SIST EN 60068-3-11:2007

Environmental testing -- Part 3-11: Supporting documentation and guidance - Calculation of uncertainty of conditions in climatic test chambers

This part of IEC 60068 demonstrates how to estimate the uncertainty of steady-state temperature and humidity conditions in temperature and humidity chambers. Since this is inextricably linked to the methods of measurement, these are also described. This standard is equally applicable to all environmental enclosures, including rooms or laboratories. The methods used apply both to temperature chambers and combined temperature and humidity chambers. This standard is meant to help everyone using climatic test chambers. Those already familiar with uncertainty of measurement will find it useful for guidance on typical sources of uncertainty and how they should be quantified and combined. It is also intended to assist the first-time or occasional user who has little or no knowledge of the subject. To discuss uncertainty, it is important first to understand what is being measured or characterized. The calibration or characterization of the performance of a chamber is concerned with the humidity and temperature of the air in the chamber, as experienced by the item under test, at a given set point. This should not be confused with characterizing or calibrating the chamber sensor, which is a separate matter.

Umgebungseinflüsse -- Teil 3-11: Unterstützende Dokumentation und Leitfaden - Berechnung der Messunsicherheit von Umgebungsbedingungen in Klimaprüfkammern

Essais d'environnement -- Partie 3-11: Documentation d’accompagnement et guide - Calcul de l’incertitude des conditions en chambres d’essais climatiques

Montre comment estimer l'incertitude des conditions de température et d'humidité à l'état stable dans une chambre d'essais de température et d'humidité. Sachant que cela est inextricablement lié aux méthodes de mesures, celles-ci sont également décrites. La présente norme est également applicable à tout type d'enceintes d'environnement, et même les salles ou laboratoires. Les méthodes sont usuellement appliquées aux chambres d'essais régulées en température et aux chambres d'essais régulées en température et humidité. La présente norme cherche à aider toute personne utilisant des chambres d'essais climatiques. Les personnes étant déjà familières avec l'incertitude de mesure la trouveront utile pour les conseils sur les composantes types d'incertitudes et sur la manière dont il convient de les quantifier et de les combiner. Elle est également destinée à aider le nouvel utilisateur ou l'utilisateur occasionnel qui n'a qu'une faible connaissance du sujet ou pas de connaissance du tout. Afin d'aborder les incertitudes il est important tout d'abord de comprendre ce qui est mesuré ou caractérisé. L'étalonnage ou la caractérisation de la performance d'une chambre d'essais fait appel à la détermination de l'humidité et de la température de l'air de la chambre, vu par l'objet en essai, à une valeur de consigne donnée. Il convient que cela ne soit pas confondu avec le calibrage ou l'étalonnage du capteur de la chambre d'essai, qui est une opération différente.

Okoljski preskusi - 3-11.del: Spremljajoča dokumentacija in vodila - Izračunavanje nezanesljivosti pogojev v komorah za klimatsko preskušanje (IEC 60068-3-11:2007)

General Information

• Status: Published
• Publication Date: 11-Sep-2007
• ICS: 19.040 - Environmental testing
• Technical Committee: I09 - Imaginarni 09
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 23-Aug-2007
• Due Date: 28-Oct-2007
• Completion Date: 12-Sep-2007
• Ref Project: EN 60068-3-11:2007 - Environmental testing - Part 3-11: Supporting documentation and guidance - Calculation of uncertainty of conditions in climatic test chambers

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN 60068-3-11:2007
01-oktober-2007
2NROMVNLSUHVNXVLGHO6SUHPOMDMRþDGRNXPHQWDFLMDLQYRGLOD,]UDþXQDYDQMH
QH]DQHVOMLYRVWLSRJRMHYYNRPRUDK]DNOLPDWVNRSUHVNXãDQMH,(&

Environmental testing -- Part 3-11: Supporting documentation and guidance - Calculation
of uncertainty of conditions in climatic test chambers
Umgebungseinflüsse - Teil 3-11: Unterstützende Dokumentation und Leitfaden -
Berechnung der Messunsicherheit von Umgebungsbedingungen in Klimaprüfkammern
Essais d'environnement - Partie 3-11: Documentation d’accompagnement et guide -
Calcul de l’incertitude des conditions en chambres d’essais climatiques
Ta slovenski standard je istoveten z: EN 60068-3-11:2007
ICS:
19.040 Preskušanje v zvezi z Environmental testing
okoljem
SIST EN 60068-3-11:2007 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

EUROPEAN STANDARD
EN 60068-3-11

NORME EUROPÉENNE
June 2007
EUROPÄISCHE NORM

ICS 19.040


English version


Environmental testing -
Part 3-11: Supporting documentation and guidance -
Calculation of uncertainty of conditions in climatic test chambers
(IEC 60068-3-11:2007)


Essais d'environnement -  Umgebungseinflüsse -
Partie 3-11: Documentation Teil 3-11: Unterstützende Dokumentation
d’accompagnement et guide - und Leitfaden -
Calcul de l’incertitude des conditions Berechnung der Messunsicherheit
en chambres d’essais climatiques von Umgebungsbedingungen
(CEI 60068-3-11:2007) in Klimaprüfkammern
(IEC 60068-3-11:2007)




This European Standard was approved by CENELEC on 2007-06-01. CENELEC members are bound to comply
with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard
the status of a national standard without any alteration.

Up-to-date lists and bibliographical references concerning such national standards may be obtained on
application to the Central Secretariat or to any CENELEC member.

This European Standard exists in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CENELEC member into its own language and notified
to the Central Secretariat has the same status as the official versions.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the
Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.

CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung

Central Secretariat: rue de Stassart 35, B - 1050 Brussels


© 2007 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 60068-3-11:2007 E

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EN 60068-3-11:2007 - 2 -
Foreword
The text of document 104/409/FDIS, future edition 1 of IEC 60068-3-11, prepared by IEC TC 104,
Environmental conditions, classification and methods of test, was submitted to the IEC-CENELEC parallel
vote and was approved by CENELEC as EN 60068-3-11 on 2007-06-01.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2008-03-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2010-06-01
Annex ZA has been added by CENELEC.
__________
Endorsement notice
The text of the International Standard IEC 60068-3-11:2007 was approved by CENELEC as a European
Standard without any modification.
__________

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- 3 - EN 60068-3-11:2007

Annex ZA
(normative)

Normative references to international publications
with their corresponding European publications

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.

NOTE  When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD
applies.

Publication Year Title EN/HD Year
1) 2)
IEC 60068-3-5 - Environmental testing - EN 60068-3-5 2002
Part 3-5: Supporting documentation and
guidance - Confirmation of the performance
of temperature chambers


1) 2)
IEC 60068-3-6 - Environmental testing - EN 60068-3-6 2002
Part 3-6: Supporting documentation and
guidance - Confirmation of the performance
of temperature/humidity chambers


ISO 3534-1 2006 Statistics - Vocabulary and symbols - - -
Part 1: General statistical terms and terms
used in probability


ISO 3534-2 2006 Statistics - Vocabulary and symbols - - -
Part 2: Applied statistics


ISO Guide 99 1996 International vocabulary of basic and general - -
terms in metrology


ISO/IEC Guide 98 1995 Guide to the expression of uncertainty in - -
measurement





1)
Undated reference.
2)
Valid edition at date of issue.

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INTERNATIONAL IEC
STANDARD
CEI



60068-3-11
NORME


First edition
INTERNATIONALE

Première édition
2007-05


Environmental testing –
Part 3-11:
Supporting documentation and guidance –
Calculation of uncertainty of conditions
in climatic test chambers

Essais d’environnement –
Partie 3-11:
Documentation d’accompagnement et guide –
Calcul de l’incertitude des conditions
en chambres d’essais climatiques
PRICE CODE
V
CODE PRIX
Commission Electrotechnique Internationale
International Electrotechnical Commission
МеждународнаяЭлектротехническаяКомиссия
For price, see current catalogue
Pour prix, voir catalogue en vigueur

---------------------- Page: 5 ----------------------

– 2 – 60068-3-11 © IEC:2007
CONTENTS
FOREWORD.4
INTRODUCTION.6

1 Scope.7
2 Normative references .7
3 Terms and definitions .8
4 Concept of uncertainty.11
4.1 Uncertainty, error and “true value”.11
4.2 Statements of uncertainty.12
4.3 Combining uncertainties .13
5 Tolerance .13
6 Humidity and temperature measurement .13
7 Methods for determining climatic test chamber uncertainties .14
7.1 Empty chamber .16
7.2 Typical load.16
7.3 Measurement of conditions in the chamber during the test .17
7.4 Conditions to measure.17
7.5 Measurements required.18
7.6 Sources of uncertainty.19
7.7 Essential contributions of uncertainty .20
8 Estimation of uncertainty components and their combination .24
9 Overall uncertainty of temperature measurement.24
9.1 General .24
9.2 Further considerations.26
10 Overall uncertainty of relative humidity measurement .26
10.1 Uncertainty of temperature measurement at each sensor point.27
10.2 Uncertainty of the relative humidity measurement.27
11 Anomalous data and presentation of results .30
11.1 Average case analysis.30
11.2 Worst case analysis .30

Annex A (informative) Measurement data sets – Loaded chamber .32

Bibliography.34

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60068-3-11 © IEC:2007 – 3 –
Figure 1 – Approaches to calibration method and uncertainty calculation.15
Figure 2 – Illustration of the fluctuation of a temperature sensor .23

Table 1 – Combination of temperature uncertainties .24
Table 2 – Combination of temperature uncertainties at each point .27
Table 3 – Combination of humidity uncertainties .28
Table A.1 – Typical temperature measurement data set and it’s analysis and refs .32
Table A.2 – Humidity measurements analysis based on Table A.1 temperatures.33

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– 4 – 60068-3-11 © IEC:2007
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________

ENVIRONMENTAL TESTING –

Part 3-11: Supporting documentation and guidance –
Calculation of uncertainty of conditions in climatic test chambers


FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60068-3-11 has been prepared by IEC technical committee 104:
Environmental conditions, classification and methods of test.
The text of this standard is based on the following documents:
FDIS Report on voting
104/409/FDIS 104/415/RVD

Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.

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60068-3-11 © IEC:2007 – 5 –
A list of all parts in the IEC 60068 series, under the general title Environmental testing can be
found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in
the data related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.

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– 6 – 60068-3-11 © IEC:2007
INTRODUCTION
This part of IEC 60068 provides guidance for analysing uncertainties of temperature and
humidity in climatic test chambers. It has been written for technicians, engineers and
managers in environmental testing, and for anyone who needs to understand the results of
environmental tests.
The performance of climatic test chambers is a key concern in environmental test engineer-
ing. To comply with any test specification, the performance of the chamber needs to be
characterized to decide whether the generated conditions fall within the specified limits. This
characterization can be a difficult task, and the analysis of uncertainties in chamber
performance is often surrounded by confusion. This publication is intended to ease that
process.
In what follows, the concept of uncertainty of measurement is introduced first and then the
significance of tolerance discussed. Aspects of humidity and temperature measurement are
considered, followed by methods for determining and combining uncertainties. The cases of
both calibrating an empty chamber and of measuring conditions in a loaded chamber are
considered. Finally, detailed guidance and worked examples are given for analysing results to
give estimates of uncertainty in the measured performance.

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60068-3-11 © IEC:2007 – 7 –
ENVIRONMENTAL TESTING –

Part 3-11: Supporting documentation and guidance –
Calculation of uncertainty of conditions in climatic test chambers



1 Scope
This part of IEC 60068 demonstrates how to estimate the uncertainty of steady-state
temperature and humidity conditions in temperature and humidity chambers. Since this is
inextricably linked to the methods of measurement, these are also described.
This standard is equally applicable to all environmental enclosures, including rooms or
laboratories. The methods used apply both to temperature chambers and combined
temperature and humidity chambers.
This standard is meant to help everyone using climatic test chambers. Those already familiar
with uncertainty of measurement will find it useful for guidance on typical sources of
uncertainty and how they should be quantified and combined. It is also intended to assist the
first-time or occasional user who has little or no knowledge of the subject.
To discuss uncertainty, it is important first to understand what is being measured or
characterized. The calibration or characterization of the performance of a chamber is
concerned with the humidity and temperature of the air in the chamber, as experienced by the
item under test, at a given set point. This should not be confused with characterizing or
calibrating the chamber sensor, which is a separate matter.
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.
IEC 60068-3-5: Environmental testing – Part 3-5: Supporting documentation and guidance –
Confirmation of the performance of temperature chambers
IEC 60068-3-6: Environmental testing – Part 3-6: Supporting documentation and guidance –
Confirmation of the performance of temperature/humidity chambers
ISO 3534-1:2006, Statistics – Vocabulary and symbols – Part 1: General statistical terms and
terms used in probability
ISO 3534-2:2006, Statistics – Vocabulary and symbols – Part 2:Applied statistics
International Vocabulary of basic and general standard terms in metrology. ISO, Geneva,
Switzerland 1993 (ISBN 92-67-10175-1) – VIM

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– 8 – 60068-3-11 © IEC:2007
Guide to the expression of uncertainty in measurement. ISO, Geneva, Switzerland 1993.
(ISBN 92-67-10188-9) – GUM
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
calibration authority
laboratory or other organization that performs calibrations and is itself accredited by the
appropriate national accreditation body
3.2
climatic test chamber
enclosure
chamber or enclosed space where the internal temperature or temperature and humidity can
be controlled within specified limits
3.3
combined standard uncertainty
standard uncertainty of the result of a measurement when that result is obtained from the
values of a number of other quantities, equal to the positive square root of a sum of terms, the
terms being the variances or covariances of these other quantities weighted according to how
the measurement result varies with changes in these quantities
See also GUM.
3.4
correction
value added algebraically to the result of a measurement to compensate determinable
systematic error
See also VIM.
3.5
confidence level
value of probability associated with a confidence interval
NOTE The confidence level is the likelihood that the “true value” lies within the stated range of uncertainty usually
expressed as a percentage, e.g. 95 %.
See also ISO 3534-1.
3.6
coverage factor
numerical factor to multiply the combined standard uncertainty to obtain an expanded
uncertainty
NOTE A coverage factor of k=2 corresponds to a confidence level of approximately 95 % if normally distributed
and if the number of degrees of freedom is sufficiently large.
See also GUM.

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60068-3-11 © IEC:2007 – 9 –
3.7
dew point
temperature at which the partial pressure of the water vapour is equal to the saturation vapour
pressure over water or ice
NOTE The temperature to which the air would have to cool (at constant pressure and constant water vapour
content) in order to reach saturation. A state of saturation exists when the air is holding the maximum amount of
water vapour possible at the existing temperature and pressure.
3.8
dispersion
spread of repeated measurements of a quantity
3.9
drift
change in the indication of a measuring system not related to a change in the quantity being
measured
See also VIM.
NOTE The drift since the last calibration can be estimated and a correction applied to measured values.
3.10
error
difference between result of a measurement and the true value
3.11
expanded uncertainty
quantity defining an interval about the result of a measurement that may be expected to
encompass a large fraction of the distribution of values that could reasonably be attributed to
the measurand
See also VIM.
3.12
fluctuation
change (from the mean) in the temperature or humidity after stabilization from time to time at
a point in space
NOTE It may be measured by standard deviation or maximum deviation.
3.13
gradient
maximum difference in mean value, after stabilization, at any moment in time between two
separate points in the working space
3.14
incident air
conditioned airstream which flows into the working space
3.15
partial vapour pressure
contribution of water vapour in a given volume of air at a constant pressure and temperature
of the atmosphere
3.16
reference instrument
previously calibrated instrument used to measure the conditions within the enclosure

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– 10 – 60068-3-11 © IEC:2007
3.17
relative humidity
ratio of actual partial vapour pressure to the saturation vapour pressure at any given
temperature and pressure, expressed as a percentage (% RH)
3.18
repeatability
closeness of agreement between independent results obtained in the normal and correct
operation of the same method on identical test material, in a short space of time, and under
the same test conditions (such as the same operator, same apparatus, same laboratory)
3.19
resolution
smallest changes between indications of the chamber controller display that can be
meaningfully distinguished
3.20
saturation vapour pressure
when a given volume of air, at a constant temperature, has water vapour present and is
incapable of holding more water vapour it is said to be saturated
3.21
stabilization
achievement of the state of temperature/humidity in the chamber when all mean values in the
working space are constant and have maintained temperature/humidity within a given
tolerance
3.22
standard deviation
measure of the dispersion of a set of measurements
NOTE The standard deviation, s, is the best estimate of sigma (the population standard deviation).
See also GUM and/or VIM.
3.23
standard uncertainty
uncertainty of the result of a measurement expressed as a standard deviation
See also GUM.
3.24
tolerance
acceptance limit specified or chosen for a process or product
See also ISO 3534-2.
3.25
traceability
property of the result of a measurement or the value of a standard whereby it can be related
to stated references, usually national or international standards, through an unbroken chain of
comparisons, all having stated uncertainties
NOTE The unbroken chain of comparisons is called a traceability chain.
See also ISO 3534-1 and VIM.

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60068-3-11 © IEC:2007 – 11 –
3.26
true value
value which characterizes a quantity, perfectly defined in the conditions which exist when that
quantity is considered
NOTE The true value of a quantity is a theoretical concept and, in general, cannot be known exactly but is
estimated by measurement.
See also ISO 3534-1.
3.27
uncertainty
parameter, associated with the result of a measurement, which characterizes the dispersion
of the values that could reasonably be attributed to it
3.28
uncertainty budget
list of sources of uncertainty compiled with a view to evaluating a combined standard
uncertainty associated with a measurement result
3.29
uncertainty contribution
input to an uncertainty budget
3.30
working space
part of the chamber in which the specified conditions can be maintained within the specified
tolerances
4 Concept of uncertainty
4.1 Uncertainty, error and “true value”
In every measurement – no matter how careful – there is always a margin of doubt about the
result. In simple terms, the uncertainty of a measurement is a quantification of the doubt
about the measurement result.
While discussing uncertainty we often also need to consider a related but separate concept,
“error”. A measurement “error” is the difference between the measured value and the “true
value” of the thing being measured.
The “true value” of any quantity is in principle unknowable. This leads to a problem since the
“error” is defined as the result of a measurement minus the “true value”. Sometimes this
difference can be estimated. Both terms are best avoided as much as possible and, when
necessary, should be used with care. Discussion of “error analysis”, which used to be
included in many scientific papers, should have been entitled “analysis of the probable limits
of error”, or more properly, ”analysis of uncertainty”. In older publications the term “error” was
widely used when ‘uncertainty’ would have been the correct term.
Uncertainty is not the same as error. If the conditions in a test chamber are measured with a
calibrated instrument and the result is 75 % RH when the chamber controller says 90 % RH,
that does not mean the uncertainty is 15 % RH. It is known that the relative humidity is 75 %
RH. One is aware that either the controller reading is wrong or the chamber is operating
incorrectly. It has an error estimated to be 15 % RH. The uncertainty is a characteristic of the
measurement that gave the answer 75 % RH. Could that be wrong and, if so, by how much?

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– 12 – 60068-3-11 © IEC:2007
When considering “true value”, uncertainty, and error, one of the most important sources of
this type of information for a measuring instrument is its calibration certificate. It is vital to use
all of the information provided by the calibration certificate to ensure that the best estimate of
the test uncertainties are obtained.
4.2 Statements of uncertainty
4.2.1 General
When reporting the results of a measurement, three numbers are necessary for a
metrologically correct and complete statement of the result of each measurement point. For
example, the complete statement could be:
The “true value” is: 39,1 °C ± 0,3 K with 95 % confidence:
• 39,1 °C is the best estimate of the true value;
• ±0,3 K is the confidence interval;
• 95 % is the confidence level.
An explanation of these three components follows.
4.2.2 Best estimate of the true value of the measured quantity
Often this will simply be the reading on the calibrated reference instrument which, in the case
of a climatic test, could be the temperature measurement system and/or hygrometer reading,
or if the chamber has been calibrated it could be the chamber controller display. If the
calibration shows either for an instrument or for a chamber controller that an error exists
(which is not an uncertainty), this should be used to apply a correction. For example, if the
calibration of a thermometer shows that it reads 1 K high, 1 K should be subtracted from the
reading to obtain the best estimate of the true value.
4.2.3 Confidence interval
This is the range of measured values within which the “true value” lies with a given level of
confidence. In our example this interval is ±0,3 K.
4.2.4 Confidence level
The “confidence level” of a measurement is a number (e.g. 95 %) expressing the degree of
confidence in the result. This is the probability that the real “true value” lies in the given
range. Most sets of data are normally distributed and about 68 % of the values will fall within
plus or minus one standard deviation of the mean. About 95 % of the values can be expected
to fall within plus or minus 2 standard deviations (95 % confidence level). Put another way,
when many such measurements are performed not more than 1 in 20 will lie outside the
stated limits. Hence multiplying the standard deviation by 2 is an accepted way of
encompassing 95 % of the range of values. With a 95 % confidence level, we are 95 % sure
that the “true value” lies in the stated range.
It is conventional to work at the 95 % confidence level. Higher confidence levels can be used
but the confidence interval will increase.
4.2.5 Statemen
...