J BUSN RES 61 1985:13:61-69

Evaluating Measures Through Data Quantification: Applying Dual Scaling to an Advertising Copytest*

Marketing researchers often assume that their measures are at the interval level, though they seldom test this assumption. Dual scaling, a procedure for resealing nonmetric data to the interval level, may be used to examine measurement-level assumptions and aid in the interpretation of measures. The procedure and its applications are discussed and illustrated with a semantic differential used in copytesting an advertisement.

Attention to the quality of measures used in empirical research is becoming a “given” in the marketing discipline. Since the landmark Journal of Marketing Research Special Section on Measurement and Marketing Research [23], a number of articles in the marketing literature have focused on measurement [e.g., 6, 211. In addition, journal editors and conference program chairs now routinely exhort authors to address issues of measure reliability and validity as a way of improving submissions.

In measuring many of the variables of importance to marketers-attitudes, intentions, and so on-researchers generally choose one of two alternatives: either assuming their scales are at the interval level, a “subtle sin” in marketing research [18] , or restricting themselves to nonparametric statistical methods appropriate to ordinal data. The view that “all observations are categorical,” either inherently (e.g., sex, marital status) or due

to the finite precision of the measurement process (e.g., age, opinion leadership), under- lies a variety of procedures for “quantifying” nonmetric data and permits a third

alternative-resealing data [26] . Addressing measurement issues through the alternating least squares optimal scaling (ALSOS) approach to quantifying data has already been addressed in the marketing literature [7, 8, 201. The purpose of this article is to discuss the application of a different scaling method, known as “dual scaling,” to the measure- ment problem. This approach is illustrated by resealing the responses to a semantic differential used in assessing feelings about a magazine advertisement. The emphasis is on resealing data to increase insights into the subjects’ use of the measure rather than to improve measure quality (reliability and validity) per se.

*This paper was selected for the Steven J. Shaw Award as the Outstanding Paper presented at the 1984 Southern Marketing Association Conference.

Address correspondence to George R. Franke, Assistant Professor, Department of Advertising, UniversityofTexas,CMA7.140,Austin,TX 78712.

Journal of Business Research 13, 61-69 (1985) 0 Elsevier Science Publishing Co., Inc. 1985 52 Vanderbilt Ave., New York, NY 10017

0148-2963/85/$3,30

62 J BUSN RES 1985:13:61-69

G. R. Franke

Several measurement considerations that may be addressed through dual scaling are discussed below. Dual scaling is then briefly described and its use is illustrated. Although the example shown is based on a semantic differential measure, dual scaling is appropriate whenever measures are categorical: both when subjects provide categorical responses directly, as in Likert scales, the semantic differential, multiple-choice measures, and so on, and when metric data are reported categorically (e.g., age: 18-24,25-34, and so on). Thus, dual scaling offers considerable flexibility for the marketing researcher.

Measurement Issues

Concepts and procedures involved in developing reliable and valid measures have been extensively discussed in the marketing literature [e.g., 3, 12,2 1,221 . Though procedures for resealing empirical data may often be used to improve measure reliability and validity [7], these procedures may also lead to greater understanding of the attributes being measured and of the measure itself.

For example, when subjects are asked to respond to an unanchored five- or seven-point scale, say good-bad, they may have a tendency to give responses around the midpoint of the scale and avoid the endpoints, or else avoid the middle responses and respond at the extremes. The use of anchors for the points along the scale may not alleviate response tendency biases, depending on the anchors used [25]. The assumption that subjects treat the intervals between all adjacent scale points as equidistant may be examined through resealing subjects’ responses, either at the pretesting stage or after completion of data collection [20]. If the resealed response categories are equidistant, the original interval- level measurement assumption is supported; otherwise, the measure may be better treated as ordinal.

Resealing data may be worthwhile even when interval- or ratio-level measures are made, as when respondents mark a position on a continuous line and the distance from an endpoint is recorded. Though the response is measured at the ratio level, the subjects’ use of the continuous scale may be as inconsistent as responses to an unanchored cate- gorical scale. Categorizing and resealing the measured responses is a useful check on whether the scale is being used as intended.

Data quantification may also be useful when nonforced-choice scales (i.e., ones allow- ing “no opinion” or “not applicable” responses) are used. In the semantic differential, for example, subjects are generally forced to choose the neutral position on the scale or else fail to respond, when they feel an adjective pair is irrelevant (e.g., bass-treble for a bank or a soft drink). This approach can bias responses toward the midpoint of the scale and confound the different mental states of unawareness and indifference [ 141. Several approaches have been suggested for handling the problematic interpretation of the scale midpoint. Allocating respondents checking the scale midpoint to positive and negative categories either at random or according to some rule can only exacerbate the problem, and deleting these respondents from the analysis can reduce sample sizes excessively. Using nonforced-choice scales and resealing the data may clarify the information con- tained in neutral and no-opinion responses. In a pretest, for example, if both responses receive approximately the same score after resealing, there may be little benefit in using a non-forced-choice scale. No-opinion responses might also reflect feelings subjects are unwilling to reveal, which could be inferred from a resealing to a score similar to the overtly positive or negative responses. In either case, resealing allows an empirical (rather than arbitrary) assignment of no-opinion respondents to interpretable categories and avoids sample depletion.

Evaluating Measures through Data .I BUSN RES 63 1985:13:61-69

bal S caling of Categorical Data

Another common measurement issue relevant to data quantification is the number of response points to use in a scale (see [4] for a review). The use of too few scale points may frustrate respondents trying to make fine distinctions, limit information transmittal,

and reduce the internal consistency of a measure, whereas too many scale points may frustrate respondents who are unable to make extremely fine distinctions and stimulate

undesirable response set tendencies in subjects [4]. Pretesting scales with different numbers of response alternatives and resealing the results might suggest the appropriate number of alternatives to use. For example, as discussed below, dual scaling maximizes the internal consistency of a scale. If a scale with few response categories has a low reliability level after resealing, it is even more unlikely to be adequate in its raw form. Conversely, if the resealed categories of a scale with many response alternatives show little face validity (a random pattern of very large or small distances between adjacent categories, or many discrepancies in the original scale ordering due to a nonmonotonic transformation), the resealing is likely to reflect capitalization on chance due to the respondents’ difficulty in using the scale. Balancing the costs and time requirements of pretesting many different versions of a scale with the dangers of not pretesting, the most practical approach is probably to pretest a reasonable version of the scale (typically with five to nine response alternatives) with a contingency plan for use if resealing suggests problems with the subjects’ interpretation of the measure.

As mentioned above, the focus of this article is on resealing data to gain insights into the use of measures rather than on improving the quality of the measures for subsequent hypothesis tests. It should be emphasized that this is a matter of focus only and not a limitation of the dual scaling procedure. Just as ALSOS procedures improve measure quality by resealing data to conform to an underlying theoretical model, dual scaling improves measure quality by resealing data for maximum internal consistency. The next section briefly discusses this and other aspects of dual scaling.

“Dual scaling” is a relatively recent term for a method of quantifying categorical data that has a long history under a variety of names [19] . This method has been extensively developed in France and is known there as “analyse factorielle des correspondances” [2] . The translation, “correspondence analysis” [ 131 , has been used in at least two marketing studies [lo, 151. Franke’s expository article on the procedure uses Nishisato’s term for its generality and lack of ambiguity [9].

Though the equations of dual scaling may be derived in a number of ways [19, 241, Guttman’s approach based on maximizing internal consistency [ 111 is particularly appro- priate for considering the measurement implications of the procedure. Given a two-way data matrix where the entries are nonnegative real numbers, such as a contingency table, dual scaling assigns weights (numerical scores) to the rows and columns of the data so as to simultaneously minimize the ratio of the variance within rows and columns and maxi- mize the ratio of the variance between rows and columns, relative to the total variance. If F is the data matrix, c is a vector of the column totals of F, DC is a diagonal matrix of Fs column totals, Dr is a diagonal matrix of the row totals of F, and t is the sum of the entries in F, then the optimal weights (resealing) X for the columns of F may be ob- tained by maximizing the ratio of quadratic forms (see [19] , Chap. 2, for a complete derivation):

17 2 - X'(F'Dr-' F - cc’/t) X

X ‘(DC - ccl/t) X

64 J BUSN RES 1985:13:61-69

G. R. Franke

where v2 is the squared correlation between the rows and columns of F. Once X has been found, the optimal row scores are determined by calculating

Considering the columns to be “X” and the rows to be “Y” is arbitrary, because the same results are obtained from scaling the transpose of the data.

Nontrivial data sets (3 X 3 and larger) generally lead to multidimensional solutions. As in principal components analysis, these may be obtained by iteratively calculating new

solutions after eliminating the effects of previous ones [ 19, pp. 45 -481. Singular value decomposition may be used to conveniently obtain all the scaling solutions (including two or more trivial ones, with q2 = 1 or 0) [ 131 : IfA = Dr-’ FDc%, the decomposition

A = U Q V’ leads to the results

X=&-” V (3)

and

Y = Dr‘% U,

with the squares of the diagonal entries of Q (the eigenvalues of AA’ and A’A) giving T+? for the j different solutions. This may be programed straightforwardly using a package of matrix procedures, and several dual scaling programs are available in published form [2, 191 and commercially [16].

A useful application of dual scaling to measure assessment involves the analysis of an item by response cross tabulation, where the rows (say) are the items the subjects are responding to, the columns are the response alternatives, and the entries are the number of times each alternative was chosen for each item. The solution matrix X would show what weights for the response alternatives would best discriminate among items while maximizing response consistency within items, with a vector of weights for each solution (dimension) obtained. For example, if a “no opinion” category were used, the weights would show where this response fell along the continuum of response alternatives-near the neutral point or toward one of the extremes. The solution matrix Y for the items could be used in detecting similarities in patterns of response; two items with very similar

scores could be redundant, suggesting that one item might be eliminated in future applica- tions of the measure. However, a complication in interpreting dual scaling results is the fact that with real data, one solution will rarely explain all the important variance in the data. Different items might receive similar scores on one or more dimensions, yet be quite different on other dimensions [2, pp. 46-471. The decision to delete items should not be based just on patterns of dual scaling scores for one or two dimensions but must also take into account standard principles of scale construction.

A more informative and also more complex application of dual scaling involves the analysis of response-pattern data, such as a respondent by response-alternative matrix, with entries being OS and 1s to show which alternatives were selected. A ten-item Likert scale with five alternatives per item (strongly agree, agree, etc.) could be analyzed at the individual level by constructing a table with 50 columns and 1 row per respondent (or, equivalently, with 50 rows and 1 column per respondent). The vectors of the solution matrix X would show the weights assigned to each response alternative for each item, for as many dimensions as were derived in the analysis. Analysis of the weights would indicate whether the response alternatives were used consistently across items by the

Evaluating Measures through Data J BUSN RES 65 1985:13:61-69

respondents, or if “strongly agree,” say, meant different things depending on the statement being evaluated. A possible drawback to this method is that dual scaling standardizes responses to a mean of 0 (in the illustration below, the weights were further standardized to range from 1 to 7, so the common mean is shown as 5.26). This should not cause problems in typical applications, though, where individual responses are summed across items to form scales.

As discussed by Lord [ 171, maximization of n2 leads to maximization of Cronbach’s measure of Internal consistency, alpha (cy) [5] . When the data are in the form of a response pattern table, there is a simple relationship between 01 and n* [ 191 :

Q2 = l/[l + (n - l)(l - a)],

and

QI = 1 - (1 - $)/ [(n - l)$] )

where n is the number of items in the scale. Since n2 is part of the dual scaling solution, equation (6) can be used to calculate coefficient (Y directly. In addition, the relationship between n2 and (Y can be used as a guide for determining the maximum number of dimensions to examine in interpreting dual scaling results. When the QI coefficient for a dimension is lower than some threshold of acceptability, that and subsequent dimensions may be ignored. A minimal useful level of 7’ is l/n, since OL is negative at lower levels

[191. In practice, the computational resources required to calculate eigenvalues may cause

difficulties in resealing long measures. A loo-item, 5-point scale administered to N subjects involves the eigenequation of an N X N or 500 X 500 matrix, whichever is smaller, when analyzed as an N X 500 response-pattern matrix. A simpler task would be to analyze the 100 X 5 item-by-response cross-tabulation and forego the resealing of response categories for each individual question.

Illustration

An Advertising Age “Critic’s Corner” column appearing March 5, 1984, asked for readers’ comments on an ad for Bandolino Shoes, which had appeared in Cosmopolitan and other magazines [l] . The ad’s headline reads, “Because great American legs deserve a little Italian touch,” and the illustration shows a man grasping one leg of a standing woman wearing Bandolino shoes. Most of the woman is not shown, with only one leg being visible. Students in an introductory advertising class were shown the ad and asked to evaluate it on a questionnaire they were given. (Though students were used for conven- ience in illustrating the application of dual scaling, 48% of the respondents read women’s magazines “often” or “occasionally,” suggesting that this sample is not entirely inappro- priate for a copytest of the ad.) The questionnaire included 18 seven-point (plus a “no opinion” alternative) semantic differential items, and two questions on magazine reader- ship and sex.

Table 1 shows the results of the analysis. (For simplicity, only the first dual scaling solution is discussed here.) Responses to the ad were quite consistent across items. Including responses from 30 students who had marked “no opinion” to one or more items and were excluded from analyses involving the raw data, resealing slightly increased an already high OL of 0.9456 to 0.9464. The responses were also generally favorable, ex- cept that many considered the ad to be sexist.

The original data and the resealed data point to essentially the same conclusions about

Tab

le

1.

Dua

l Sc

alin

g W

eigh

ts,

Des

crip

tive

Stat

istic

s,

and

Prin

cipa

l C

ompo

nent

s L

oadi

ngs

Item

s’

1 2

3

Res

eale

d R

espo

nses

b

No

Item

M

eans

/Std

. D

evsC

4 5

6 I

Opn

. O

rigi

nal

Res

eale

d

Hig

hest

L

oadi

ng,

3-Fa

ctor

So

lutio

nd

orig

hd

0.78

’

0.74

*

o.74

2

o.73

2

0.65

’

0.60

’

0.55

1

0.84

’

0.67

’

0.79

’

0.69

’

0.75

’

0.60

’

o.88

3

0.73

a

0.73

s

o.73

3

0.52

2

Scal

ed

’

0.79

’

0.78

’

0.74

’

0.74

’

0.69

’

0.57

’

0.57

’

0.82

s

0.72

=

o.70

2

0.68

2

0.66

l

0.56

’

0.78

3

0.75

s

o.73

3 o.

683

0.61

3

Inte

rest

in

bra

nd

Pers

uasi

ve

Goo

d sa

les

mes

sage

Eff

ectiv

e

Goo

d ad

vert

isin

g

Inte

rest

ing

Inte

llige

nt

Not

of

fens

ive

Not

se

xist

Not

de

basi

ng

Not

an

noyi

ng

Tas

tefu

l

Goo

d

Sexy

Attr

activ

e

Rom

antic

Atte

ntio

n ge

tting

Cre

ativ

e

Ave

raee

3.57

4.

24

4.43

5.

07

5.51

6.

07

6.61

4.

25

3.54

4.

31

4.36

5.

35

6.20

6.

25

7.00

3.

45

2.58

3.

60

4.91

4.

96

5.13

6.

35

6.62

3.

91

3.49

3.

65

3.80

4.

74

5.51

6.

13

6.72

2.

85

2.81

3.

58

3.82

4.

87

5.75

6.

31

6.79

4.

21

2.45

4.

28

4.93

4.

97

5.39

6.

28

6.47

3.

47

3.24

3.

83

4.21

5.

75

5.72

6.

38

6.29

6.

00

3.07

3.

44

3.96

4.

95

5.06

5.

90

6.29

5.

50

4.42

4.

54

5.49

5.

71

5.49

6.

20

6.35

5.

20

3.91

3.

88

4.56

5.

51

5.87

6.

27

6.06

4.

03

3.69

4.

10

3.66

4.

49

5.38

5.

80

6.50

5.

31

2.69

3.

73

4.16

4.

93

5.98

6.

56

6.69

3.

31

1.79

3.

21

3.74

4.

67

5.15

6.

07

6.82

4.

74

3.24

3.

96

4.28

4.

48

5.15

5.

27

6.15

2.

38

3.19

3.

36

3.66

4.

00

4.86

5.

86

6.45

4.

43

2.91

4.

26

4.56

4.

56

4.87

5.

98

6.21

4.

11

1.00

2.

84

3.66

4.

05

4.56

5.

21

6.11

5.

26

2.92

4.

19

4.84

4.

58

5.26

5.

98

6.38

5.

63

3.03

3.

83

4.28

4.

87

5.42

6.

05

6.47

4.

34

4.48

12.1

I

5.26

/1.0

8-

4.01

11.8

7 5.

2611

.09

4.42

11.5

8 5.

2611

.04

4.71

11.7

4 5.

2611

.1

1

4.63

11.7

2 5.

2611

.19

4.46

/1.7

4 5.

2611

.00

3.91

l1.6

0 5.

26/1

.04

5.01

/1.7

6 5.

2610

.98

3.34

/1.8

9 5.

2610

.68

4.22

11.8

6 5.

2610

.91

4.87

11.9

2 5.

2610

.98

4.44

11.5

0 5.

26/1

.11

4.96

11.5

5 5.

2611

.15

5.50

/1.5

7 5.

2610

.79

5.31

/1.5

9 5.

26/1

.08

5.09

11.7

7 5.

2610

.95

5.89

11.3

0 5.

2610

.90

4.81

/1.7

7 5.

26/0

.96

$ It

ems

on t

he

ques

tionn

aire

w

ere

rand

omly

or

dere

d an

d ha

lf

wer

e re

vers

ed.

Fros

t du

al

scal

ing

solu

tion,

nz

=

0.52

3.

Scor

es

wer

e sc

aled

to

ra

nge

from

1.

00

to

7.00

. ’

n =

94

orig

inal

, IZ

= 1

24

rese

aled

. d

The

su

pers

crip

t sh

ow

whi

ch

fact

or

the

item

lo

aded

hi

ghes

t on

. V

aria

nce

acco

unte

d fo

r af

ter

rota

tion:

or

igin

al:

1 (i

nOff

enS1

vene

SS)

= 36

.2%

, 2

(eff

ectiv

enes

s)

= 34

.8%

, 3

(app

eal)

=

29.0

%;

rese

aled

: 1

(eff

ectiv

enes

s)

= 37

.80/

o, 2

(in

offe

nsiv

enes

s)

= 31

.90/

o,

3 (a

ppea

l)

= 30

.3%

.

Evaluating Measures through Data J BUSN RES 67 19&X5:13:61-69

the ad. Some interesting insights into the scale are afforded by the resealing, though. “No opinion” generally appears to reflect a negative rather than a neutral or positive

evaluation of the ad. The average “no opinion” score across the 18 items is 4.34, closer

to the average value of scores assigned to the original scale point 3 (4.28) than to the average of the scores assigned to the “neutral” response category (4.87). Additionally, the polarity of the response categories varies considerably across the items. For example, the original scale point “1” is much more unfavorable for “attention-getting” (1 .OO after

resealing) than for “sexist” (4.42 after resealing). Put another way, many students describing the ad as sexist were generally favorable otherwise, while students who thought the ad was not attention-getting tended to be unfavorable overall. Finally, several of the resealings are not monotonic transformations of the original categories (l-7), suggesting that the scale was not always used as intended, or that multidimensional aspects of the evaluation process led to different patterns of responses. For example, “sexist” and “annoying” might be inseparable for one person but totally independent for another. To obtain a monotonic transformation, the disordered categories could be collapsed and the analysis repeated [19] . If a follow-up questionnaire were administered, the disordered items might be examined in more depth-for example, dividing “creative” into “creative headline” and “creative illustration”-to try to capture the extra evaluative dimensions.

Principal components analysis reveals three interpretable factors with eigenvalues greater than 1: effectiveness, inoffensiveness, and appeal. The raw data and the resealed data produce similar eigenvalues (9.60, 1.66, and 1.07; and 9.65,1.47, and 1 .Ol, respec- tively), but the ordering of the factors differs after rotation (Table 1). Effectiveness is first in proportion of variance accounted for with the resealed data but second with the raw data, with appeal being third in both cases. The loadings within the factors differ for only two items. With the resealed data, “intelligent” loads on effectiveness and “creative” loads on appeal, whereas they load on inoffensiveness and effectiveness, respectively, in the original metric. The resealed loadings appear to be more reasonable.

Possibly the greatest impact of the resealing is on the number of usable subjects. Almost one quarter would be lost by eliminating those with “no opinion” responses, and, as the weights show, any arbitrary treatment of no-opinion responses would be unlikely to contribute to the internal consistency of the measure. Although this makes little dif- ference in the example, it could be crucial in other situations. With longer questionnaires or more sensitive questions, many subjects might overlook or skip a small number of items. If nonresponses were not too numerous, dual scaling could be used to estimate scores for the missing items, allowing the retention of subjects who might otherwise be deleted from the data analysis.

Conclusion

Dual scaling is a very useful tool for analyzing categorical data. It and other methods of quantifying categorical data can be effectively applied to evaluating and improving measures used in research. Though ALSOS procedures have the advantage of being able to analyze mixed-metric data [20] , the capacity for multidimensional solutions and the simplicity of the analysis may in some cases make dual scaling more appealing or acces- sible to marketing researchers. Further work comparing the results of different scaling methods or developing new methods could lead to improvements in the state of measure- ment in marketing research [7].

The process of developing and validating measures can be complex, costly, and time consuming, and yet attention to these issues is critical to the advancement of marketing

68 J BUSN RES 1985:13:61-69

G. R. Franke

research [3]. Dual scaling may be used to gain insights into the meaning of measures,

potentially playing a useful role in this vital process.

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