculation of the medium . 7
9.7 Incubation . 7
9.8 Randomization and counting of colonies. 8
10 Statistical evaluation . 10
10.1 Adequacy of the data set. 10
10.2 Evaluation of the complete data set (see Figure 2) . 10
Annex A (informative) Weighted mean and homogeneity testing of colony counts. 27
Annex B (Informative) BASIC programme for calculating the likelihood ratio index G . 33
Bibliography . 34

IDF 169-1:2005(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee has
been established has the right to be represented on that committee. International organizations, governmental
and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 14461-1IDF 169-1 was prepared by Technical Committee ISO/TC 34, Food products, Subcommittee
SC 5, Milk and milk products, and the International Dairy Federation (IDF), in collaboration with AOAC
International. It is being published jointly by ISO and IDF and separately by AOAC International.
ISO 14461IDF 169 consists of the following parts, under the general title Milk and milk products — Quality
control in microbiological laboratories:
 Part 1: Analyst performance assessment for colony counts
 Part 2: Determination of the reliability of colony counts of parallel plates and subsequent dilution steps
iv © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
Foreword
IDF (the International Dairy Federation) is a worldwide federation of the dairy sector with a National
Committee in every member country. Every National Committee has the right to be represented on the IDF
Standing Committees carrying out the technical work. IDF collaborates with ISO and AOAC International in
the development of standard methods of analysis and sampling for milk and milk products.
Draft International Standards adopted by the Action Teams and Standing Committees are circulated to the
National Committees for voting. Publication as an International Standard requires approval by at least 50 % of
the National Committees casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. IDF shall not be held responsible for identifying any or all such patent rights.
This part of International Standard ISO 14461-1IDF 169 was prepared by Technical Committee ISO/TC 34,
Food products, Subcommittee SC 5, Milk and milk products, and the International Dairy Federation (IDF), in
collaboration with AOAC International. It is being published jointly by ISO and IDF and separately by AOAC
International.
All work was carried out by the Joint ISO/IDF/AOAC Action Team, Statistics of analytical data, of the Standing
Committee on Quality assurance, statistics of analytical data and sampling, under the aegis of its project
leaders, Dr. H. Glaeser (EU) and Prof. Dr. H. Weiss (DE).
This edition of ISO 14461-1IDF 169-1, together with ISO 14461-2IDF 169-2, cancels and replaces
IDF 169:1994, which has been technically revised.
ISO 14461IDF 169 consists of the following parts, under the general title Milk and milk products — Quality
control in microbiological laboratories:
 Part 1: Analyst performance assessment for colony counts
 Part 2: Determination of the reliability of colony counts of parallel plates and subsequent dilution steps
IDF 169-1:2005(E)
Introduction
Every microbiological method consists of several steps that are followed in a specific sequence (sub-sampling,
diluting, plating and counting). The final result has a margin of uncertainty that is determined by the variability
of all the steps involved.
In order to obtain results with a margin of uncertainty not much larger than what can be expected from the
correct application of the method, it is necessary to follow the rules of Good Laboratory Practice (GLP).
The three most important factors in obtaining a correct plate count are
 the homogeneity of the sample material,
 the exactness with which the dilutions are performed, and
 the technique of inoculation and/or counting of the plates.
By homogenizing a sample material very well, making multiple dilution series, and inoculating several plates
from the same dilution, it is possible to assess how well a laboratory can perform the colony-count technique,
taking into account the expected variability of the method.
A too large variability indicates that at least one of the steps in the performance of the method is out of control.
The identification of those steps is done by comparison of the replicate inoculations, the different dilution
levels and the dilution series. When the steps with excessive variability have been identified, the necessary
measures should be taken to bring these steps under control.

vi © ISO and IDF 2005 – All rights reserved

INTERNATIONAL STANDARD
IDF 169-1:2005(E)
Milk and milk products — Quality control in microbiological
laboratories —
Part 1:
Analyst performance assessment for colony counts
1 Scope
This part of ISO 14461IDF 169 describes a procedure for testing the performance of the colony-count
technique within a laboratory by establishing the within-laboratory variability of its technique and identifying
those steps that are associated with excessive variability.
The procedure is also suitable for checking the proper observance of Good Laboratory Practice (GLP), which
may be a prerequisite for participation in interlaboratory tests of colony-count methods.
EXAMPLE Appropriate test samples are raw milk, pasteurized milk and dried milk.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 648:1977, Laboratory glassware — One-mark pipettes
ISO 835-4, Laboratory glassware — Graduated pipettes — Part 4: Blow-out pipettes
ISO 4788, Laboratory glassware — Graduated measuring cylinders
ISO 7218, Microbiology of food and animal feedings stuffs — General rules for microbiological examinations
ISO 8261IDF 122, Milk and milk products — Preparation of samples and dilutions for microbiological
examination
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
colony-count technique
counting of the number of microorganisms as determined by the procedure specified in this part of
ISO 14461IDF 169
NOTE The number of microorganisms is expressed per gram or per millilitre of test sample.
IDF 169-1:2005(E)
4 Principle (see Figure 1)
Figure 1 — Quality assurance in the microbiological laboratory:
Design of pilot studies for plate count
4.1 A test sample is homogenized then diluted to a suitable working density. (e.g. 500 CFU to 10 000 CFU
per millilitre). A suspension is prepared.
4.2 From this first dilution, four dilution series are prepared, each consisting of 12 binary dilution steps.
NOTE Binary (two-fold) dilution steps are used, not decimal (10-fold) dilutions as is the usual practice. With binary
dilutions it is possible to count colonies on plates originating from five to six dilutions, and this large number of counts
improves considerably the testing of the dilution steps.
2 © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
4.3 Three parallel plates are poured from each dilution of each series.
4.4 The plates are incubated.
4.5 The sequence of the plates is randomized and the colonies on each plate are counted.
4.6 The counts are tabulated and the “statistical homogeneity” of the counts in two steps is calculated.
4.7 If the values obtained are statistically homogeneous, then the quality of the application of the method is
satisfactory and no further evaluation is needed.
4.8 If the results are not statistically homogeneous, an analysis of variance (ANOVA) is performed in order
to identify the variation of the results with one or more of the factors that were varied (i.e. dilution series,
dilution levels, plating). Further investigations are carried out and the factor(s) identified are adjusted.
NOTE Users will designate the particularly important sources of error in the performance of the method.
5 Diluent, culture media and reagents
The operations described in detail in this clause and in Clause 9 shall either be carried out by one person
alone or be divided over a group with clearly defined tasks for each participant.
Use only reagents of recognized analytical grade and distilled water or water of at least equivalent purity,
unless otherwise specified. The reagents and the water shall be free from substances that may adversely
influence the growth of microorganisms under the test conditions. The culture medium shall be of recognized
bacteriological quality. Any dehydrated medium shall be prepared according to the manufacturer's instructions.
5.1 Sodium hydroxide solution or hydrochloric acid (approx. 0,1 mol/l), to adjust the pH of the diluent and
the culture medium.
5.2 Culture medium: Tryptone-glucose-yeast extract agar, with addition of skimmed milk powder.
5.2.1 Composition
Yeast extract 2,5 g
Tryptic digest of casein (tryptone) 5,0 g
Glucose monohydrate (C H O ⋅HO) 1,0 g
6 12 6 2
Skimmed milk powder 1,0 g
a
Agar 10 g to 15 g
Water 1 000 ml
a
Depending on the gel strength of the agar.
In all cases it is necessary to add the skimmed milk powder, even if the dehydrated complete medium is
purchased and even if the suppliers consider such an addition unnecessary.
5.2.2 Preparation
For the experiment 2 litres of medium of the same lot will be needed. If a commercial dehydrated complete
medium is used, follow the manufacturer's instructions but add the skimmed milk powder. Adjust the pH so
that after sterilization it is 7,0 ± 0,2 at about 45 °C.
IDF 169-1:2005(E)
If the medium is prepared from dehydrated basic components, then dissolve and disperse in preheated water,
in the following order: yeast extract, tryptone, glucose and, finally, the skimmed milk powder. Heating the
water will assist in the dissolving and dispersion procedure. Add the agar and heat to boiling, while stirring
frequently, until the agar is completely dissolved. Alternatively, steam the mixture for about 30 min. Filter the
medium through filter paper, if necessary. Adjust the pH so that after sterilization it is 7,0 ± 0,2 at about 45 °C.
Dispense the culture medium in amounts of 250 ml into bottles (6.10). Sterilize all the bottles at one time in the
autoclave (6.1) set at 121 °C for 15 min.
Store the prepared medium in the dark at a temperature between 0 °C and 5 °C for no longer than 1 month.
5.3 Diluents: Peptone/salt solution or quarter-strength Ringer's solution, from a single lot.
5.3.1 Peptone/salt solution
This is the diluent selected for general use.
5.3.1.1 Composition
Peptone 1,0 g
Sodium chloride (NaCl) 8,5 g
Water up to 1 000 ml
5.3.1.2 Preparation
Dissolve the components in the water, by heating if necessary. Adjust the pH so that after sterilization it is
7,0 ± 0,2 at 25 °C.
5.3.2 Quarter-strength Ringer's solution
5.3.2.1 Composition
Sodium chloride (NaCl) 2,25 g
Potassium chloride (KCl) 0,105 g
Calcium chloride, anhydrous (CaCl) 0,06 g
Sodium hydrogen carbonate (NaHCO) 0,05 g
Water up to 1 000 ml
5.3.2.2 Preparation
Dissolve the salts in the water. Adjust the pH so that after sterilization it is 6,9 ± 0,2 at 25 °C.
5.3.3 Preparation of the diluent
Sterilize the diluent by autoclaving, in quantities not greater than 500 ml. Then dispense portions of 90 ml at
room temperature into sterile dilution bottles (6.8) using sterile graduated measuring cylinders or other
dispensing devices (6.11), and portions of 5 ml into sterile test tubes (6.9) using 5 ml one-mark or graduated
pipettes or other dispensing devices (6.12). When emptying a pipette touch the tip against an inclined wall of
the container in order to ensure correct delivery.
4 © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
NOTE Dispensing the portions before autoclaving can lead to unequal evaporation during sterilization, resulting in
differences in the final strength of the portions.
Cool and store both the bulk and the dispensed portions of the diluent at a temperature between 0 °C and
5 °C. Use both the bulk and the dispensed portions the next day at the latest.
6 Apparatus and glassware
Sterilize all apparatus that will come into contact with the test sample, the diluent, the dilutions or the culture
medium in accordance with ISO 7218 and ISO 8261IDF 122.
Usual microbiological laboratory equipment and, in particular, the following.
6.1 Autoclave, capable of operating at 121 °C ± 3 °C.
6.2 Hot-air oven, capable of operating at above 180 °C.
6.3 Incubator, capable of operating at 30 °C ± 1 °C at all points within it.
6.4 pH-meter, with temperature compensation, accurate to ± 0,1 pH units.
6.5 Water baths, capable of operating at 20 °C ± 1 °C, 45 °C ± 1 °C and between 44 °C and 47 °C.
6.6 Lenses, of magnification 2× to 4× and of at least 8×.
6.7 Glass beads, of diameter about 6 mm.
6.8 Dilution bottles, of nominal volume 150 ml to 250 ml, with watertight stoppers, containing 5 to 10 glass
beads (6.7). Add the beads before sterilizing the bottles.
6.9 Test tubes, of height about 150 mm and diameter about 15 mm, with stoppers.
6.10 Bottles, of nominal volume 500 ml, with stoppers, for storing 250 ml portions of culture medium.
6.11 Graduated measuring cylinders, with main-point graduations, complying with ISO 4788, or other
dispensing devices with a proven equivalent level of accuracy.
6.12 One-mark or graduated pipettes, calibrated, capable of delivering 1 ml, 5 ml and 10 ml, complying
with ISO 648:1977, class A, or ISO 835-4, or other dispensing devices with a proven equivalent level of
accuracy.
6.13 Petri dishes, made of clear uncoloured glass or plastic material, the bottom having an internal diameter
of about 90 mm and no irregularities interfering with colony counting.
6.14 Mechanical stirrer, capable of mixing the contents of the test tubes, working on the principle of
eccentric rotation (e.g. a vortex mixer).
6.15 Top-loading balance, of sufficient weighing capacity, capable of weighing to the nearest 0,05 g.
7 Sampling
A representative sample should have been sent to the laboratory. It should not have been damaged or
changed during transport or storage.
IDF 169-1:2005(E)
Sampling is not part of the method specified in this part of ISO 14461IDF 169. A recommended sampling
method is given in ISO 707.
8 Preparation of test sample
8.1 Milk
Agitate the test sample thoroughly by rapidly inverting the sample container 25 times, so that the
microorganisms are distributed as evenly as possible. Avoid foaming or allow any foam to disperse. The
interval between mixing and removing the test portion shall not exceed 3 min.
8.2 Dried milk
Thoroughly mix the contents of the closed container by repeatedly shaking and inverting it. If the test sample
is in the original unopened container and this is too full to permit thorough mixing, transfer it to a larger
container, then mix.
9 Procedure
9.1 General
In colony-count methods plates are often partially or completely uncountable due to various reasons
(spreading, mould growth, etc.). For the present method, only a limited number of missing values may be
tolerated (see 10.1). Too many missing values indicate either that the material used is not suitable for the test,
or that the technique is faulty. In such a case, repeat the procedure with another, more suitable sample
material or with stricter adherence to the instructions.
9.2 Number of decimal dilution steps
The expected microbiological density of the sample determines the number of decimal dilution steps, as
follows:
a) when the expected count is less than 100 000 per millilitre or per gram, make a decimal dilution to
0,1 (one decimal step);
b) when the expected count is between 100 000 and 1 000 000 per millilitre or per gram, make a serial

–2
dilution to 10 (two decimal steps);

–3
c) when the expected count is higher than 1 000 000 per millilitre or per gram, make a serial dilution to 10
(three decimal steps).
9.3 Preparation of first decimal dilution
9.3.1 Milk
Remove 1 ml of test sample (8.1) with a sterile pipette (6.12) and add to 9 ml of diluent (5.3) (or 10 ml of test
sample to 90 ml of diluent, or 11 ml of test sample to 99 ml of diluent). Shake this primary dilution
[e.g. 25 times with a movement of about 300 mm for 7 s manually or, using a mechanical stirrer (6.14), for
–1
5 s to 10 s] to obtain a 10 dilution.
6 © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
9.3.2 Dried milk
9.3.2.1 Open the container (8.2), remove the amount of test portion required with a spatula and proceed
as indicated in 9.3.2.2. Immediately close the container again.
9.3.2.2 Weigh 10 g of test sample into a suitable glass vessel (e.g. a beaker) and then add the powder to
the dilution bottle containing a suitable diluent (5.3). Alternatively, weigh 10 g of test sample directly into the
bottle with the diluent. To dissolve the test sample, swirl slowly to wet the powder then shake the bottle
(e.g. 25 times with a movement of about 300 mm, for about 7 s). A peristaltic-type blender may be used as an
alternative to shaking. Allow to stand for 5 min, shaking occasionally.
9.4 Preparation of further decimal dilutions
Prepare further dilutions in accordance with ISO 8261IDF 122.
9.5 Melting the medium
Before starting the operations described in 9.6, melt the culture medium (5.2) and cool it in the water bath
(6.5) set at between 44 °C and 47°C. Check the temperature of the medium by placing a thermometer into a
250 ml portion of agar (e.g. water agar) in a separate container, which is identical to that used for the medium.
Pour the molten agar within 2 h after melting.
9.6 Preparation of binary dilutions and inoculation of the medium
9.6.1 First dilution series (S )
Take 12 dilution test tubes (6.9) with 5 ml of diluent from cold storage (5.3.3).
Make serial binary dilutions (D , D , …) by transferring with a fresh pipette 5 ml of the suspension from the
1 2
previous dilution (9.4) into a tube with 5 ml of diluent. Mix the suspension 5 times during 5 s with the stirrer
(6.14) before each transfer. The first inoculum is taken from the last decimal dilution bottle (9.4), which is
immediately placed back in the refrigerator.
Before starting the next binary dilution series, inoculate three Petri dishes (P , P and P ) from each of the
1 2 3
twelve dilutions using 1 ml one-mark or graduated pipettes (6.12). Use a fresh sterile pipette for each dilution
level.
After inoculating all plates of the series (S ), pour 12 ml to 15 ml of molten and tempered (44 °C to 47°C)
culture medium (9.5) into each Petri dish in the same working order as the inoculation. Mix the medium
carefully with the inoculum by rotating the Petri dishes sufficiently to obtain evenly dispersed colonies after
incubation. Allow the mixture to solidify by leaving the Petri dishes to stand on a cool horizontal surface.
9.6.2 Subsequent dilutions (S , S and S )
2 3 4
After completion of the first series of dilutions and plating, prepare the second, third and fourth dilution series
(S , S and S ) similarly, starting each time with the mixing of the contents of the last decimal dilution bottle
2 3 4
(9.4) stored in the refrigerator in the meantime. Use two or three 250 ml portions of molten culture medium for
plating each dilution series and discard the rest.
9.7 Incubation
Invert the prepared dishes and place them in the incubator (6.3) set at 30 °C for 72 h ± 2 h. Do not stack the
dishes more than three high. Mark the position of each dish in a stack (low – middle – high).
NOTE This information may be useful if it turns out that the variability between the plates is too large and a possible
stacking effect is to be investigated.
Separate stacks of dishes from one another and from the walls and top of the incubator. Do not leave trays in
the incubator.
IDF 169-1:2005(E)
9.8 Randomization and counting of colonies
9.8.1 Randomization
Do not count the plates in order of the dilutions or grouped according to the dilution step, as this may result in
an underestimation of the variability because the person who performs the counting will have an idea of what
to expect. Therefore, the plates shall first be examined and randomized as described in this subclause by a
person not involved in the counting in 9.8.2.
Starting from the most diluted series, select “countable” dilutions, i.e. dilutions for which the expected average
count is between 5 and 300 colonies per plate.
Recode all plates of the countable dilutions, using random numbers in order to randomize the countable plates
over all series and dilutions. See Table 1 for one such set of numbers; other random sequences from 1 to
144 may also be used. Remove the original markings of the plates; the use of removable adhesive labels is
recommended. Designate the uncountable plates with a minus sign in the protocol (see Table 2).
Table 1 —Example of random recoding of the plates for use with Table 2
Dilution series
Dilution steps Plate S S S S
1 2 3 4
1 129 2 82 96
–1
2 2 29 21 105 46
3 143 80 6 35
1 140 130 124 122
–2
2 2 100 65 135 45
3 93 88 107 87
1 127 117 115 106
–3
2 2 108 138 18 20
3 89 10 63 75
1 50 123 49 61
–4
2 2 17 97 72 99
3 32 104 26 128
1 52 13 64 5
–5
2 2 22 14 40 34
3 134 25 37 70
1 69 113 11 1
–6
2 2 136 109 48 78
3 95 31 19 28
1 4 74 59 57
–7
2 2 79 67 39 71
3 73 51 141 23
1 92 12 55 62
–8
2 2 30 66 133 81
3 27 131 91 121
1 101 144 15 58
–9
2 2 36 98 116 24
3 16 83 56 47
1 68 94 120 142
–10
2 2 43 38 119 132
3 90 41 85 33
1 125 139 137 111
–11
2 2 114 126 53 8
3 54 9 76 86
1 102 42 3 103
–12
2 2 77 44 110 7
3 84 112 118 60
8 © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
9.8.2 Counting of colonies
Examine the plates under subdued light. To facilitate counting, a suitable lens (6.6) and/or a tally counter may
be used. Take care to avoid mistaking particles of undissolved sample or precipitated matter in dishes for
pinpoint colonies. Examine doubtful objects carefully, using a lens of higher magnification (6.6) where required,
to distinguish colonies from foreign matter.
Enter the colony counts as given in Table 2.
Deviations from normal appearance that might influence the evaluation, such as overgrown or partially
overgrown plates, should be indicated in the table (Figure 2).
Coding and counting shall take place on the day the incubation is completed.
Table 2 — Example of a note sheet for colony counts, for use during the counting of the plates
recoded according to Table 1 in numerical order
Plate Count Plate Count Plate Count Plate Count
1 37 73 109
2 38 74 110
3 39 75 111
4 40 76 112
5 41 77 113
6 42 78 114
7 43 79 115
8 44 80 116
9 45 81 117
10 46 82 118
11 47 83 119
12 48 84 120
13 49 85 121
14 50 86 122
15 51 87 123
16 52 88 124
17 53 89 125
18 54 90 126
19 55 91 127
20 56 92 128
21 57 93 129
22 58 94 130
23 59 95 131
24 60 96 132
25 61 97 133
26 62 98 134
27 63 99 135
28 64 100 136
29 65 101 137
30 66 102 138
31 67 103 139
32 68 104 140
33 69 105 141
34 70 106 142
35 71 107 143
36 72 108 144
NOTE Plates not counted or uncountable are noted as “—”, plates without colonies are noted as “O”.
IDF 169-1:2005(E)
10 Statistical evaluation
10.1 Adequacy of the data set
NOTE In the tables and formulae, the symbols i, j and k are indices denoting the dilution series S, dilutions D and
plates P, respectively.
When all three parallel plates of any suspension are uncountable, then discard the counts for that dilution in
the other three dilution series.
The experiment can be evaluated statistically if at least five successive binary dilution levels are available.
Altogether about 5 % of missing counts [i.e. 3 plates out of 60 (5 dilution levels), or 4 plates out of
72 (6 dilution levels)] can be tolerated, except when they include a whole set of three parallel plates. In this
case all the plates of the corresponding dilution shall be discarded.
Additionally, the expected average counts of the five or six acceptable dilution levels shall lie within the range
from 5 to 300 colonies per plate.
If these conditions are not met, then the data set is considered incomplete. Repeat the procedure, choosing a
more suitable sample material (if there are too many uncountable plates) or following more closely the
instructions given, or both.
10.2 Evaluation of the complete data set (see Figure 2)
10.2.1 Tabulation of the counts
Each count belongs to a specific dilution series S (S , S , S or S ), to a specific dilution D (D , D ,….D ,
i 1 2 3 4 j 1 2 6
where D is the lowest dilution for which countable plates were obtained), and to a specific plate P (P , P or
1 k 1 2
P ). For a better overview of the results, reorganize the counts of Table 2 according to dilution series S , to
3 i
dilution D and to plate P as shown in Table 3.
j k
Table 3 — Tabulation of the counts
P
k
S D
i j
P P P
1 2 3
D C C C
1 111 112 113
D C C C
2 121 122 123
S
D C
… …
j 1j1
… … … …
D C
… …
1 211
S D
… … …
2 2
D
… … …
j
… … … …
S D C
… …
i j ij2
… … … … …
NOTE The entry C is the count from the third plate of the first series for the second dilution.
10 © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
10.2.2 Testing the homogeneity of the plating: G -test
P
The first step in the statistical evaluation of the counts (see Figure 2) consists of the determination of the
magnitude of the statistical homogeneity of the replicate plates. This test is performed to detect results that
are “too good”; i.e. to detect the case in which the variability of the counts between parallel plates P , P and
1 2
P is smaller than expected (“under-dispersion”). This can, for example, be caused by insufficient
randomization of the plates before counting.
This statistical homogeneity is a single number that is obtained as follows (see Annex A for more information
on the G test and also the example in Table 6).
P
a) Determine for each group of three parallel plates the mean value C . (e.g. C = (C + C + C )/3,
ij 12 121 122 123
the mean of the results of one row in the table).
b) Calculate for each plate with count C the value C ⋅In (C /C ), with C the mean for that set of parallel
ijk, ijk ijk ij ij
plates.
c) Sum the three values in each row (the parallel plates) and multiply by two to obtain the individual G
values for each set of parallels. Write these in the table. Sum those values over all the dilutions and
series to obtain the test value:
p
sd
C
ijk

GC=2ln

P ∑∑∑ ijk

C
ij
ij k

where s is the number of the dilution series, d is the number of dilution steps, and p is the number of
plates.
NOTE An alternative form is given in Annex A, Equations (A.6) and (A.7).
d) Compare the value of G with the tabulated values of χ (chi-squared) in Table 4 for 40 degrees of
P
freedom (df = 40) in the case of 5 dilutions, and 48 degrees of freedom (df = 48) in the case of 6 dilutions.
If some results are missing (see 10.1), subtract the number of missing results from the df before
comparing with the values in Table 4.
If the value of G is less than the tabulated 0,995 probability value, then the counts of the parallel plates
P
show less variation then could be expected: the values are statistically too homogeneous. The analyst shall
confirm this by randomly recoding the plates and recounting them. In the case of confirmation, the experiment
shall be repeated with stricter adherence to the procedure.
If the value of G is greater than the tabulated probability value (P) of 0,995 %, then the variability between
P
the parallel plates is not too low. Proceed with the next test in 10.2.3.
If the value of G is considerably greater than the tabulated 0,01 probability value, the parallel plates show
P
larger variation than is to be expected. This observation should be kept in mind for possible future use in the
interpretation of great overall variation in later stages of the evaluation.
Table 4 — Values for χ (P = 0,01 and P = 0,995)
2 2 2 2
df χ χ df χ χ
0,01 0,995 0,01 0,995
37 59,89 18,59 44 68,71 23,58
38 61,16 19,29 45 69,96 24,31
39 62,43 20,00 46 71,20 25,05
40 63,69 20,71 47 72,44 25,78
48 73,68 26,51
IDF 169-1:2005(E)
Figure 2 — Flow diagram of the statistical analysis of a laboratory performance
study of the plate count
12 © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
10.2.3 Testing the overall homogeneity of the counts
10.2.3.1 The G -test
A
The second step (see Figure 2) consists of the determination of the magnitude of the statistical homogeneity
of the whole data set. In this test, the counts are compared with their expected values, taking into account the
effects of the dilutions.
This overall statistical homogeneity is a single number that is obtained as follows (see also Example).
a) Determine the total number of colonies in the table (ΣC ) and in the total sample volume (ΣV ) for which
ijk ijk
colonies were counted.
b) The sample volume of the highest dilution step D for which colonies were counted (D or D ) is taken as
d 5 6
the unit volume (V = 1). For each lower dilution step D the corresponding sample volume V can be
d i i
determined as
a
V = V◊2
i d
where a is the number of binary dilutions between D and the highest dilution D .
i d
EXAMPLE Suppose the highest dilution for which valid counts were obtained is D , corresponding to a dilution of
–10
2 ; the sample volume of this dilution is taken as the unit volume (V = 1). The corresponding volume V for dilution
5 3
–8 2
D (2 ), two binary dilution steps from D , is calculated as V = V × 2 = 4 unit volumes V .
3 5 3 5 5
1) Calculate the expected number of colonies per unit of sample volume e = ΣC /ΣV and from this
ijk ijk
calculate the expected number of colonies E(C ) = e◊V for each dilution.
ijk ijk
2) Calculate for each plate with count C , the value C ◊In [C /E(C )].
ijk ijk ijk ijk
3) If C = 0, then this term is set equal to 0.
ijk
2 2
4) Calculate for each row (set of parallel plates) the G value (i.e. G with 2 degrees of freedom if no
(2)
data are missing) by summing the values for the three plates and multiplying the sum by two:
p


C
ijk


G = 2l⋅n
C
(2) ijk
∑

E()

C
ijk
k


Note this value down in the table.
5) Sum those G values over all the series and dilutions in the table. In this way, the following test
(2)
value is obtained:
sd
G = G
A(∑∑2)
ij
Compare the value of G with the tabulated values of χ (chi-squared) in Table 5, where df equals the
A
number of counts used in the calculations minus 1. If the value of G is less than the tabulated 0,01
A
probability value, then the counts are statistically homogeneous. All steps in the performance of the method
(sub-sampling, diluting, plating, counting) may be considered acceptable. No further evaluation is necessary
and the analysis may be concluded here.
IDF 169-1:2005(E)
Table 5 — Values for χ (P = 0,01)
2 2
df χ df χ
0,01 0,01
56 83,53 67 96,82
57 84,75 68 98,02
58 85,96 69 99,22
59 87,17 70 100,42
71 101,62
If the value of G is greater than the tabulated 0,01 probability value, then perform an analysis of variance
A
(ANOVA) on the data in order to identify and to quantify the sources of the excessive variability (sub-sampling,
diluting and plating/counting).
There are two possible reasons for a high value of G .
A
a) When the excess is moderate, the reason is probably that there are a few steps in the method which
show a somewhat larger variability than would be expected if the method were applied correctly. However,
this excessive variability is not so large that the results cannot be used in practice. In this case, a G
A
function is a warning sign: the method may still be applied in this way, but regular control is necessary to
make sure that the variability does not worsen.
b) When the excess is considerable (G much greater than the P = 0,01 value), one or more steps have an
A
unacceptably high variability.
Scrutinize and correct factors with a too high variability.
EXAMPLE Four dilution series, S , S , S and S , were taken from a well-homogenized and appropriately diluted
1 2 3 4
sample. From each sub-sample, a binary dilution series was laid out and from each dilution D three parallel plates, P , P
,
j 1 2
and P , were inoculated. Six dilutions provided countable results. The counts are presented in Table 6. All values have
been calculated with the full power of the calculator, after which the results have been rounded to 2 or 3 decimal places.
In Table 6, column C contains the means of the three parallel plates; column E(C ) contains the expected
ij ijk
means for the dilutions.
–6 –11
The values for E(C ) are calculated as follows (dilution steps used: D = 2 to D = 2 ).
ijk 1 6
–11
Volumes are expressed in relative units (the highest dilution 2 is taken as the unit volume):
 V (corresponding to D) = 2 V = 32
1 1 6
 V (corresponding to D) = 2 V = 16
2 2 6
 V (corresponding to D) = 2 V = 8
3 3 6
 V (corresponding to D) = 2 V = 4
4 4 6
 V (corresponding to D) = 2 V = 2
5 5 6
 V (corresponding to D) = 1
6 6
 Total number of colonies: 84 + 113 + 109 + 74 + … + 1 + 7 + 4 = 4862
 Total volume (in units of V ): (12 × 32) + (12 × 16) + (12 × 8) + (12 × 4) + (12 × 2) + (12 × 1) = 756
14 © ISO and IDF 2005 – All rights reserved

IDF 169-1:2005(E)
 Expected number of counts E(C ) for a volume V = 4862/756 = 6,43
ijk 6
 Expected number of counts E(C ) for a volume V = 4862/756 x 2 = 12,86
ijk 5
 Expected number of counts E(C ) for a volume V = 4862/756 x 4 = 25,72
ijk 4
 Expected number of counts E(C ) for a volume V = 4862/756 x 8 = 51,45
ijk 3
 Expected number of counts E(C ) for a volume V = 4862/756 x 16 = 102,90
ijk 2
 Expected number of counts E(C ) for a volume V = 4862/756 x 32 = 205,80
ijk 1
Table 6 — Original data
P
k
S D C E(C ) G
i j ij ijk
P P P
1 2 3
–6
D 2 84 113 109 102,00 205,80 4,997
–7
D 2 74 82 70 75,33 102,90 0,984
–8
D 2 35 43 33 37,00 51,45 1,483

S
–9
D 2 10 13 16 13,00 25,72 1,397
–10
D 2 7 11 9 9,00 12,86 0,896
–11
D 2 0 2 3 1,67 6,43 4,256
–6
D 2 238 236 226 233,33 205,80 0,356
–7
D 2 154 153 153 153,33 102,90 0,004
–8
D 2 154 126 111 130,33 51,45 7,226

S
–9
D 2 33 34 38 35,00 25,72 0,395
–10
D 2 16 15 21 17,33 12,86 1,161
–11
D 2 4 5 6 5,00 6,43 0,403
–-6
D 2 154 151 136 147,00 205,80 1,280
–7
D 2 84 68 72 74,67 102,90 1,831
–-8
D 2 44 65 63 57,33 51,45 4,899
S
–9
D 2 25 35 25 28,33 25,72 2,275

–10
D 2 13 13 13 13,00 12,86 0,000
–11
D 2 5 0 3 2,67 6,43 6,993
–6
D 2 238 236 224 232,67 205,80 0,496
–7
D 2 154 156 146 152,00 102,90 0,371
–8
D 2 63 61 56 60,00 51,45 0,437
S
–-9
D 2 17 32 28 25,67 25,72 4,980
–10
D 2 11 10 12 11,00 12,86 0,182
–11
D 2 1 7 4 4,00 6,43 5,062
Sum = G = 52,364
P
Indices: i = 4, j = 6, k = 3
IDF 169-1:2005(E)
The data for each dilution series are shown graphically in Figure 3. The straight line in each of the four figures
indicates what would be expected if the dilutions within each series were made perfectly. Each value within a
dilution series is represented by the symbol “+”.
Figure 4 a) shows the four straight lines of Figure 3 in the same graph. Their mutual deviations give an
indication of the quality of the sub-sampling. Figure 4 b) shows the means of the parallel plates (column C of
ij
Table 6) for each series. In the ideal case,
...