measurement scales in cartography

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Measurement Scales in CartographyKang-tsung ChangPublished online: 14 Mar 2013.

To cite this article: Kang-tsung Chang (1978) Measurement Scales in Cartography, The AmericanCartographer, 5:1, 57-64

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Measurement Scales in CartographyKang-tsung Chang

ABSTRACT. Nominal, ordinal, interval, and ratio scales are a convenient nomenclature adaptedto cartographic measurements from other fields. Each is associated with different rules for assign-ing values and with different permissible operations. Scaling in mapmaking raises such issues as:the lack of one-to-one correspondence between measurement scale and map symbol, combina-tions of measurement scales in thematic mapping, and the addition of higher order information,sllch as degree of importance when mapping nominally-scaled data. In the context of map read-ing, measurement scale is complicated by complex stimulus-response relationships, the meaningof measurement scale in map reading, and problems of accllracy and consistency in the case ofresponses on interval and ratio scales.

THE GENERAL CONCEPT OFMEASUREMENT SCALES

It is generally accepted that measure-ment consists of rules for assigningnumbers to objects in such a way as torepresent quantities of attributes.! Dif·ferent rules for the assignment of num-bers would therefore constitute dif-ferent measurement scales. The con-cept of four measurement scales-nominal, ordinal, interval, and ratio-was well publicized by Stevens in his1951 article "Mathematics, Measure-ment, and Psychophysics;"2 and later inSiegel's widely-read book, Nonpara-metric Statistics.3 The concept hasbeen discussed in geography textbooksin quantitative analysis since at least thelate 1960' S,4 and scaling terminology be-came a part of the everyday vocabularyof cartographers with the third editionof Elements of Cartography by Robin-son and Sale (1969)5 and has sub-sequently been discussed in works byMuehrcke and Chang.6

The numerical properties of measure-ment scales are familiar to us: Anominal scale partitions objects into aset of mutually exclusive classes amongwhich the relation is one of equiva-

Kang-tsung (Karl) Chang is associate professorof geography at the University of North Dakota,Grand Forks, N.D. 58202.

lence; an ordinal scale groups objectsinto a set of mutually exclusive classes,but the classes can be ranked bydescriptions such as "greater than;" aninterval scale has the properties of anordinal scale, but, in addition, thedistance between any two objects isknown; and, finally, a ratio scale has allthe properties of an interval scale plus atrue zero point. Concomitantly, the ad-missible operations differ with thesedifferent measurement scales. For anominal scale, classes may berepresented by words or any set ofsymbols, e.g., numbers or letters, aslong as the classes can be distinguished.For example, a series of numerals canbe used for different types of land use,e.g., "1" for built-up area, "2" for vacantland, and so on. These numerals may besubstituted by letters without losing thecharacteristics of the data. With ordinalscales, on the other hand, a transforma-tion can be made only so long as it doesnot change the order, or ranking, of theclasses. For example, the quality ofthree soil types may be ranked accord-ing to good-I, average-2, and bad-3or according to bad-I, average-2, andgood-3 so long as the order is notchanged. With an interval scale, the ad-missible operation can be described as a

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linear transformation in the form off(x) = ax + b. This means that eachnumber can be transformed by mul-tiplying by a constant and by adding aconstant. A good example is the changeof scale of temperature reading fromCelsius to Fahrenheit scale; in this case,the const~nt a takes the value 9/5 andthe constant b has the value 32. Finally,with a ratio scale, the admissible opera-tion is limited to multiplication by apositive constant, or f (x) = ax. Forexample, the distance measure may bechanged from kilometers to miles, giventhat the constant a takes a value of0.62137.

A distinction often recognized bypsychologists is between two types ofratio scales, fundamental and derived.Fundamental scales are represented byabsolute magnitudes, such as length orweight, whereas derived scales consistof magnitudes which are functions offundamental magnitudes, such asdensity or velocity. Incidentally, thisdistinction is also used in thecartographic literature; for example,county populations are fundamentalmagnitudes, or absolute values as theyare sometimes called in cartography,and county population densities arederived magnitudes.

The concept of measurement scaleshas been advocated most vigorously inits application to statistical analysis.The distinguishing of scale types is fun-damental in choosing the appropriatestatistical procedure. For example, chi-square is associated with the nominalscale, rank correlations with the ordinalscale, and parametric statistics, such asproduct-moment correlation with theinterval and ratio scales. This kind ofassociation has been somewhatweakened in recent years. Geographers,for example, seem to have put more em-phasis on the application of nonpara-metric statistics.7 The reason is thatgeographical data often do not meetsuch assumptions as nonnality andhomoscedasticity that are required inmany parametric statistical methods.

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Therefore, data measured on an intervalor ratio scale are transfo1111ed intoranked data for the application of non-parametric statistics.

The issue of measurement scales hasbrought about a number of questions.For example, can the nominal scale beconsidered a legitimate measurementscale? A nominal scale simply groupsobjects into mutually exclusive cate-gories, and the process of categorizingdoes not necessarily involve quantifica-tion of any kind, although the numbersof occurrences within categories can becounted. Moreover, problems oftenexist in grouping objects into exclusiveclasses. As Muehrcke points out, the de-cision to put an object into a particularclass may be difficult to reach and maybe quite arbitrary at times.s Anotherquestion centers on whether there aremeasurement scales other than the fourabove. Psychologists have consideredvarious scales, such as difference,power, and logarithmic interval, whichlie between the ordinal, interval, andratio scales. Each of these is againassociated with a certain admissibletransformation. For difference, additionof a constant is admissible, i.e., f (x) =x + a; for power, exponentiation is ad-missible, i.e., f (x) = x"; and forlogarithmic interval, multiplication by aconstant and exponentiation are ad-missible, i.e., f (x) = axb .9

The general concept of measurementscales will remain important in manydisciplines, and the questions raisedtend to increase understanding of scal-ing rather than weaken the concept.The general concept, however, maynecessarily be modified when appliedto measurement problems in individualdisciplines; thus the field of cartographywould benefit from closely examiningthe concept within the practices of bothmapmaking and mapreading.

MEASUREMENT SCALES INMAPMAKING

The process of mapmaking requiresdata to be generalized and symbolized.

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TABLE 1. Transformation of Data Characteristics in the Cartographic Process

nominal

ordinal

interval/ratio

Dutil Presentedill .HaJJ COlltext

classed

categorized

categorized

noncategorizedisarithms

E,Hlllip(es of-'-tap SY'libol

point symbols of differentdesignslarge, medium and smallcircles (specific values notindicated)standardized circles (range ofvalues associated with each)graduated circlesisolines

,Hea:wremcllf S(:alefrolll .Hap SYlllbo(

nominal

ordinal

ordinal or modifiedintervallratiointervallratiointerval/ratio

The concept of measurement scales isuseful, as it provides a basis for relatingmap data to map symbolization. But inits application the concept is no longerpure and simple. There are at leastthree issues of interest at the mapmak-ing stage and they include the symbol-scale correspondence, combination ofscales, and the problems of nominalscale representation.

Correspondence Between MeasurementScale and Map Symbol

The concept of measurement scaleshas certainly enriched the discussion ofthe relationship between data types andmap symbols, but there is no one-to-onerelationship between measurementtype and the specific map symbol. Thisis particularly critical in the use of areasymbols for area and volume data.There is practically no distinctionbetween ordinal and interval/ratioscales as far as the use of area patterns isconcerned (see Table 1). Muehrckerecognizes this in his diagrams of dif-ferent scalings of map symbols andstates that:

The map reader will quickly recognize that visualdimensions which intuitively evoke images of themagnitude of the data, i.e., size, texture, value,and intensity, do not suffice in differentiatingbetween ordinal, interval, and ratio information... In order for the map-maker to employ in-terval scaling on a map it is necessary to resort tonumerical legend annotation or to incorporatenumerals into the map context itself, such as in the

Vol. 5, No.1, April 1978

case with temperature maps, contour maps and soforth. 10

Even assuming the presence of suchadditional cues, the designation ofmeasurement type is less than straight-forward in symbolization, and the prob-lem has to do with the generalizationthat is inherent in cartography.Generalization is applied to almostevery element of a map and quantitativedata are no exception. A commonmethod of generalization for quantita-tive data is classing, that is, groupinginto categories with each member of acategory being symbolized identicallyin the case of, say choropleth or grad-uated circle maps. As far as the mapis concerned, some of the original in-formation of individual values is lost inthis process and the data cannot be in-terval or ratio in the usual sense be-cause the property of known distancebetween any two values is no longerknown exactly and permissible opera-tions on the original set of data are nolonger applicable (see Table 1),

A unique situation is found withisarithmic maps. The process of classingis also involved in preparing isarithmicmaps, and the isarithm values on thesemaps are essentially class limits. Yet,due to the specific assumptions(smoothness and continuity) about thenature of the surface represented bysuch a map, the relative position of anyvalue within the class is retained withincertain error limits. Since essentially no

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loss of measurement information oc-curs, the interval or ratio scaling of theoriginal data is retained.

Combination of Measurement ScalesA thematic map may contain data that

are measured at two or more differentscales. For example, a map may showdistribution of city populations as wellas their racial composition inpercentages. Population sizes aremeasured on a ratio scale; compositioninvolves nominal differentiation ofraces and ratio scale percentages. Sucha map, therefore, represents a combina-tion of the nominal and ratio scales. It isprobably inconceivable, in fact, to havea map on which only one type of scale isapplicable. The concept of combinationof measurement scales was used byRobinson and Sale as the basis of dis-cussion of cartographic symbolismll andwas discussed by Chang.12 It is im-pOltant to emphasize, then, that it is notthe map, as one whole entity, to which ascale applies, but it is only the specificattributes represented on the map thatcan be so labeled.

Special Problems with Nominal ScaleSymbols

Equivalence is the property thatcharacterizes classes of nominal scaling.Since the property of a measurementscale must be considered in the designof map symbols, the question is then:How can the nominal scale property beshown on a map? Because they areequivalent classes, they should appearon the map with the same visual im-portance. In showing different land usecategories, for example, the mapmakershould select patterns such that nonewould visually stand out. This is adifficult task at best, and many times thearea patterns that are used can beranked visually. In the case of nominalscaling, there exists a straightforwardprinciple that is simply impracticalmuch of the time.

Another interesting aspect of nominal

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scale data in mapmaking was raised byRobinson, however. He asserted that, invarying the design of the nonnumericalsymbols, one is not only trying to obtaindata differentiation at a nominal scale,but,In many cases in general or reference cartography,and in most cases in thematic cartography, one isalso concerned with the relative significance orimportance of the particular items in the totalgraphic communication,I3

If data are assigned relative im-portance, then they no longer need toremain simply nominally-scaled but canassume at least an ordinal scale, thusfacilitating symbolization.

MEASUREMENT SCALES IN MAPREADING

The map-reading stage has beendescribed as a decoding process, and animplicit assumption made byMuehrcke, when he discussed conceptsof scaling from the map reader's point ofview, is that the process of map readingshould not alter the nature of the datamapped, i.e., the same type of measure-ment scale from the mapmaking stageshould still remain valid at the map-reading stage.14 His discussion,therefore, concentrated on aspects ofmeasurement scales which wereessentially important to the mapmaker,rather than the map reader.

Is it appropriate to assume that theconcept of measurement scales has thesame application to both the mapmakerand the map reader? The discussion inthe previous section has explained thatthe concept may be used as a frameworkin which data characteristics can beassociated with particular map symbols,although the association raises severalproblems. Can the concept again beused as a framework to assist the mapreader in receiving map information orto aid our understanding of the informa-tion received by readers? To answerthis question, the following discussionsfocus on the psychophysical relation-ship as related to map reading, the


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meaning of measurement scale in mapreading, and the problems of accuracyand consistency with responsesmeasured on an interval or ratio scale.

Psychophysical Relationship

The underlying framework in variousstudies of map perception dealing withquantitative symbols is the relationshipbetween stimulus and response. Stim-ulus (5) refers to the quantity repre-sented by a map symbol, and response(R) refers to the quantity perceived bythe map reader. The relationshipbetween 5 and R can, therefore, beexpressed R = f(5).

The relative value represented by astimulus should be equivalent to therelative numerical value used by themapmaker for symbolization. But since,generalization, such as classification ofvalues, is often practiced in mapmaking,even when the numerical values avail-able to the mapmaker can be measuredon an interval or ratio scale, the stim-ulus values presented to the map readermay convey the characteristics ofsomething between an ordinal and aninterval or ratio scale. On the otherhanel, if the mapmaker incorporates or-dinal or higher scaling to represent im-portance while mapping nominal data,then the map reader is presented withboth scales at once. In short, the type ofmeasurement for the expected responsevalues should be predetermined by thetype of measurement for the stimulusvalues.

Psychophysical studies in cartog-raphy have so far been limited to simplemap symbols, such as graduated circles,dots, and gray tones, and have beenconducted mainly under experimentalconditions, i.e., not concerned with realmap situations. A map showing multiplecomponents often involves combina-tions of measurement scales and usescomplex map symbols; therefore, thetransmission of this type of map in-formation is obviously more difficultthan that of single characteristics.Imagine the use of pie charts for show-

Vol, 5, No.1, April 1978

ing population size and racial composi-tion. Among the possible reader tasks isthe estimation of different percentageswithin the pie chart representing dif-ferent racial components and, at thesame time, comparison of thesepercentages between different loca-tions. \-Ve know from our ownexperience that in many cases the seg-ments within pie charts are so small thatestimation of them is nearly impossible,that we simply do not focus attention onsome of the information, and so on. Dataavailable to the map reader in the mapcontext are often different from data thathave been manipulated and symbolizedby the mapmaker. Thus we do notgenerally assume that the readerprocesses the full extent of quantitativeinformation encoded on the map.

The Meaning of Measurement Scale in MapReading

It is important to assess the meaningof measurement scale with respect tothe response values, i.e., from the mapreader's point of view. If information ona map is nominal in scale, the reader isat least implicitly expected to dif-ferentiate map symbols; if ordinal scale,to rank map symbols according to suchrelations as "greater than" or "lessthan;" if interval scale, to interpret theinterval or distance between mapsymbols; and if ratio scale, to derive theratio between map symbols and to baseestimation of map symbol characteris-tics on an "absolute zero."

Of the four measurement scales, thenominal scale should be one of theeasiest from the map reader's point ofview. After all, if a map is carefullydesigned and executed, the map readershould be able to differentiate mapsymbol kind. This may not be such astraightforward task, however, if all themap symbols are of the same visual im-portance, and as mentioned earlier,higher order characteristics are oftenutilized to aid in distinction. At any rate,if the map reader fails to make nominal

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distinctions, the map would beconsidered a failure in map communica-tion.

The ordinal scale involves ranking ofmap symbols and this is probably themost readily performed observation of amap reader. We might describe one paltof a dot map as appearing to have moredots or higher density than another part.Also, we might describe a map in whichgraduated circles are used to show a dis-tribution of population sizes and saythat Circle A appears to be larger thanCircle B and Circle B appears to belarger than Circle C. Such responses in-volve an ordinal scale and can usuallybe considered as part of normal mapreading. However, there are studieswhich point out the limitations of ourability to differentiate small differencesand advise built-in corrections to allowthe perception of ordinally scaled data.Meihoefer, for example, uses themethod of noticeable differences in hisstudy of graduated circles and suggestsa series of noticeably different-sizedcircles to represent sequences ofvalues.15 Also, it is generally acceptedby cartographers that the use of dif-ferent shades of gray, through pre-printed area pattems, should be limitedto six or seven on an isoplethic or choro-plethic map, if their differentiation and,thus, ranking is to be assured.16

Conceming the higher level intervaland ratio scales, we know from experi-mental studies that at least whendirected to do so, persons can assignvalues to symbols that take on moreexactness than simple ranking. Al-though the process of assigning valuesis not clearly understood, we mayspeculate about it from available stud-ies. It seems reasonable to assume thatordinal ranking is usually performedprior to the assignment of interval andratio values. Suppose that, in an experi-mental situation, we are asked to esti-mate the values represented by circleson a test map, using a medium-sizedcircle as the key. We will most likelycompare circles to be estimated with

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the key circle (in terms of greater thanor smaller than) before assigning a valueto it. In other words, ordinal ranking is anecessary part of the conception ofhigher order value. Following this prin-ciple, higher order values can be betterestimated if more than one key circlewere included in the legend, becausethese circles can serve as upper and/orlower limits for estimation. Chang's ex-periments with the estimation ofgraduated circles supported this asser-tion.17 The assignment of value sub-sequent to the initial ranking is a morecomplex task and should perhaps beconsidered as something beyondnormal map reading; the map readermust distinctly pause and think beforeproducing a particular value. Psycholo-gists apparently believe that the value islikely to be reached based on the ratio(of a ratio scale) between the estimatedcircle and key circle, rather than thedistance (of an interval scale) betweenthem.ls

Nominal and ordinal scale responses,then, seem to be inherent in map read-ing and response values on interval andratio scales can be obtained at leastunder experimental conditions. A majorconcem of accuracy and consistencystill remains and deserves brief atten-tion.

Problems of Accuracy and Consistency

The problems of accuracy and con-sistency in the estimation of graduatedcircles are well documented in theliterature.19 The estimation of graduatedcircles can be examined within theframework of the psychophysical rela-tionship. Both cartographers andpsychologists express the relationshipbetween the physical size (5) and theapparent (response) size (R) ofgraduated circles in the form of Stevens'power law, R = k511

, where k is aconstant and n is the exponent.20 Thenature of the relationship is, however,affected by two important factors. First,the relationship is generally applied atthe group level, i.e., the R value in the


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equation is some central tendencymeasure for a group of responses. Whenexamined at the individual level, Rvalues vary greatly. Secondly, the ex-ponent value in the equation is not sta-ble because it can be influenced bysuch factors as the range of stimulusvalues, the position of the standardsymbol within the stimulus range, andthe testing method.21 The wide varia-tion in individual responses and the in-stability of the exponent are examples ofproblems of accuracy and consistency.They suggest that interval and ratioscalings applied to the response valuesneed to be viewed differently thanthose applied to the stimulus values byintroducing error terms, as well as theexponent for the nonlinearity, into ad-missible operations, e.g., for ratio re-sponses, f{x) = axb + e 1 + e2 ... , wherex is the value represented.

SUMMARY

The concept of measurement scaleshas been examined as it is involved indifferent stages of the cartographicprocess. It seems to be most useful atthe data collection stage in distinguish-ing different types of data to be mapped.At the stage of cartographic symboliza-tion, the mapmaker generally associatesdata types with map symbol characteris-tics. The application of the concept atthis stage is, however, complicated bythree factors: There is no one-to-onerelationship between measurementtype and map symbol, combinations ofmeasurement scales are frequently in-corporated into complex map symbols,and data of nominal scaling are oftentransformed to that of ordinal scaling inmapping.

Map reading of quantitative symbolscan be examined in terms of psy-chophysical relationships. The mapreader is often presented with data inthe map context that have beenprocessed and manipulated by themapmaker. It seems reasonable toassume that nominal and ordinal scaleobservations are an inherent part of the

Vol.5,No.I,AprilI978

"normal" map-reading process.Responses on interval and ratio scalescan at least be obtained under specificinstructions in experimental situations.Such response values, however, haveinherent problems of accuracy andconsistency.

REFERENCES

1. Nunnally, Jim C., Introduction to Statisticsfor Psychology and Education, McGraw-Hili,New York, (1975), p. 19.

2. Stevens, S. S., "Mathematics, Measurement,and Psychophysics," in S. S. Stevens (ed.), Hand-book of Experimental Psychology, Wiley, NewYork, (1951).

3. Siegel, Sidney, Nonparametric Statistics,McGraw-Hili, New York, (1956).

4. For example, see Cole, John P. and C. A. M.King, Quantitative Geography, Wiley, New York,(1968); and King, Leslie J., Statistical Analysis inGeography, Prentice-Hall, Englewood Cliffs,N.J., (1969).

5. Robinson, Arthur H. and Randall D. Sale,Elements of Cartograph~/, 3rd ed., Wiley, NewYork, (1969).

6. Muehrcke, Phillip C., Thematic Cartog-raphy, Commission on College E;eography,resource paper no. 19, Association of AmericanGeographers, Washington, D.C., (1972); Chang,Kang-tsung, "Data Differentiation andCartographic Symbolization," The CanadianCartographer, 13 (1976),60-68.

7. For example, see Hammond, Robert andPatrick McCullagh, Quantitative Techniques inGeography: An Introduction, Oxford UniversityPress, London, (1974). Throughout the text, non-parametric statistical methods are treated equallywith and, in many cases, emphilsized overparametric statistical methods.

8. Muehrcke, Phillip c., "Concepts of Scalingfrom the Map Reader's Point of View," TheAmerican Cartographer, 3 (1976),123-141.

9. Marks, Lawrence E., Sensory Processes: TheNew Psychophysics, Academic Press; New York,(1974),244-249.

10. Muehrcke, op. cit. (footnote 8),131.11. Robinson and Sale, op. cit. (footnote 5).12. Chang, op. cit. (footnote 6).13. Robinson, Althur R., "Scaling Nonnu-

merical Map Symbols," Proceedings of theAmerican Congress on Surveying and Mapping,(1968),213.

14. Muehrcke, op. cit. (footnote 8).15. Meihoefer, Hans-Joachim, "The Utility of

the Circle As An Effective Cartographic Symbol,"The Canadian Cartographer, 6 (1969), 105-117.

16. Robinson and Sale, op. cit. (footnote 5), 257.17. Chang, Kang-tsung, "A Psychophysical

Study of Quantitative Point Symbols,"unpublished master's thesis, Graduate School of

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Geography, Clark University, (1969).18. Psychologists usually instruct the subject in

a magnitude estimation experiment to derive anestimate based on the ratio between a circle andthe standard symbol. For example, given the sizeof the standard symbol as "100," they will instructthe subject that "if a circle appears twice as largeas the standard, call it '200'; if it appears one-fourth as large, call it '25.''' Interval estimation,on the other hand, is not well understood in psy-chophysics. Mark and Cain found from an experi-ment on interval estimation that numerical esti-mates of perceptual intervals were not propor-tional to intervals between magnitude estimatesof the same circles and suggested that this wasdue to ambiguity between intervals and ratios. Asimilar finding was also reported by Dawson. SeeMark, Lawrence E. and VVilliam S. Cain, "Percep-tion of Intervals and Magnitudes for ThreeProthetic Continua," journal of Experi.mentalPsychology, 94 (1972),6-17; and Dawson, W. E.,"Magnitude Estimation of Apparent Sums and

• Directory of Soviet Geographers. A new Di-rector!! of Soviet Geographers, (includingcmtographers, with 3,000 entries, giving fullname, education, professional speCialty, and insti-tutional affiliation, has been compiled by Theo-dore Shabad, editor of Soviet Geography. The100-page reference work, based on biographicalinformation published in Soviet sources, is anexpanded revision of a directory first published in1967. In the absence of an official directorypublished in the U.S.S.R., this is the onlycomprehensive listing of professional informationabout Soviet geographers. Regular subscriberswill receive the directory as the September 1977issue of Soviet Geography. Extra copies can beobtained at the price of $13.50 fi'OITI:Scripta Pub-lishing Co., 1511 K St., N.W., Washington, D.C.20005. [Source: T. Shabad]• Archives Publications. Some recent publica-tions of the National Archives and RecordsService:Cartographic Records of the Bureau of Indian Af-

fairs (Special List 13), compiled by Laura E.Kelsay. Washington: National Archives andRecords Service, 1977. 187 pp. Issued originallyin 1954. This work has been extensively revisedand expanded. It describes some 40,000 mapsprepared by the Bureau of Indian Affairs fromits establishment within the War Department in1824 to about 1967.

Agricultural Maps in the National Archives of theUnited States Ca. 1860-1930 (Reference In-formation Paper No. 75), compiled by William J.

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Differences," Perception and PS[fchoph!!sics,9 (1971), 368-374.

19. For example, see IvlcCleary, George F., "Be-yond Simple Psychophysics: Approaches to theUnderstanding of Map Perception," Proceedingsof the American Congress on Surveying and Map-ping, 30th Annual Meeting, Washington, D.C.,(1970), 189-209; Cox, Carleton W., "Anchor Ef-fects and the Estimation of Graduated Circles andSquares," The American Cartographer, 3 (1976),65-74.

20. Stevens, S. S., "On the PsychophysicalLaw," PS[fchological Review, 64 (1957), 153-181.

21. Marks, op. cit. (footnote 9), 36-38; Stevens,S. S., Ps!!chophysics, Wiley, New York, (1975),281-283; Baird, J. C., Psychophysical Analysis ofVisual Space, Pergamon Press, New York, (1970),48-60; MacMillan, N. A., C. F. Moschetto, F. M.Bialostozky, and L. Engel, "Size Judgment: ThePresence of a Standard Increases the Exponent ofthe Power Law," Perception and P";~/chophysiGs,16 (1974),340-346. •

Heynen. Washington: National Archives andRecords Service, 1976. 25 pp. This is a generalintroduction to maps in the National Archivespeltaining to agriculture and related topics,such as rural land use, vegetation, and climatefrom about 1860 and 1930. Copies of both ofthese publications may be obtained uponrequest by wliting to Ralph Ehrenberg, Direc-tor, Cartographic Archives Division, NationalArchives and Records Service, \Vashington,D.C. 20408.

Prologue: The Journal of the National Archives(Fall 1977) Vol. 9, No.3. This entire issue is de-voted to the history of caltography and containsthe following articles: "Taking the Measure ofthe Land," by Ralph E. Ehrenherg; "Now andThen: Comparisons of OrdinalY Americans'Symbol Conventions With Those of PastCartographers," by Denise Wood; "The Maps,Plans, and Sketches of Herman Ehrenberg," byDiane M. T. Hose; "Revolutionary WarMapmakers," by Peter .T. Guthorn; and "Noteson [Cmtographic] Genealogy," by Gary L.Morgan. Copies of this issue are available for$2.50 from Publication Sales Branch, NationalArchives and Records Service, Washington,D.C. 20408. Check or money order should bemade payable to National Archives Trust Fund(NEPS). [Source: Halph E. Ehrenberg]

• News Briefs are compiled by Mary Clawson ofthe Cmtography Division Cartographic Informa-tion Service and by other contributors.


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Geography, Clark University, (1969).18. Psychologists usually instruct the subject in

a magnitude estimation experiment to derive anestimate based on the ratio between a circle andthe standard symbol. For example, given the sizeof the standard symbol as "100," they will instructthe subject that "if a circle appears twice as largeas the standard, call it '200'; if it appears one-fourth as large, call it '25.''' Interval estimation,on the other hand, is not well understood in psy-chophysics. Mark and Cain found from an experi-ment on interval estimation that numerical esti-mates of perceptual intervals were not propor-tional to intervals between magnitude estimatesof the same circles and suggested that this wasdue to ambiguity between intervals and ratios. Asimilar finding was also reported by Dawson. SeeMark, Lawrence E. and VVilliam S. Cain, "Percep-tion of Intervals and Magnitudes for ThreeProthetic Continua," journal of Experi.mentalPsychology, 94 (1972),6-17; and Dawson, W. E.,"Magnitude Estimation of Apparent Sums and

• Directory of Soviet Geographers. A new Di-rector!! of Soviet Geographers, (includingcmtographers, with 3,000 entries, giving fullname, education, professional speCialty, and insti-tutional affiliation, has been compiled by Theo-dore Shabad, editor of Soviet Geography. The100-page reference work, based on biographicalinformation published in Soviet sources, is anexpanded revision of a directory first published in1967. In the absence of an official directorypublished in the U.S.S.R., this is the onlycomprehensive listing of professional informationabout Soviet geographers. Regular subscriberswill receive the directory as the September 1977issue of Soviet Geography. Extra copies can beobtained at the price of $13.50 fi'OITI:Scripta Pub-lishing Co., 1511 K St., N.W., Washington, D.C.20005. [Source: T. Shabad]• Archives Publications. Some recent publica-tions of the National Archives and RecordsService:Cartographic Records of the Bureau of Indian Af-fairs (Special List 13), compiled by Laura E.Kelsay. Washington: National Archives andRecords Service, 1977. 187 pp. Issued originallyin 1954. This work has been extensively revisedand expanded. It describes some 40,000 mapsprepared by the Bureau of Indian Affairs fromits establishment within the War Department in1824 to about 1967.

Agricultural Maps in the National Archives of theUnited States Ca. 1860-1930 (Reference In-formation Paper No. 75), compiled by William J.

64

Differences," Perception and PS[fchoph!!sics,9 (1971), 368-374.

19. For example, see IvlcCleary, George F., "Be-yond Simple Psychophysics: Approaches to theUnderstanding of Map Perception," Proceedingsof the American Congress on Surveying and Map-ping, 30th Annual Meeting, Washington, D.C.,(1970), 189-209; Cox, Carleton W., "Anchor Ef-fects and the Estimation of Graduated Circles andSquares," The American Cartographer, 3 (1976),65-74.

20. Stevens, S. S., "On the PsychophysicalLaw," PS[fchological Review, 64 (1957), 153-181.

21. Marks, op. cit. (footnote 9), 36-38; Stevens,S. S., Ps!!chophysics, Wiley, New York, (1975),281-283; Baird, J. C., Psychophysical Analysis ofVisual Space, Pergamon Press, New York, (1970),48-60; MacMillan, N. A., C. F. Moschetto, F. M.Bialostozky, and L. Engel, "Size Judgment: ThePresence of a Standard Increases the Exponent ofthe Power Law," Perception and P";~/chophysiGs,16 (1974),340-346. •

Heynen. Washington: National Archives andRecords Service, 1976. 25 pp. This is a generalintroduction to maps in the National Archivespeltaining to agriculture and related topics,such as rural land use, vegetation, and climatefrom about 1860 and 1930. Copies of both ofthese publications may be obtained uponrequest by wliting to Ralph Ehrenberg, Direc-tor, Cartographic Archives Division, NationalArchives and Records Service, \Vashington,D.C. 20408.

Prologue: The Journal of the National Archives(Fall 1977) Vol. 9, No.3. This entire issue is de-voted to the history of caltography and containsthe following articles: "Taking the Measure ofthe Land," by Ralph E. Ehrenherg; "Now andThen: Comparisons of OrdinalY Americans'Symbol Conventions With Those of PastCartographers," by Denise Wood; "The Maps,Plans, and Sketches of Herman Ehrenberg," byDiane M. T. Hose; "Revolutionary WarMapmakers," by Peter .T. Guthorn; and "Noteson [Cmtographic] Genealogy," by Gary L.Morgan. Copies of this issue are available for$2.50 from Publication Sales Branch, NationalArchives and Records Service, Washington,D.C. 20408. Check or money order should bemade payable to National Archives Trust Fund(NEPS). [Source: Halph E. Ehrenberg]

• News Briefs are compiled by Mary Clawson ofthe Cmtography Division Cartographic Informa-tion Service and by other contributors.


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