63

The Responsiveness of Food Sales to Shelf SpaceChanges in Supermarkets

KEITH COX*

y Thh article tastt tha hypothetei that food product lalet are ratponsiva to changes in (half ipacaand that "impulie" items ara relatively more rponsive than staples.

Many supermarket executives assume that sales ofmost food products sold in supermarkets wiU be re-sponsive to changes in shelf space. However, therehas been very little experimental work to test this im-plied hypothesis. Pessemier en^hasizes the importanceof measuring this relationship. "Ideally, if managementknew just how sensitive were the sales of each item tothe particular space allocated to it and just how large acontribution each item produced, it would be possibleto make allocations which would retum the larg^tprofit" [12]

The objective of this paper is to measure this re-lationship between shelf space and product sales. Oneproblem with measuring the responsiveness of shelfspace to sales is the fact that this effect upon sales maybe minor, and therefore difficult to detect Also, variableeffects up(Hi sales besides test effects must be controlledfor the test results to have much validity.

An expoimental design will be used to test this re-lationship in the marketplace. The study will analysethe responsiveness of product sales to shelf space fromthe viewpoint of the supermarket, rather than themanufacturer. Supermarket executives seek to maxi-mize total sales within supermarkets, while manufac-turers try to maximize sales of their brands. These twogoals are not always compatible, resulting at times in a"battle of shelf space" between manufacturers andretailos.

AVAILABLE TECHNIQUESOne analytical technique to use in this problem

would be to ask a sample of cusUnners what they wouldbtqr if the shelf space for that product was changed.However, this method would only tdl us what cus-tomers say they would do, which may be different fromwhat t h ^ would actually do.

Anothn technique is the before-and-after study.Some Steves are used as control stores, where the testvariaUe is not changed during two difiterent timepoiods. In oths states, the test variable (shelf space)is changed from the first to die s^xmd period ci time.

* Keith Cox is assistant pnrfeaaor of taaAeOat, Kent StateUnivmUy.

Any differences between control stores in the twotime periods is subtracted from the differences betweentest stores. After this adjustment, farther differencebetween test stores are attributed to the test variable.This method does not control differences between timeperiods, so that the results are weakened when timeperiod variations are large. Also, the assumption thatvariation between supermarkets is adequately controlledby selection of the same type of supermarkets in boththe control and test groups is frequendy questionable.From an operational viewpoint, this assumption maybe difficult to justify.

A third technique uses analysis of variance. Accord-ing to Hoel [8]: "One of the most meful techniques forincreasing the sensitivity of an experiment is the desigOring of the experiment in such a way that the total varia-tion of the variable being studied can be separated intocomponents that are of experimental interest or im-portance. Splitting up the total variation in this mannerenables the experimenter to utilize statistical methods toeliminate the effects of certain interfering variables andthus to increase the sensitivity of his experiment. Theanalysis of variance is a technique for carryii^ out theanalysis c^ an experiment designed from this point ofview."

After considerii^ these differoit techniques, theanalysis of variance was selected as the most efficientfor these e:q)eriments. A number of different experi-mental des^ns could be used utilizing analysis of vari-ance. The simplest type of design is where all of thetest treatments are allocated entirely by chance withinthe experiment This is called a completely randomizeddesigtL Another design is randomized blocks, which isa wig\e grouping design. One major source of variationin addition to the treatment variation can be M ^from die residual error. (The residual error in analysisof variance is diat part of the total variance that cannotbe statistically accounted for in the expenmsat. It isconsidered as that part of the vari^ion due to randomflnctuadons, and is used as an unlMased estimate of theuniverse variance.)

A latin square design is a doable groupiiig design,wbere two major scmrces of variation can be controUed.The latin square design proviiks more opportonity for

64 JOURNAL OF MARKETING RESEARCH, MAY 1964

reducing the residual error than the randomized blocksor completely randomized design, when there are atleast two major sources of variation in the experimentnot subject to direct control. In previous supermarkettests [5, 10], variations between stores and variatiraisbetween time periods were indeed difficult to control.Hence, the latin square design was selected for theseseries of tests.

RESEARCH METHODOLOGYIn setting up the experimental tests to measure the

relationship between self space and product sales, allother variations besides variation between treatments(shelf spaces), variation between stores, and variationbetween time periods needed to be controlled (kept con-stant). Prices of test products remained the samethroughout the testing period. The same shelf level ineach store at the start of the experiments was used dur-ing the tests. No sales promotional materials or ad-vertising of the different test products were used. Thetesting period comprised the summer of 1962, so thatany effect upon sales due to seasonal variation wasminimized.

Selection of Size of Latin SquaresFour factors were considered in choosing the size of

the latin square design. These factors were (1) pre-cision desired from the test results, (2) total cost ofcollecting the data, (3) time required to collect thedata, and (4) number of shelf treatments being tested.It was decided that a 6 by 6 latin square design, usingsix supermarkets over six weeks of time, was the mostdesirable size for this study.

Selection of Test ProductsIdeally, different food products should be tested in

measuring the relationship between shelf space andsales. A number of limiting factors prevented manyproducts from being chosen for the tests. Products whereprice specials were used had to be discarded, since anyvariation in sales due to price changes could not becontrolled. Products such as coffee, sugar, com, ffour,pickles, and peas feU into this category. Another groupof products, including frozen foods, milk, and meat,were rejected because of the limited shelf space avail-able for testing. Candy, cookies, and nuts were elimi-nated because of the difficulty of performing a physicalaudit of the unit sales of these products. Salt was dis-carded because one of the proposed test supermarketshad three times more shelf space for salt than any ofthe other proposed supermarkets.

After such considerations, baking soda. Tang,hoiAiny, and powdered coffee cream were selected astest products. Baking soda was classified as a stapleproduct, while Tang, hominy, and powdered coffeecream were classified as impulse products. The hy-pothesis was advanced that staple goods would be

relatively unresponsive to changes in shelf spacs whileimpulse goods would be relatively responsive.

Selection of Test StoresThe desirability of selecting the six supermarkets

randomly from all supermarkets in the area was c

THE RBPONSiyB4ESS OF FOCH> SALES TO SUPBtNiARKEt SHBf SPACE CHAN(^S 65Inventory and Audit Records

In estimating weekty sales of each of the four productlines in the six test supermarkets, a procedure wasoriginally considered of subtracting the ending shelfinventory and the ending back-room inventory from thesum of the beginning shelf inventory, the beginningback-room inventory, and purchases during the week.However, this mediod was not acceptable for tworeasons. A great amount of time and sldll were neededto record accurately actual purchases during the week.Also, the back-room inventory was almost impossibleto count in some of the supermarkets. Because in-accurate recording of either back-room inventory orweekly purchases would distort the experimental results,the following alternative system of counting inventorywas devised and used:Beginning Shelf , Additions Ending Shelf _ Weekly

Inventory ~^ to Shelf Inventory SalesAn audit was taken four times every week for all

four products in all six of the test supermarkets. Besidestaking this physical inventory, additions of new stockto the shelves were made whenever possible. Otheradditions to the shelves by grocery clerks could gen-erally be verified by the clerks. Additions to the shelveswere easy to count, since the stock was always addedin full-case lots of 12, 24, or 48 units at one time.

Testing ProceduresUsing the staple and impulse assumptions concerning

shelf space and supermarket sales, the following hypoth-eses were tested:

1) There is no significant relationship between theamount of shelf space given to baking soda andtotal unit sales of baking soda.

2) There is a significant relationship between theamount of shelf space given to hominy. Tang, andpowdered coffee cream, and total unit sales of eachof these products.

In all latm square tests, the total variation is sub-divided into the variation between stores, variation be-

tween time periods, variaticm between treatments, andtlw residual variation. In terms of the usual notation:The total sum of squares (total SS) is equal to the rowsum of squares (row SS) plus the column sum ofsquares (column ^ ) plus the treatment sum of squares(treatment SS) plus the residual sum of squares (resid-ual SS).

2(Yt - Y)* + 2 ( Y - Y, - Yk - Y;-f-2 Y) 'where Y := experimental variable,

Y = overall mean,Y, = row mean,Yk = column mean,Yt = treatment mean.

Each sum of squares, when divided by the appro-priate degrees of freedom, can be used as an estimateof the variance, the results being the so-called meansquares.

In the analysis, both a regression analysis test and ananalysis of variance test can be used in measuring theeffect of the treatment shelf spaces upon product sales.Regression analysis is appropriate in this study becausethe different treatments are quantitative differences ofone factor (shelf space). The treatment means can betested for linearity by fitting a linear regression line tothe treatment means [11], though the linear relation-ship can be assumed only within the range of the actualshelf treatments. The treatment sum of squares with fivedegrees of freedom is subdivided into a linear regressionsum of squares with one degree of freedom and thedeviation from linearity sum of squares with four de-grees of freedom. The null hypothesis should be rejectedwhen the F ratio is greater than 4.35 using a S percentlevel of significance with 1 and 20 degrees of freedom,where

Linear regression mean square" Residual error mean square

Table 2MEAN SQUARES AND F RATIOS FOR FOUR PRODUCTS TESTED

Hominy Baking toda TangPowdered

coffee cream

Source

Rows (stores)Columns (weab)Treatments (shelf spaces]

Linear regrsionDeviation from linearity

Rasidual airar

Total

freedom

555

14

20

3E

Mean square

8.891.2690.1

1,426.24,230.7

725.1335.7

F ratio

25.001.944.01

11.892.04

Mean square

I.657J196379.0

113.270574.4

F ratio

22.282.64\M1.52.95

Mean square

1^38.463.232v4

145.34.1

49.6

F ratio

24.971.27.65

2.93.08

Mean square

1,295.2105.9101.7159.787.263.9

F ratio

20.271.661.592.501.36

66 JOURNAL OF AAARKETING REKARCH, MAY 1964

TEST RESULTSThe results oi the hominy shelf space experiment are

given in Table 2 and the data appendix. In analyzingdie results in the data appendix, the shelf space treat-ments are given in parenthesis for each cell. The othernumber in each cell is the actual unit sales of hominy.For example, there were 140 cans of hominy sold instore 1 during the first test week with twelve shelf spacesased in the shelf display. In Table 2, the F ratio is seento be 11.89, which exceeds the 5 percent level ofsignificance of 4.35. The null hypothesis is thereforerejected, and the alternative hypothesis accepted ofsignificant differences between the average treatmentsales of hominy.

The baking soda results are also given in Table 2 andthe data appendix. From the results in Table 2, the Fratio is 1.52, which is less than the 5 percent level ofsignificance of 4.35, and the null hypothesis is acceptedof no significant difference between the average treat-ment sales of baking soda. Similarly, no significantdifference due to shelf space was obtained for Tang andfor powdered coffee cream.

IMPLICATIONSHominy was the only test product for which the al-

ternative hypothesis was accepted. The test resultstherefore reject the original hypothesis that impulseitems respond more to variations in.shelf space than dostaples. Also, the assumption that sales of food productswill be responsive to changes in shelf space is open toserious question. For many food products, increasingthe amount of shelf space may be an inefficient way ofincreasing food product sales in supermarkets. Fromthe viewpoint of the retailer, shelf allocation decisionsmay be infiuenced more by minimum restraints such as(1) oat of stock policies, (2) full-case stocking tominimiTft labor costs, and (3) assortment policies of theretailer. One practical solution to stocking fast-movingproducts may be to stock the products more frequentiywithin a snuller amount of shelf space, rather thanincreasing the amount of shelf space for the product.

For manufacturers of food products, the resultssuggest that the cost of gaining additional shelf spacef(H their product may not increase sales sufficiendy tojustify tte expense. Farther research in this area isreccnnmended for both retailers and manufacturers.

Finally, this study shows how distorting variationsbetween test stor and between different time periodscan be statistically eliminated by asing latin squaredeigns. This type of mearch design should be useful inotha types of supomarket testing, such as for selecticmof better point-of-puichase d is^ys , making packagingannparisons, testing the most profitable price deals, andtoting the effects d difiooit assortment policies.

DATA APPENDIXPRIMARY RESULTS FROM 6 BY 6 LATIN SQUARE TESTS

HOMINY

Stores

\

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

T

(12)140(14)131(8)67(4)109(i)58(10)37

(12)22(6)65(4)58(2)43(10)40(8)38

(12)25(9)59(18)36(21)39(15)23(6)22

(IS)27(21)34(9)39(12)40(15)15(6)16

2

(10)150(&)126(14)94(12)134(8)71(4)36

Weeks

3

(4)71(8)130(A)49(10)96(14)59(12)52

4

(8)III(12)188(4)93(6)123(10)62(14)58

BAKING SODA

(10)30(4)61(6)42(8)41(12)26(2)23

(18)38(21)48(12)48()19(M17(15)18

POWDERED

(15)14(18)31(21)67(i)57(12)15(9)15

(6)36(2)74(8)73(12)47(4)33(10)42

TAN

(21)31(6)47(9)55(15)27(18)24(12)19

COFFEE

(12)18(15)34(18)31(9)39(6)II(21)14

(8)40(10)83(12)63(4)65(2)27(6)31

30(18)65(15)54(12)41(21)26(9)9

CREAM

[t>)35(12)46(15)49(21)70(9)9

(18)12

5

(6)121(4)133(10)112(14)127(12)49(8)38

(4)42(8)67(2)40(10)43(6)35(12)37

(9)35(15)62(21)54(6)29(12)25(18)25

(21)28(9)37(6)38(15)37(18)18

(12)19

6

(14)127(10)154(12)161(8)84(4)27(6)51

(2)36(12)84(10)69(6)65(8)17(4)36

(15)25(12)43(6)47(18)33(9)II

(21)22

(9)22(6)23(12)48(18)50(21)17

(15)22

THE REa>ONSIVENESS OF FOOD SALES TO SUPBtMARKET SHBF SPACE CHANGES 67

REFERENCES1. Sejmuxir Banks, "Marketing Experiments," Joumal of Ad-

vertising Researeh, 3 (Maidi 1963), 34-41.2. WiUiam Brown and W. T. Tucker, "Hie Marketing Center:

Vanishing Shelf Space," Atlanta Economic Review, 11(October 1961), 9-13.

3. Max Brunk and Walter Federer, "Experimental Doignsand Probability Sampling in Marketing Research," Jour-nal of the AmeHcetn Statistical Association, 48 (SeptembCT1953), 440-452.

4. William Cockran and Gertrude Cox, Experimental Designs,New YOTk: John WUey & Sons, Inc, 1954.

5. Bennett Dominick, Jr., "An Illustration of the Use of theLatin Square in Measuring the Effectiveness of Retail Mer-chandising Practices," Methods of Research in Marketing,Paper #2, Cornell University, June 1952.

6. Churdull Eisenhart, "The Assumptions Underlying theAnalysis of Variance," Biometrika, 3 (March 1947), 1-21.

7. Rcmald Fisher, The Design of Experiments, 6th ed. revised,: OUver & Boyd, 1951.

8. Paul Hoel, Introduction to Mathematical Statistics, NewYork: John Wiley & Sons, Inc., 1954.

9. Jerome Li, Introduction to Statistical lnferetice, Ann Ar-bor: J. W. Edwaids, Publisher, Inc., 1957.

10. Murray MacOregor, "Uniformity Trial Experinmits inMarketing Research," Methods af Research in Marketing,Paper 6, Cornell University, September 1958.

11. Bernard Ostle, Statistics in Research, Ames: Iowa SUteUniversity Press, 1954.

12. Edgar Pessemier, "Applying Supermarket Techniques toNon-Food Retailing," Joumal of Retailing, 36 (Summer1960), 108-113.

13. James Shaffer, "The Influence of Impulse Buying' of In-The-Store Deciuons on Consumers' Food Purchases,"Journal of Farm Economics, 42 (May 1960), in-3U.

14. U. S. Department of Agriculture, Better Utilization of Sell-ing Space in Food Stores, Marketing Research Report #30,November 1952.

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