15
This article was downloaded by: [Queensland University of Technology] On: 06 November 2014, At: 14:11 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Ergonomics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/terg20 Explicit and Implicit Tabulation Formats PATRICIA WEIGHT a & KATHRYN FOX a a Applied Psychology Unit, Medical Research Council , 15 Chaucer Road, Cambridge, England Published online: 27 Mar 2007. To cite this article: PATRICIA WEIGHT & KATHRYN FOX (1972) Explicit and Implicit Tabulation Formats, Ergonomics, 15:2, 175-188, DOI: 10.1080/00140137208924422 To link to this article: http://dx.doi.org/10.1080/00140137208924422 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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Page 1: Explicit and Implicit Tabulation Formats

This article was downloaded by: [Queensland University of Technology]On: 06 November 2014, At: 14:11Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

ErgonomicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/terg20

Explicit and Implicit Tabulation FormatsPATRICIA WEIGHT a & KATHRYN FOX aa Applied Psychology Unit, Medical Research Council , 15 Chaucer Road, Cambridge, EnglandPublished online: 27 Mar 2007.

To cite this article: PATRICIA WEIGHT & KATHRYN FOX (1972) Explicit and Implicit Tabulation Formats, Ergonomics, 15:2,175-188, DOI: 10.1080/00140137208924422

To link to this article: http://dx.doi.org/10.1080/00140137208924422

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Explicit and Implicit Tabulation Formats

ERGONOMICS, 1972, VOL. 15, No.2, 175-187

Explicit and Implicit Tabulation Formats

By PATRICIA WRIGHT and KATHRYN FoxMedical Research Council, Applied Psychology Unit,

15 Chaucer Road. Cambridge, England

Five studies are reported of performance with currency conversion tables basedon two alternative principles of tabulation. In a simulated shopping situationthere was an initial speed advantage for the table which explicitly listed all pairsof equivalent prices. The other table, which gave conversions of shillings separatelyfrom the conversion of pence, was not only slower to use, it was more often incorrectlyused. Data from a modified Market. Survey technique showed that many of thegeneral public incorrectly used this more difficult 'implicit' format even whengiven an illustrative example. Presenting school children with both numerical andnon-numerical tables indicated that the difficulty of the implicit format was notcaused by the mental arithmetic involved. although it was associated with corn­bining separate items of information. Juxtaposition of the items was more easilyachieved than a synthesis.

1. IntroductionInformation is displayed in tabulated form in a wide variety of situations,

both in the working environment and outside it (cf Wright and Fox 1970) butvery little is known about the optimal design of tabulation formats. Indeedto casual observation it often appears that the major criterion used in designinga table has been economy of space. Experiments reported by Wright (1968)showed that economy of space was sometimes bought at the cost of the easewith which the table could be used; for example, highly compact matrix formatswere found difficult for some people to understand. The present experimentspursue another of the comparisons reported by \Vright, namely that peoplewere able to find information within a conversion table more rapidly when thetable was designed so that the user had to search through a list of 100 pairs ofconversions, rather than when they had to search through two much shorterlists and add the results of .lfaQI!, search. The first of these formats -will betermed' explicit' since it provides the user with the information that he wantsdirectly, requiring nothing but a search process. The second type of tablewill here be termed' implicit' since although the same information is potentiallyavailable to the user it is no longer directly available and requires additionalwork on the part of the person making the conversion.

The difference in speed of use between these two types of table was found tobe initially in the order of 1 second per conversion in the previous pencil andpaper tests, but with a little practice the difference between the tables ceasedto be statistically significant. These findings are probably validly applicableto tables being used in clerical situations, but it seemed conceivable that such asmall initial difference might turn out to be of little practical importance inthose conditions where a multiplicity of other factors require the subject'sattention. For example, a one second difference between two conversiontable formats might cease to be of consequence in the context of a shoppingsituation, where numerous distractions and time consuming activities, such as

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176 Patricia Wright and Kathryn Fox

looking for and handling merchandise, would affect performance by muchmore than this. Moreover the ideal conversion table for shoppers would be assmall a table as practicable. Perhaps it would be premature to reject theschematic table at this stage solely on the previous data.

Nevertheless it is also conceivable that a table found slightly more difficultunder relatively ideal working conditions, where distractions are minimal,would appear appreciably more difficult as the complexity ofthe task increased.If this should be the case, then the practice effects obtained in the previouspencil and paper tests might no longer be found. That is to say, if differenttest conditions enhance the difficulty of the implicit format, it is possible thatthis difficulty will not disappear with practice. Therefore Experiment I wasdesigned to examine performance with these two tables in simulated shoppingconditions.

2. Experiment 1

2.1. Method

2.1.1. Apparatus

Subjects were given a 24 item shopping list and' shopped' in a miniaturesuper-market, which displayed real merchandise in three tiers along four 6 mcounters. Subjects were each given one of the conversion tables shown inFigure 1, the actual size of the tables being 8·3 em x 9·7 em. These tableshad been duplicated by a photo reproductive process which reduced typewrittenoriginals to two-thirds of their initial size.

Half the price tickets in the shop showed as conversions amounts which didnot correspond to those on a conversion table; e.g. a ticket might show5p ... Illd, whereas the table gave 5p ... 1/-.

The prices which corresponded to the 24 items on the shopping list coveredthe range Id to 10/- with each l d price point occurring twice (in combinationwith different shilling amounts) and each of the shilling values occurring atleast twice. The merchandise was arranged systematically in the shop sothat successive items on the shopping list could be collected in a single tour ofthe counters. The tickets, used on an initial practice list, had no prices buteither a black or white band down the centre of the tickets.

As well as the shopping list and conversion table, subjects were also given awire basket such as is normally used in supermarkets. This basket had beenpartitioned in the centre, with one section made distinctively white and theother distinctively black.

A 50 item mental arithmetic test was prepared. This test consisting ofproblems such as: 48 + 16 - 9 =.

2.1.2. Subjects

Nine men and 55 women within the age range 15 to 67 took part in theexperiment. They were all employees of Marks and Spencer, Birmingham,either cleaners, canteen staff or sales assistants. Thirty-two people workedwith the explicit table, another 32 with the implicit table. All were unpaidvolunteers.

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Explicit and Implicit Tabulation Formats 177

FIgure 1. (a) Errrplicif pocket table.

Old New Old News d Pence s d Pence

Id ip u:a 51'2d 11' 2/-d lOp3d 11' 3/-d 15p

4<1 lip5d 21' 4/-<1 201'

6d 2~p5/-d 25p

7d 31'6/-d 30p

8<1 3!p 7/-d 351'9<1 41' 8/--<l 401'

10d 41' 9/--<l 45p11d 4~p

u-« 51' 10/-d 50p

I/ 1d 5~p

1/2d 6p1/3d 6p

1/4d 6ip1/·5d 7p1/0d 7ip

l/7d 81'1/8d 8ip1/9d 91'

I110d 91'I/11d 9ip

2/--<l 101'..

Old New Old New

I

Old New Old New Old Newe <I Penco sd Pence a d Pence s d Pence s d Pence

1<1 ip 2/1d lO~p 4/ 1<1 20ip 0/1<1 aOip 8/1d 40ip2<1 II' 2/2<1 III' 4/2d 211' °/2d 311' 8/2d 411'3d II' 2/a<l 111' 4/ a<l 211' 6/3d all' 8/ad 411'

4<1 Ijp 2/4p 11II' 4/41' 214p 6/4<1 31ip 8/4d 41ip5<1 2p 2/5'1 121' 4/ 5d 22p 615d 321' 8/5<1 421'0<1 2!p 2/6d 12ip 4/6<1 224p 6/6<1 32ip 8/6d 42!p

7d 3p 2/7<1 131' 4{7<1 2ap 6/7'1 331' 8/7d 43p8d 3ip 2/ 8<1 13!p 4/8d 2311' 0{8d 3311' 8/8d 4311'9d 41' 2/ 9<1 141' 4/91' 241' 6/9<1 341' 8/9d 44p

10d 41' 2/10d 141' 4/ 10,1 24p 6/10d 341' 8/10d 441'11<1 4ip 2{11<1 14ip 4/ 1l d 24~p 6/11d a4!p 8/ 11d 44~p

I/-d 51' 3{-<I Hlp 5/-<1 251' 7/-d :{5p 9/-d 45p

1/1<1 5ip 3/1d H)~p 5/1d 25ip 7/1d 35tr 9/1d 4511'1/2<1 61' 3/2,1 16p 5{2<1 261' 7/2d :J6p ll/2d 461'1/3<1 01' 3/ 3<1 16p .5/3<1 26p 7/3d a6p 9/3<1 46p

1/4<1 6~p 3/4d 16ip 5/4<1 2611' 7/4d 36!p 9/4d 46ip1/5<1 71' 3/ 5d 17p 5/5d 271' 7/,;d 371' 9/·5<1 471'1/6d 7ip 3/ 6d 1711' 516d 2711' 7/6<1 37ip 9/6d 47·11'

1/7d 81' 3/7d 181' 5/7<1 281' 7/7d 38p !l/7<1 481'1/8d 8!p 3/8d 18!p 5/8d 28~p 7/8d 38!p 9/8d 4811'1/9d 91' 3/ 9d 191' ';/!hl 20p 7/9d 391' 9/9d 491'

1/10<1 IIp 3/10d 191' 5/10d 29p 7/ 10d 391' 9/10d 4!lpI/ 11d 911' 3/11<1 19!p 5/1ld 29~p 7/11d 39!p ll/l1d 49!p

2/--<l 101' 4/-<1 201' 6/-<1 301' 8/-<1 401' 10/-<1 501'

Figure 1. (b) Explicit pocket table.

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178 Patricia Wright and Kathryn Fox

2.1.3. Procedure

Before starting the experiment everyone did the mental arithmetic test.The number of correct answers obtained in 2 minutes provided a rough indexof each individual's numerical ability. This test was followed by a practiceshopping trial in which subjects were required to collect the items listed on ashopping list, putting them in the white section of the wire basket if there wasa white stripe on the ticket and in the black section if the stripe was black.The time taken on this practice list corresponded to the time taken up by thehum-drum aspects of the experimental task such as reading the shopping list,looking for the merchandise, etc.

The practice trial was followed by five experimental trials. On each experi­mental trial subjects collected the items on the shopping list, checked theaccuracy of the conversion shown on the price ticket against that shown onthe conversion table, putting merchandise in the white section of the basketwhen the price ticket was correct and in the black side when the ticket wasincorrect. The time to complete each trial and the number of items not inthe appropriate side of the basket were noted.

2.2. Results

The data from 5 subjects were discarded because these subjects were notusing the table correctly, or were not following the designated experimentalprocedure. This was evident from their error rates and confirmed in laterdiscussion with the subjects. All 5 had been given the implicit table.

Using the data from the arithmetic test and the practice trial it was possibleto form two matched groups each numbering 23 persons. All results discussedbelow refer to these matched groups. The average times taken for each trialare shown in Figure 2.

E~ 650~

J!- 600z-c

'"}. 550v"'8 500

...--Implicit pockettable

lsr 2nd 3rd 4 th

Successive shoppinq lists

450i \"\\~.~ 400 'a." -.lU Explicit pocket..-::-....o ..... ""'x.§ table .....'" 350 ''00'

~

'"s

Figure 2. Average trial times using explicit and implicit pocket tables.

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Page 6: Explicit and Implicit Tabulation Formats

Explicit and Implicit Tabulation Formats 179

Statistical analysis, using Student's related t-test indicated that the per­formance of those using the explicit table was significantly faster on trial 1(p < 0'01), trial 2 (p < 0,02), and trial 3 (p < 0,05) but the difference was notstatistically significant on trial 4. Errors, apart from those made by peopleexcluded from the main analysis of results, were too few to be amenable tostatistical treatment.

2.3. DiscussionThese results do not give full support to either of the alternatives proposed

in the introduction. The faster performance with the explicit table is stillclearly evident, and indeed the initial difference between the tables has grownfrom 1 second per conversion in the previous pencil and paper tests to nearly6 seconds per conversion in the present study. However the advantage ofthe explicit format again disappeared with practice. This suggests that it isnot inevitable that performance with the implicit table should be slower thanwith the explicit table, but rather there is an initial handicap that has to beovercome by those using the implicit format.

It seems plausible to suggest that anything slowing down the time taken tolocate items within the explicit format will tend to shorten the amount ofpractice necessary before the two tabulation schemes can be used with compar­able dexterity. One way of lengthening the search time is to increase a numberof items in the table. So far, the studies have used explicit tables listing only100 or 120 pairs of conversions. Giving all 240 price points from Id to £1would double the size of the explicit table, while the implicit table would beincreased by only 30% to cover a similar price range.

In addition, the search task may become slower as the physical size of thetable increases, since with larger tables, more than just eye movements arerequired of the user as he scans through the various columns. It is thereforeconceivable that the implicit format might be preferable for large wall chartsalthough it was not ideal for small desk or pocket tables. Consequentlyperformance with implicit and explicit wall charts is examined in Experiment 2.

3. Experiment 23.1. J1fethod3.1.1. Apparatus

Another, essentially similar shop, was set up. This time a wall chart givingall conversions from Id to £1 was displayed in the shop at a height of 2 m fromthe floor. The dimensions of the explicit table were 1·73 m x 0·71 m and ofthe implicit table were 0·46 m x 0·76 m , and the numerals within the tablewere 12·7 mm high. Divided wire baskets were again used.. The arithmetic test was modified slightly so that arithmetic operations were

always carried out in the same order for each problem. The first two numberswere added and the third subtracted.

3.1.2. SubjectsSeventy-nine people took part in the experiment. They were all Sainsbury's

employees, either factory staff or trainee sales assistants. Forty-five peopleworked with the implicit wall chart, ::14 with the explicit wall chart. All wereunpaid volunteers.

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Page 7: Explicit and Implicit Tabulation Formats

180 Patricia Wright and Kathryn Fox

3.1.3. Procedure

The procedure corresponded with that used in Experiment I, with the minordifference that in order to help people find the merchandise, each ticket hadone of six background colourings, and these colours matched the colour of theshopping list on which that particular item was listed.

3.2. Results

The data from 12 subjects were discarded because they were either notusing the wall chart correctly, or were not following the designated experimentalprocedure. Of these people, 11 had been working with the implicit wall chart,only 1 had used the explicit wall chart.

The data from the arithmetic test and the practice trial, again made itpossible to form two matched groups, each numbering 23 persons. As inExperiment 1, the results discussed below apply only to these matched subjects.Thc average times taken for each trial are shown in Figure 3.

Statistical analysis was carried out using Student's related t-test and indicatedthat the performance of those using the explicit table was significantly fasteron trial 1 (p < 0·01), trial 2 (p < 0,02), but the difference was not significant ontrials 3 and 4. Again errors were too few to permit statistical treatment.

E~ 650 x~

\""" wo u

"S? 600 --chartr:c

"! 550v~ x0v 500E

'\ \.;; 450c \0u ExpIIClt---\~c 400 wall chart 0,,,-,

" ••••x~

l 350'0",_

" ,0-

.~

.!i 300

'0-c lst 2nd 3rd 4th

Successive shoppinq lists

F'iguro a. Average trial times using explicit unci implicit wall charts.

3. i3. Discussion

Thc results of the comparison using wall charts are similar to those of]~xpcriment 1 where pocket tables were used. Again performance is muchfaster with the explicitformat (it is again about 6 seconds per conversion) but,after slightly less practice than before, the difference between the tables ceasesto be significant. Clearly the initial difficulty with the implicit format is avery robust phenomenon.

It is possible that one of the difficulties associated with using the implicitformat comes from presenting the information in two vertical columns. This

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Explicit and Implicit Tabulation Formats 181

means that the user has to add horizontally numbers such as 35 +4t. Probablysuch arithmetic additions are more easily performed if the figures to be addedare arranged vertically. For example: 35

4t

This can be approximated within the implicit table by having the two columnsarranged horizontally, so that to locate an item one searches horizontally alonga row of figures rather than as previously searching vertically down a column.After finding both the shillings and the pence amounts, the number from thetop row is added to the value in the bottom row, although it is true that perfectalignment of the numbers will be the exception rather than the rule. Experi­ment 3 compares how easily horizontal and vertical arrangements of theimplicit table can be used.

4. Experiment 3

4.1. Method

4.1.]. Apparatus and procedure

The procedure was identical to that used in Experiment 2, only the con­version tables were changed. In Experiment 3 both conversion tables wereimplicit, one arranged vertically like that shown in Figure 1, the other arrangedhorizontally, as in Figure 4 but with the prices 1/- to 20/- all on one row.

Shillings

New Pence

Old Pence

New Pence

Shillings

1/- 2/-

.51' 101'

Id 2d

II' II'

12/- 13/- 14/-

3/- 4/- 5/-

151' 201' 251'

3d 4d 5d

II' III' 21'

15/- 16/- 17/-

6/- 7/- 8/-

301' :151' 401'

6d 7d 8d

211' 31' 311'

18/- I ~/- 20/-

~/- 10/- 11/-

451' 501' 551'

9d 10d lid

41' 41' 411'

New Pence GOp 65p 70p

Old Pence I/-d I/Id 1/2d

751' 801' 8.51'

1/3d 1/4d 1/5d

~Op 951' 1001'

1/6d 1/7<1 1/8<1 l/9d 1/IOd I/lld

New Pence fip 5~p Ilp Up 6~p 7p 711' 81' 811' ~p ill' Hlp

Figure 4. Horizontal arrangement of implicit table.

4.1.2. Subjects

Eighty-four people took part in the experiment from the same subjectpopulation as Experiment 2. Thirty-nine people worked with the horizontaltable, 45 with the vertical table; the subjects using the vertical table were thesame group as in Experiment 2, but in this case a different' matched' subsetof 23 subjects was selected from this group, although the data from] 9 subjectswere included in the analysis of both Experiment 2 and Experiment 3.

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182 Patricia Wright and Kathryn Fox

4.2. Results

The data from 18 subjects were discarded because they were not using thetable correctly, or were not following the designated experimental procedure.Of these people 11 had been shown the vertical table, and 7 the horizontal table.

Again using the mental arithmetic test and the practice trial it was possibleto form two matched groups, each numbering 23 persons. The average timestaken for each trial are shown in Figure 5.

Statistical analysis using Student's related t-test indicated that on each ofthe four trials the differences between the tables could be due to chance(p > 0,05).

E~

3 650..s>-f: 600~

~

!U 550.!10u

500E.;; -,~ 4500u5(

5 400~

Vertical implicit x~xE

~ 350 wall chart ~"'o

o-

"~ 300>« I,t 2nd 3rd 4thSuccessive shopping lists

Figure 5. Average trial times using an implicit wall chart arranged either horizontally orvertically.

4.3. Discussion

Clearly the data do not support the expectation that a horizontal layoutwould be preferable for the implicit table. Probably the considerable distancebetween amounts such as 19/- and 4d lessen any advantage that there mightbe for the horizontal arrangement. The only other way by which the initialslowness associated with the implicit format might be overcome would seemto be through the use of instructions, and this is examined in the nextexperiment.

But one other aspect of the data deserves comment at this point. So farthe major data analysis has been confined to the times taken to collect specifiedmerchandise on relatively error-free trials. In all three experiments it hasbeen necessary to discard the data from some subjects because their abnormallyhigh error rates suggested that they were not following the designated experi­mental procedure. For example a few subjects insisted on sorting the mer­chandise into the wire baskets on the basis of whether or not they thoughtthat it was good value for money, ignoring the conversion element altogether.

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Explicit and Implicit Tabulation Formats 183

It might be expected that such behaviour would occur randomly in allconditions, but in fact the number of subjects dropped from those workingwith the explicit table was 0 in experiment 1, and only 1 of the 34 subjectsin Experiment 2 (mean discard rate was therefore 1·5%); whereas when peoplewere working with the implicit format, 5 of the 32 subjects in Experiment 1were dropped, 11 of the 45 in Experiment 2, and 7 of the 39 in Experiment 3where the horizontal arrangement was used (mean discard rate 19·8%). Thissuggests the high error rates were not due simply to misunderstanding theexperimental procedure, but that they reflect a difficulty in understanding theconversion table. Discussion with some of these people after the experimentsuggested that they often tended to round prices to the nearest whole shilling,i.e. 4/9d would be treated as 5/-, and then reference was made only to theshillings part of the conversion table. It often became clear in conversationthat people carried out such rounding because they were uncertain how tocombine the shillings and pence amounts to give a more accurate conversion.If such difficulty with the implicit format should be common among membersof the general public, this is undoubtedly a much more important observationthan the transient speed difference apparent in the data so far. In order toassess the difficulty that the general public might have with implicit andexplicit formats a Market Survey technique was adapted for the nextexperiment.

5. Experiment 45.1. .111eihod

5.1.1. Apparatus and procedure

Question space was bought in an on-going market survey concerned withascertaining public awareness of the impending currency change in Britain.Interviewers were provided with cards on which were small sections of con­version tables such as those shown in Figure 6. Each person interviewed sawonly one of the tables. The interviewer read the following instructions:

, Here is a small part of a table that shows how today's prices will be writtenwhen Britain changes to decimal currency. Now I am going to read outsome prices in shillings and pence and ask you how you would say them asdecimal currency: First (1) 7/6d

(2) 8/4d.

And now I am going to read out some prices in decimal currency and ask youhow you would say them as shillings and pence:

First (3) 42p(4) 46!p.

7/4d 36jpi /;"jd 37p7/0cl. a7jp

Section of Explicit Table

8/4d 41~p

8/5d 42p8/0cl 42jp

9/4d 46jp9/5d 47p9/6d 47~p

Section of Implicit. Table

i/-d 35p 4d LJp8/-d 40p fid 2p9/-d .451' Gd 2\ I'

Figure 6. Sections of table used in Market Survey experiment.

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184 Patricia Wright and Kathryn Fox

Approximately one-third of these subjects were given the following additionalinstructions with the implicit table.

, To write a price such as 9/5d in the new money:First look in the table for the shillings: 9/0d 45pThen look in the table for the pence: 5d 2pThen add together: 9/5d 47p.

The interviewer noted the response given by each person.

5.1.2 Subjects

The sample was chosen to be representative of the distribution of age andsocio-economic background in the British population as a whole. The sectionof the explicit table was seen by 752 people; 740 people saw the section of theimplicit table; 676 people saw the section of the implicit table together with theinstructions.

5.2. Results

Averaging the proportion of correct answers for each of the four conversionsgives the data shown in Figure 7. The groupings on the abscissa of Figure 7correspond roughly to thirds of the population. Thus from the data shown,it is clear the performance is appreciably poorer when people are using theimplicit table, and that instructions tend to be helpful only for the lowersocio-economic groupings, but are in fact a handicap for the over 55 age group.

But it may also have been noticed that performance with the explicit tableis far from perfect. Possibly this is in part due to the market survey techniqueadopted, which may carry a proportion of 'don't know' responses as an

PROPORTIONS OF THE GENERAL PUBLIC ABLE TOUSE VARIOUS CONVERSION TABLES

0 90°'0 90°/0..>0:.... 0,>~

BOo,o ...' ....... 80%

0:'""Z '""' ....... '0,,-'u ,

70°'0.... 70°/0 "00: , ,.. 0: , .. LARGE"8 o TABLE.....60°'0 60°/00"

Z ... ,0"->

Sp~~;L TABLE sool..... 50°/0,,:<,

~o , INSTRUCTIONS

0" ,0:;040°'0 40°/c, • SMALL

TABLE

AB+C. C2 DE

SOCIAL GRADE

ItI-34

SMALL TABLE

SMALL TABLEPLUS INSTRUCTIONS

35-54 OVER 55

AGE IN YEARS

Figure 7. Results of Market Survey experiment.

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integral feature of the procedure. Table 1 shows the distribution .of correct,incorrect and don't know answers. Clearly, for the explicit table, the occur­rence of classifiable errors was much less frequent than with the implicit format.

Table 1. Distribution of responses in Market Survey Experiment(averaged over all four questions)

Tabulation format Percentage of rcsponeca which were:Correct Incorrect Don't know

ExplicitImplicitImplicit pIns

instes.

74·057·3

60·8

8·018·7

18·2

18·024·0

20·2

.5. B. DiscussionThese results bear out the suggestion made earlier that there are a substantial

proportion of people unable to understand how to use the implicit format.The types of errors made included many instances of people converting onlythe shillings amount (e.g. responding B5p to 7/6d), or adding £sd to decimalamounts (e.g. 7/6d was converted as B5p plus 6d making 41p).

It seemed possible that part of the difficulty in using implicit currencyconversion tables might be quite specifically due to some aspects of numeracy,such as a lack of awareness of the commutative properties of numbers. Thatis to say; perhaps people think of an amount such as 42p as an indivisibleentity and have difficulty thinking of it as '40p + 2p '. Even though theymay be able to split up 42p in this way in order to convert each part separately,it would seem that they have not sufficiently grasped the meaning of the' plussign' relation to be confident of knowing what to do with these parts oncethey have been converted. From the data obtained so far it is not clearwhether the implicit format is inherently difficult because it involves operationsof both analysis and synthesis or whether the difficulty is specific to tablesinvolving numbers. One way of distinguishing between these alternatives isto examine performance with a non-numerical table. This was done in thenext experiment.

6. Experiment 56.1. Method

6.1.1. Appamtus and procedure

The conversion tables used were the same sections of the explicit and implicitcurrency conversion tables, used in the Market Survey. A non-numericalanalogue of these tables was also devised. The non-numerical tables werepreceded by the following written preamble.

'You are a foreign spy and must contact a secret agent by leaving particularplaying cards under a beer mat in a public house. The table shows you whichcards to use for different messages.'

The implicit non-numerical version read as follows:

Meet me here ace tonight hearts

New orders king at weekend clubs

Enemy agent coming queen in three days time diamondsN ERG.

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186 Patricia Wright and Kathryn Fox

Subjects were then asked what cards they would leave for the followingmessagos:

(a) Meet me here in three days time

(b) New orders tonight

'I'hey were also asked what it would mean if they found the following cards:

(a.) King of Clubs

(b) Queen of Hearts '

Testing took place on two separate occasions. On the first occasion eachsubject was given a copy of the currency conversion test. No examplesillustrating the use of either the explicit or implicit format were given. Tenweeks later the same subjects were given the non-numericaJ table, Of thosewho had originally been given the explicit currency table half were given theexplicit non-numerical table and half the implicit version, a similar divisionwas made among those children who had originally worked with the implicitcurrency tabie., " ' .., After the test with the non-numerical table, all children were shown a playing

card depicting the Jack of Spades lind were asked to write down the name ofthe card. This'was done to determine whether any difficulties using the tablecould be attributed' to unfamiliarity with the names of the playing cards.

'6.1.2. Subjects

The data on the currency conversion tables were collected in several schoolswith' children of a variety of ages, until a group was found which gave resultssimilar to those obtained in the Market Survey; namely a low error rate on theexplicit table and a higher error rate with the implicit table. This targetpopulation"was found with a class of grammar school boys aged between IIand 13. Children younger than .this tended to get many more exampleswrong, children' older. tended to do too well with both tables, There were 32boys in the group chosen for the experiment. Owing to absentees on eitherthe first or second occasion of testing, only 28 boys had both tahles.,

6.2. Results

Two boys wrongly identified the Jack of Spades. These both had theexplicit non-numerical table and neither of the boys made mistakes whenworking with that table. The percentage of correct conversions made withthe implicit and explicit formats for both numerical and non-numerical tablesare shown in Table 2.

Table 2. Tho percentage of correct answers for the numerical and non-numerical tables

Tabulation format Content of tableNumerical Non-numerical

ExplicitImplicit

96·775·0

94·776·7

From Table 2 it is' apparent that the difficulty of the implicit format is byno means confined to numerical tables. Again consideration of the kinds oferrors made suggests that the difficulty seems to lie in re-combining the

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different elements. Of the 14 errors made with the implicit verbal table onlythree actually contained wrong information (e.g. had hearts instead ofdiamonds), four mentioned only one of the pieces of information, and theremaining seven mistakes were counted as errors because the children had notcombined the two items, e.g. to give King of Hearts but either wrote down justKing Hearts or used some other connective such as or to give King or Hearts,or and to give King and Hearts. It is interesting to note in this connectionthat when the 'conversion' was from the name of a card to its intendedmessage then juxtaposition of the information was all that was required, andonly three of the 14 errors occurred on these two questions.

6.3. Discussion

This experiment suggests that the difficulty some people have in using theimplicit tabulation format is not confined to numerical tables but seems to bemainly associated with combining information from two sources to form a new, whole'. Frequently people seem able to locate the appropriate information.Therefore whether or not an error is made will be largely a function of thenumber of alternatives open to the person. For example, if the school-childrenhad been shown the nine playing cards and simply asked to pick our the rightone, in all probability the error-rate would have dropped by half. This isbecause half the children making errors knew both the correct suit and thecorrect value of the message card. Their only problem was in combining thisinformation to give the name of the card. Since they had no difficulty innaming the playing card shown them after the test, the difficulty with theimplicit format must have arisen from the way in which the information hadto be combined. Requiring only the juxtaposition of the two pieces ofinformation is much simpler than attempting a synthesis. Numerical tablesmost frequently require some degree of synthesis. Consequently the implicitformat should be avoided for such tables, unless the range of alternatives opento the user would tend to minimise combinatorial errors.

Tho authors would liko to thank Marks and Spencer, and J. Sainsbury for providing themerchandise and subjects used in these experiments. We are also indebted to the DecimalCurrency BORi:d for their encouragement and financial support.

Cet article presente cinq etudes concernant los operations do conversion monetaire baseeeSUf deux principes differente de tabulation.

Dans une situation d'achats simules, In table qui lietnit oxplicitement toutes les paires de prixequivalents presente.it. Ull avantage initial en ce qui concerne la rapidite. L'autre table quiindiquait aeparemenb une conversion pour les shillings et uno pour les pence, exigeait non seule­ment un temps d'operution plus long, mais donnait egalement lieu it.des erreurs plus nombreuses.Des donnees en provenance d'une technique adaptee d'une etude de marohe ont mantra quebeaucoup d'utilisatenrs se aervaient d'une meniere incorrecte de co format" implicite II et plusdifficile, meme s'il etait illustre par un exemple.

Lorsqu'on a presenec a des ecoliers les tables nurner-iques et non-numeriquea il s'est evere queJIl difficulte afferente au format implicite n'ete.it pas due aux necessaires operations aribhmetiquea,bion qu'elle fut en partie I attribuable a la combinaison d'elements separea d'information. Lajuxtaposition des elements etait plus facilement effectuee que leur syneheee.

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188 Explicit and Implicit Tabulation Formats

'Es wird libel' 5 Studien mit \Vahrungsumrechnungs-Tabellen berichtet., die nach zweiverschicdenen Prinzipien aufgestellt worden warcn. In einer simulierten Einkaufssituet.ionhatto die Tubelle oincn anfiingliche Geschwindigkeitsvorteil, die eamtdicbe Paere Rquivalenter­Preise explicit auffuhr-te. Die andere Tabellc, wclche die Umrechnung von Shillings gctrennt vondel' Umrechnung del' Pence angab, war nicht nul' langsamcr zu henutzen: sie wurde auehotter fehlerhaft gebraucht. Daten oiner modifizierten Marktiiberwachungs-Tochnik zeigten, dasaoin grosser Toil des allgemeinen Publikums diese " Schwicrigerc II Tabellenforn faIsch benutete,obwohl ein crlauternde Beispiel gegoben wurde. Versuche an Schulkindern zcigten, dess dieSoliwictgkcitcn nicht an dol' mentalen Arithmetik lag, obwohl die Kombination vcrschiedenerInformation verlangt wurde. Das Nebeneinanderstellen von Werten war Jeicbter- uls die Synthcse.

References\VmOHT, P., 1968, Ueing tabulated information. Ergonomics, 11, 331-343.WRIGHT, P., and Fox, K., 1970, Present.ing information in tables. Applied Brgorwmic8, 1,

234-242.

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