JOURNAL OF RESEARC H of the National Bureau of Standards - A. Phys ics a nd Chem istry Vol. 76A, No.2, M arch- April 1972

Guidelines for the Reporting of Numerical Data and Experimental Procedures

David Garvin

Institute for Materials Research, National Buredu of Standards, Washington, D.C. 20234

(December 2,1971)

Gene ral recomm endat ions are made about th e reportin g of data and ex pe rim e ntal procedures. These are intend ed as in struc tions to aut hors of pape rs in which quantitative physica l a nd che mica.1 data a re reported. Th ere is in c luded a bib liography of s tanda rd s docum ents and more de tail ed guide lin es.

Key wo rd s: Chemis try; expe rim ental procedures; num e ri ca l data ; physics.

1. Introduction

Scientific journals give general guidan ce on the prep­aration of papers in editorial sections e ntitled " ins truc­tions to authors" and the like. Two guides of this type are presented here. They are concerned with numeri­cal da ta and experimental procedures. They re fl ect the experience of data evaluators in decoding results re­ported in th e primary literature . These guides indicate how numbers s hould be re ported and what auxiliary in­formation is needed if it is to be possible for a conscie n­tious reader to reinterpret or re peat the measure me nts.

Th ese guides are general. More specific directions have bee n writte n for particular types of experim e nts. A bibliography appended to th is paper li sts a number of these, together with some generally applicable docu­ments that treat symbols, nomenclature and s tandard s.

2. The Presentation of Numerical Data

Quantitative measure me nts of physical properties and molecular parameters have surpri singly long lives. They ofte n survive several changes in interpre tation. The author can enhan ce their survival value by pre­senting the m in a form that will permit reinterpre tation , permit comparison with other work and permit as assessment of both accuracy and precision.

A vital preliminary to the reporting of numerical results is an adequate description of the experimental procedures used to obtain them. What is needed is outlined in a separate section.

The suggestions below are guides to be used in planning the presentation of numerical data.

1. In the reporting of experimental measurements and of derived quantities, use internationally approved nomenclature, symbols, units, and

standards. If there are over-riding reasons for using other symbols for units, identify these in terms of the internationally approved ones.

2. Report data in a form as free from interpre­tation as possible. The reader should be able to recover the measured quantities so that he may re­analyze the m in terms of a different hypotheSIS. Often thi s means si mply the addition of another column of data to a table . If there is a commonly accepted form for re porting the particular type of data, it should be used in addition to any form preferred by th~ author.

3. Present quantitative data that still show the scatter in the measurements. Whenever possible, publish experime ntal results in numerical form. If a choice must be made, plot or tabulate unsmoothed data instead of smoothed final results. Small , unex­pected effects can be lost when data are smoothed or fit to a predetermined function.

4. Put the final numerical results, those the author wants accepted, in a table. Do not bury them in a disc ussion section - they will be lost.

5. Report the "imprecision" of the measure­ments (stati sti cal or random uncertainty), and define it unaIDbiguously, e.g. " twice the standard deviation of the mean" etc. Avoid qualitative estimates of this quantity.

6. Estimate the "inaccuracy" of the measure­ments. Quantitative data presented without an esti­mate of possible systematic errors deserves summary rejection. The' components of this estimate include

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·(a) the sensitivity or resolution possible in the measurements ,

(b) the effect of assumptions made in processing the data ,

(c) the effect of possible systematic trends , both those for which corrections were made and those for which this could not be done, and

(d) uncertainties in auxiliary data taken from other work.

If possible , state this estimate in the same terms as that used for imprecision. They should be comparable in meaning even though they may differ in magnitude. Experience has shown that systematic differences between two sets of data usually are more important than random errors. Attempts to estimate these pos· sible effects usually lead to improved experimental design.

7. Explain the method used to reduce the primary data. This is the chain linking the measure­ments and the results. Often it is long and complex. Frequently, it is difficult for a reader to reconstruct it. An example is desirable. Importa nt co mponents of this chain are lis ted below. It is worthwhile to cover each point, but the detail depends upon the precision of the experiments_

(a) Mathematical expressions used to convert the data to results.

(b) Assumptions made about the experiments. Invariably some parameters are assumed to be unimportant , some are held constant and some are subject to substantial corrections. The treat­ment of all of these s hould be justified, prefer­ably by experiment.

(c) Auxiliary data and constants taken from other sources. Both their values and impre,: ision s hould be stated.

(d) The use of standards in relating the measure­me nts to the fundamental units of measure. The standards should be identified explicitly, particularly where changes have bee n made recently (as in the International Practical Temperature Scale, or atomic weights and masses).

(e) Cite the statistical procedures used.

3. The Reporting of Experimental Procedures

The quality of the information provided about how measurements were made often determines the ac­ceptability of the results in the future. When it becomes necessary for a reader to compare the results of several studies, or to reinterpret data, he must ask, "Did the author pay attention to details that I now know to be important?" or "Could he have observed this (newly reported) effect?" If these questions can­not be answered, the work may be rejected.

The major topics that should be included in a de­scription of the experimental procedures are listed below. Consideration of these points when planning the work will, inevitably, improve the experimental design and simplify the preparation of the final paper.

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- Description of apparatus with dimensions (eith er directly or by reference to earlier work).

- Calibration of equipment , including a discussion of the magnitudes of possible systematic biases for which corrections were not made.

- Indication of whether and how th e calibration IS

traceable to an established standard. - Description of experim e ntal procedure. - Description of environmental conditions. - Identification of analytical methods used (and

proof of them if novel). - Indication of the purity of materials and th e

e vide nce for it. - Statement of sensi tivity or resolution possible in

the experiments and the proof thereof. - Reporting on negative experiments.

4 . Discussion

General directions for the preparation of a scientifi c paper serve several purposes. They se t minimum standards for and promote uniformity of presentation of material. Also, they remind an author to tell his reader about what has been done as well as what has been deduced. But, in both cases such guides rely heavily upon the judgeme nt of the author concerning what should be included.

More detailed guides are desirable when quanti­tative data are important per se as opposed to being aids in the developme nt of concepts. These must summarize all the features of the work that should be recorded so that a step by s tep reanalysis can be made. Each such guide can only treat a specific type of work. Those few that have been written appear to have improved the quality of reporting of data. More are desirable.

S. Bibliography

5.1. Symbols, standards and basic quantities

SYMBOLS, UNITS, AND NOMENCLATURE

American National Standards Institute " I SO Recommendation RIOOO, Feb. 1969. Rules fOJ' the use of units of the International Systems of Units and a Selection of the Dccimal Multiples and Sub-multiples of the SI Units." American Na tional Standards Institute (New York, 1969) 1st Edition

(Bas ic statement on units in the SI system.)

Page, c., and Vigoreux, P. " The Inte rnational System Units (SI)" Nat. Bur. Stand. (U.S.), Special Publ. 330, 42 pages (J anuary 1971) .

(Su mmary of the SI system, history of development of the sys· ! tern of units, discussion of practical realization of the base I

units. This is a tran slation of "Le Systeme International d'Unites" published by BIPM. An iden tical English language I

document was published by the British S landards Institution, London, 1970.)

International Un ion of Pure and Applied Physics, Commiss ion for Symbols, Un its a nd Nomenclature "Symbols, Units and Nomenclature in Physics" Document U.J.P. 11 (S.U.N. 65- 3) (1965)

McG lashan , M. L. "Man ual of Symbols and T e r'mino logy for Physicochemical Quantities a nd Units" Pure and Applied Chemistry (1970) 21, I

(Sym bols ctc. approved by l UPAC)

Ame rican Society for Tes ting and Mate rial s " AST M Standar'd Metl'i c Pr'ac tice C uide (A Gu ide to the Use of SI - The Inte rnational System of Units" Ame rica n Soc. for Tes ting and Material s (New York , 1970)

(In clud es factors for conve rsion of customary units to 51 and procedu res for round ing co nve rted values)

America n Chemi cal Society " Ha ndboo k for Author's of pape r's in th e j ou rna ls of the Ame r'ica n Che mica l Socie ty" Amer ica n Chem. Soc. Pu blications (Washington, 1967)

(This handbook in cl udes a bibliography (pg. 49-53) on nomen­cla ture of chemica l compound s and , to a limi ted extent , on terminology and symbols .)

Int ern ational Union of Pu re and Applied C hemistry " Infor' llla tion Bull e tin "

(Thi s seri es inc lud es appe nd ices on nomenclature, sym bols, unit s and standards for spec ialized fi eld s. Many of th ese a re aboul the nomenclature of compounds, but so me are on repo rt· ing of data. See "G uidelines")

CODATA Newsle tte r s (This se ri es regula rl y pub li shes an nouncement s of books, handbooks, and a rti c les tha t are comp ilations of da ta , or that trea t nomenclature, symbols, unit s and stand a rds)

ATOMIC WEIGHTS

Inte rna ti onal Union of Pu re and Applied C hemi stry, Inorga nic Chemistry Divi sion , Comm iss ion on Atomic We ights " Atomi c We ights of th e E le m e nts 1969" Pure and Applied Chemis try (1970) 21, 1

(Th is i the current se t of a tomic weights for the natura ll y occuning isotopic mixtures: Re vi s ions to this atomic weight sca le for th e element s H, F , Na, AI , P , K, Zn , Cs, Ho and Bi were reco mmended to I UPAC by the Co mmission on Atom ic Weights a t their meeting in Washington , D. C. in J uly 1.971 )

ENERGY Gi nnings, D. C. , editor " Heat," vo l. 6 of "P"ecision Measure m e nt and Ca lilu'ation" Nat. Bur. Stand. (U.S.), Special Pub!. 300 , vo!' 6, 387 pages (Feb­ru ary 1970)

(Collection of N.B.S. pape rs on calor imetry (techniqu es, high temperature, low temperature, reaction) , c ryoscopic measure­ment s and heat tran sfer. )

PHYSICAL CONSTANTS

Taylor, B. N. , Pa rker, W. H. , and Langenberg, D. N. " Dete r'mination of e/ h, Using Mac r'oscopic Quantum Phase Coher'en ce in S upe r co nductor's: Iml)lications fOl' Quantum Electr'odynamics and the Fundamental Physical Co nstants" Rev. Mod . Ph ysics (1969) 41 ,375

(New data, incl uded here, force a revision in the values for the physical constants now accepted (Cohen and DuMond .) A CODATA Tas k Croup is preparing a revised se t for considera­tion by the scientific community.)

Cohen, E. R., and DuMond , J. W. M. "OUI' Knowledge of th e Fundamental Constants of Ph ys ics and Ch emistr'y in 1965" Rev. Mod. Ph ys ics (1965) 3 7, 4

(Rev iew and selec ti on of data and table of ph ys ical constants. Th e va lues given he re are also printed in the 1965 report of the S.U.N. Co mmission and in Na t. Bur. S tand. Tech. News. Bull. (1963) 47, 175. In both of th ese the error is given as 3

standard errors (one standard e rror is given in the Rev. Mod . Ph ys ics a rti cle) and the valu es are rounded correspond ingly.

The first radia tion constant , c" is in e rror in the NBS T ech. News. Bu ll. arti cle. It should be 3.7415 X 10" Wm ' not 3.7405 X 10" Wm '.)

PRECISION AND ACCURACY

Ku , 1-1 . 1-1 . edit or " Statis tical COn Ce l)t s and Pr'ocedur'es," vol. 1 of "Precision Meas Ul'e m e nt and Calibr'a tion" Na t. Bur. S tand . (U.S.), S pecia l Pub!. 300 (1969)

(Collecti ve volum e on the treatment of errors of measurem ent. Almos t all pape rs a re of int e rest to the experime ntalist. Two of prime int erest concerning the express ion of precision indices and e rro rs a re: Eisenh art , C., " Express ion of the Uncertainties of Fina l Results," pape r 1.6 pg 69 (reprinted from Science (1968) 160, 1201), and Ku , H. 1-1 ., " Exp ress ion of Imp recision , Syste· matic Error, and Uncertainty Associated with a Reported Value'; pape r 1.7 pg. 73 (repri nted from Meas urements and Data (July-August 1968).)

STANDARDS

National Ph ys ica l La boratory (U.K. ) " Units and S tandar d s of Measure m e nt Employed at the Na­tional Ph ys ic,,1 La bor'a tor',,"

{pamphlets issued irregula rly on standard s and the ir practi cal realiza tion. Topics: Length , Mass, Tim e; Ligh t ; Electric ity: Te mperature.)

TEMPERATURE

Intern ati ona l Bureau of Weight s and Measures (BIPM), Subco mmit ­on Th ermometry " lnte r'national Pr'ac ti ca l T c mpe ratur'e Scale of 1968" Metrologia (1 969) 5, 35

Bedford , R. E., Duri eux, M. , Muij li vij k, R. , and Barbe r, C. R. " R e lationships be twee n th e I nt e r'national Pr'actica l T e mpe r. ature Sca le of L 968 and th e NBS- 55, NPL- 6J, PRMl- 54, a nd P SU- 54 T e mpe r'atur'e Scales in th e Range fr'om 13.81 to 90.18 K" Metrologia (1969) 5,47

Douglas, T. B. "Conver's ion of Exis ting Calor'imetr'ically De te rmine d The r', mod ynami c Pr'ope rties to the Bas is o f th e International Pr·ac· tical Tempe rature Scale of 1968" J . Research Nat. Bur. Stand. (U.s .). (1969) 73A, 45 ]

Swindells, J . F. , editor " T e mperatlll'e," vol 2 of "Pr'ecisio n Measure m e nt and Ca libration" Nal. Bur. S tand . (U.S.), Special Pub!. 300 vo l. 2, 513 pages (Augu st 1968)

(Coll ection of N.B .S. articles on temperature scales, therm om­et ry, pyrom etry and spectroscopic temperatu re measurement, )

5.2 . Guidelines for Reporting Data in Various Fields

INFRARED SPECTRA

Coblentz ocie ty Board of Managers "Speci fication s for' Evaluation of Infr'a r'e d Refer'e nce S pectr'a" Analytical C hemis try (1966) 38, 27 A

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" R ecomme ndation s for' Infr'a r'ed Spectra of New Com­I)ounds" Analyti cal Chemistry (1968) 40, 2272

OPTICAL SPECTRA

Meggers, W. F. , a nd Moore, C. E. [Joint Commission for Spect"oscopy (IAU , I U PAP)] "Re port of Subcommittee e (Notation fo,' Atomic S p ect,'a)" J . O ptical Soc. Ame rica (1953) 43, 422

Jen kin s, F. A. !J oint Commiss ion for S pectroscopy (lAU, TUPAP)! " R e port o f Subcommittee f (Notation 1'0" the S p ect,'a of Diatomic M olecules)" .J . Optical Soc. America (1953) 43 ,425

.J o int Commi ss ion for S pectroscopy (IAU, IUP AP ) " Report on Notation fo,' th e S p ec t,'a of Pol yatomi c Molecules" .J. Che rn . Phys. (1955) 23, 1997

Triple Commiss ion for Spectroscopy (lAU , IUPAP, IU PAC) " Minute s of the Mee ting at Tokyo 9 Se pt. 1962. Appe ndix A, Re po"t of Subcommitte c on Units and T e l'lninology" .J. O ptica l Soc. Am erica (1963) 53 ,883

(S ugges ted c ha nges in ea rli e r recomm endations)

Internationa l Union of Pure and Applied C he mi stry Inform ation Bull et in , App endices on Te nta ti ve No me nc lature Sy mbols Units a nd S ta nda rd s No. 1 (1969) " Nomenclature, Symbol s , U nits and The ;" U sage in S I}ectro·Che mical Analysis -I" No. 11 (J 97 L) " Recomme ndation s fo, ' th e P,'esc ntation of Raman S p ect,'a fo,' Cataloging and Doc ume ntation in Pe ," nUlnent Data Collections"

"S I}ect,'ome t"y NomenclatUJ'e", An alyti ca l C hemistry (1968) 40,2271

CHEMICAL KINETICS

(The CODATA Task Group on Data fo r C he mi cal Kin eti cs is pre· pa ring (1971) guid elines on the reporting of ra te data. These a re based on sugges tions made by V. N. Kondrati ev).

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CRYSTALLOGRAP HY

Ibers, J . A. " Informa tion and Sugges tions on Presentation of th e Results o f Crys tal S t,'u c ture Studies" lnorg. C him . Ac ta (Sept. 30 , 1969), No.3 (9th P relim. page)

Kennard, 0., Speak ma n, J. C., a nd Donn ay, J . D. H. " P"imary C ,'ys tallog ra phi c Da ta" Acta CrystalJ ogr. (1967) 22, 445

GAS CHROMATOGRAPHY

AST M Comm ittee E- 19 " P,'oposed R ecomme nd e d P,'ac tice for Gas Chromatog' raph y T e ,' ms and Relati o ns hips" J. Gas Chromatog. (1968) 6 , 1

THERMOCHEMISTRY AND THERMODYNAMICS

McC uli ough , J . P . , Westrum , E. F., Jr. . a nd Evans, W. H . " Calorime t'·y G,'oup Adopts He vi sed Resolution on Data Publi c ation " Scie nce (1960) 132 , 1658

(A rev ision of thi s recomm end ation was submitted by E. F . Wes trum , Jr. , e t a l. for approval of the co mmiss ion on Thermo· dyna mics and The rm ochemi stry at th e 1971 IUP AC Confere nce at Washington, D. C. With approva l by t hi s a nd higher IUPA C co mmittees it will be publi s hed in the Journ al " Pure and App/ied Chemistry")

THERMAL CONDUCTIVITY

Hanley, H. M. et a l. "Recommend a tion s fo,' Data Compilations and fo,' th e He po"ting of Meas ure m e nts of th e The rmal Conductivity of Ga ses" J. Heat T ra nsfer (1971) 93 Series C, 479

(Paper 76A2- 699)