This paper exaw”nes the current status of models used to estimate the reach andfrequency distributions for advertising rnzdia schedules. Two categories of issues are examined: (1) model building issues; and (2) model testing issues. In thejirst category, problems arising in the use ofprobability models are exam”ned in the DirichIet, loglinear, and aggregation procedures in magazines; problems arising in broadcast estimation using curve fitting, the beta binomial distribution and the poisson binom”al are discussed. In the second, issues relating to criterion data sets, sample size and error definition are exwru”ned. In conclusion, the need for true mu!tivariate probability models in print and broadcast estimation, Ihe need for standard data sets, the use of smaller sampie sizes in testing, and the need for standard error &finitions in testing are emphasized.
Proceedings of the 1992 Coderence of
The American Academy of Advertising,
Lcmard N. Reid, Editor
the estimation of reach and frequency disrnbutions have now been available publicly since at least 1958 @Iyett 1958). Some have come to find commonplace acceptance in practice, for example, the beta binomial disrnbution in one form or another (Schreiber 1969; Leckenby and Boyd, 1984), while others have been developed for proprietary purposes and largely hidden from public view
(Liebman and Lee, 1974). Still others such as the Ditichlet multinomialdistribution have been developed by academicians for their own interests (Leckenby et. al.,
1984).
Such models have gained wide-spread acceptance in both academia and practice. Yet there are many unresolved problems with these models which mitigate their validity as well as utility. These problems have not been discussed in a comprehensive manner except on rare occasion (L~kenby et. al., 1990), Limited discussion of model problems ordinarily has been developed for the purpose of showing improvement in one newly developed model over some currently competing model (cf., Danaher 1985). But this type of discussion avoids many larger issues which may be distinct from any particular model which, nonetheless, has prevented further progress in the field.
It is the purpose of this paper to examine somewhat more comprehensively the issues involving such models which remain to be resolved from two standpoints: (1)
Model Building Issues; and (2) Model Testing Issues. The consequences of ignoring these issues are inefficiency yin the allocation of advertising media dollars and a lack of knowledge of on-going, everyday practice both on the part of academicians and practitioners.
1[ is clear that the exposure distribution estimation models have been, and will probably continue to be, an important element in media planning by serving as essential building blocks for advertising decision making. Several studies have now indicated there is strong interest in further improvement in exposure disrnbution models (Leckenby et. al., 1982; Leckenby and Boyd, 1984; Kreshel e~ al., 1985;
Lancaster et. al., 1986). Ever-increming media costs, the “new media”, competition, and clutter make improvement in exposure estimation even more critical than in the past. This paper will attempt LO pint to some areas needing improvement and suggest ways for achieving such advances.
Before discussing the main topic of this paper, it is appropriate to review the position of media exposure estimation in the overall context of the estimation of advertising effectiveness. This brief review will se.wc
tO
clarify the importance of the main issues of this paper which will discuss inherent problems of media exposure distribution estimation models themselves and the testing procedures used to assess model performance.
I
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American Academy of Advertising
It is clear that the most effective message which is carried in a media schedule which always reaches few people will not provide for overall advertising effectiveness. It is equally apparent that a meti schedule with high reach and frequency which carries a message which is very ineffmtive will also not yield desirable overall advertising effectiveness. This simple idea that messages rmd media vehicles carg’ing the message
interact to provide their contribution to advertising effectiveness underlies the interest in and importance of the concept of
“effective frequency.” Media exposure estimation is a Iirnitcxi but important part of this picture in that it provides the basis for calculating the number of prospects reached with vehicles at each level of frequency of exposure to those vehicles.
The concept, “effective frequency”, is generally understood to be that frequency or a range of frequencies at which the responses by target market consumers to the effectiveness of a particular message in a particular media vehicle are at desirable levels consistent with the objectives of the advertising program
(Sissors and Bumba, 1989). Since the importance of the effective frequency concept is widely recognized by both practitioners and academicians, the question about how to measure “effective frequency” has been raised. Most of the
“effective frequent y“ studies manipulate frequencies of advertising to fmd the optimal effects of varying degrees of advertising repetition (Naples 1979; Sissors 1982). Consequently, there are some limitations in using this concept directly in media planning since there is no generally accepted indicator which explains the relationship between vehicle frequency and advertising frequency.
Several different approaches have been developed to address this problem. These efforts can be broadly classit%d as two types. One can be characterized as research measuring a direct ,Aationship between vehicle exposure and various measures of advertising effectiveness (vehicle exposure leading to advernsing effectiveness). The other is concentrated on the relationship between vehicle exposure and a particular indicator of advertising effectiveness, advertising exposure (vehicle exposure leading to advertising exposure).
There are two approaches in the study of vehicle exposure leading toadvertisingeffectiveness. For example, McDonald’s study measures advertising effectiveness in terms of purchasing patterns (brand switching) in relation to different levels of
OTS (opportunity to see the ad) (Naples 1979). Leckenby and
Wedding’s approach is an attempt to estimate Message/Media
Response Values (MMR) as an indicator of effective frequency of a given advertisement. In a particular media schedule after producing the vehicle exposure distribution, each level of vehicle exposures is multiplied by each score on one or more measures of advertisement effectiveness for the message (e.g.,
DAR) at the corresponding level of message exposure to get
101 effective frequency (Leckenby and Wedding, 1984). In othex words, this approach ties to calculate effective frequency by accounting for the effectiveness cf each tested advertisement.
Abemethy’s study is an example of the second approach
(vehicle exposure leading to advertising exposure) (Abernathy
1990). This approach suggests the norm of advernsing avoidance rates by reviewing several studies which examine qualitative aspects of television viewing (e.g., proportion of the set-inuse time with no viewers or inattentive viewers). A@ some media model researchers try to tackle the problem of vehicle exposure leading to advertising exposure by using a built-in deviee in their vehicle exposure distribution estimation functions (Litde and Lodish, 1986 Gensch 1969; Genseh 1970;
Rust 1985; Rust and Stoutj 1989). For example, Gensch’s simulation model includes judgmental inputs in his media evaluation stage. Little & Lodish include media weights in their formula, and Rust includes the conditional probability of exp@ sure to the ad, given exposure to the program, in his VID EAC model.
With technological development in data collection, information provided by BehaviorSean may give another way to explain “effective frequency.” Since it can trace who saw an ad and who bought a brand in a test market, BehaviorScan may explain the general relationship between ad exposure frequencies and the sales effectiveness of an ad. These can be obtained by analyzing a large amount of cases which include combinations of different types of ad content over different product categories. However, the information about ad exposure frequencies or ad ratings alone cannot be used in media planning for two reasons: firs4 few individuals turn on the television to watch an ad rather than the program, so that the ad rating is not independent with program rating, and secondly, ad space must be purchased in terms of the time and program context when a specific ad was aired and cannot repurchased only with respect to an ad rating. Because of this dependency, BehaviorSean data can be used in the second approach mentioned above (vehicle exposure leading toad exposure). The cumulated BehaviorSean information may suggest norms for explaining the discrepancy between vehicle exposure and ad exposure by analyzing combinations of different types of vehicle contexts, ad message contents, and product categories. At any rate, ad exposure disrnbutions generated via BehaviorScan data could not be used alone for media planning purpose without relating them to vehicle exposure distributions.
Although the issue discussed so far is very important and deseNeS extra effort in study, this paper will confhe consideration to media vehicle exposure disrnbution estimation only.
As can be seen above, either of the two approaches to the study and measurement of effective frequency requ”resknowkdge of vehicle exposure.
There cannot be an advrmee in media planning without improvement in exposure estimation since this serves as the essential building block for the development of effective reach approaches.
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102
There are problems which have developed which relate to particular issues in the print media field and the broadcast media area, especially television, both spot and network as well as cable. These will be considered in turn.
Print Models
Muhivariate Beta Binomial. The first magazine reachJ frequency model to follow a known probability distribution was the beta, develo~ by George Hyett in 1958 (Hyett 1958).
This later became known as the Metheringham Method
(Metheringham, 1964). It quickly became clear that the beta binomial, a univariate probability distribution, required a large amount of audience and duplication averaging which “washed out” peaks and valleys in actual distributions. The beta binomial also often yielded an over-estimation in reach. As in the field of statistics generally, this has led to the search for multivariate distributions which might preserve individual vehicle integrity as opposti to averaging them into a “composite” vehicle and then estimating the ensuing distribution (Headen et.
al., 1976).
The multivariate beta binomial was the fiist application in practice of amultivariatedistribution (Liebman and Lee, 1974), of which there is public representation. But because of the excessive computational problems, the true n-space (where “n” corresponds to the number of vehicles in a schedule) distribution was never employed. Instead, a bivariate, sequential strategy was developed (now called “sequential aggregation”) whereby two-vehicle, bivariate distributions were collapsed to form anew “composite” vehicle which was then combined with a third in twodimensional space and so on until all vehicles in the schedule were aggregated into the disrnbution (Lee 1988).
Occasionally, models used by practitioners might use true multivariate BBD’s up to six vehicles and then aggregate pods of six-vehicle composite distributions; six was usually the limit of computational possibilities. Either of these two procedures cannot be called “multivariate probability densities” in the true sense of this term (Johnson and Kotz, 1969).
Why is it desirable that a reach/frequency model foIlow a true multivariate probability density? There are several reasons for tlis. Flrs~ such probability distributions have been studied by probability theorists as well as those in applied fields of statistics and are, therefore, known to behave in certain predictable ways. Also, the assumptions inherent in the parameters of the distribution must be made explicit with respect to media exposure processes so that a theory of media exposure is made clear; this is not required in most ad hoc reach/frequency models. Probability distributions also must add (
O unity by definition, prohibiting such anomalies as reach greater than 100 per cent, for example. Finally, multivariate distributions are important to pursue because &ey allow for the most realistic and complex modeling of the media exposure process without a burdensome number 01’ simplifying or “averaging” assumptions required by uni~~riate probability functions. These sim -
Proceedings of the 1992 Conference plifying assumptions ordinarily distort the true, complex shape of the exposure distribution.
Dirichlet Mui(inovu”ai Dis~ribution. This distribution was the first true multivariate distribution to be applied fully to the magazine expcsure distribution process without device-s which distorted the tne multivariate proee.ss (Leckenby eL al., 1984).
The problem which arose with this distribution was tha$ by natu-e of the mathematical speciiieation underlying the distribution as formulated, it was applicable in exact form only to schedules which include an equal number of infections or buys in each vehicle in the schedule (referred to as symmernc schedules). Chandon (1976) suggested a hypergtmmetric recursion relation be applied post hoe to the results of Lhe DMD to solve this problem. This is unpleasing since the mai.ia
assumptions following the hypergeometric application are unclear.
Multivariate Sequential Aggregation. Lee (Lee 1988) be-
gan with the DMD as a basis and then employed it in a sequential aggregation procedure. This is still short of tie goal of finding a true multivariate distribution though his results were amazingly accurate as predictors of actual exposure dStsibutions. Squential aggregation amounts to a compromise in the interest of computational ease.
Log/inearApproximation Models. In an attempt to apply the
DMD in schedules with unequal insertions in the vehicles
(asymmetric schedules), Boyd (1985) developed, after a suggestion by Kishi (1982), a loglinear application of the DirichIet.
The testing process showed this model not to be empirically accurate as a predictor of actual magazine disrnbutions as derived from Simmons Market Research Bureau data. Also, its application beyond six or seven vehicles in a schedule was prohibitive because of computational limits (Boyd 1985).
Another application of the DMD using loglinear models was developed by Danaher (1985) which proved to be accurate, in contrast to the Boyd test, on magazine schedules using a New
Zealand data base as the means for the judgment of model performance. This application suffered, however, from the same computational limitation as the Boyd formulation; a maximum of six vehicles could be deployed in any given media schedule, an obvious limitation in practice of any model.
Subsequently, an approximate Ioglinear modeling process was developed which sacrificed accuracy of prediction for computational ease (Danaher 1988). Recent tests by the authors show, however, that computation of the distribution for 60 test schedules on a 286 PC personal computer took approximately two days to complete; use of a 486 work station cut this to about two hours, the same as on a VAX mainframe. Clearly, even this approximation is computational burdensome.
Finally, Danaher (1991) has produced a canonical variate approximation to expand the DMD. This appears to have solved the computational problems but at considerable sacrifice in predictive accuracy for certain types of media schedules. It is also an approximation rather than a true multi variate disrnbution.

Ameriean Academy of Advertising
In summary, the ~ch for a true multivariate probability distribution to be applied to any magazine schedule is still only an elusive one.
Broadcast Models
Curve Fitting Approaches. The earliest methods forestimation of reaeh in the broadcast media field are those associated with various curve fitting methods. In these approaches, typically, media schedules would be tabulated from Nielsen or
Arbitron data to reveal their actual reach according to the survey dam then the relation between Gross Rating Points (GRP’s) as the indepmdent variable and reach as the dependent variable in a two-variable analysis would reveal a non-linear curve showing a strong relationship between the two so that GRP’s for any subsequent schedule could be used as input to predict reach from the empirically derived curve.
A more sophisticated version of this approach is illustrated by equation (1) below:
AF=a+bl*GRP+b2*AP (1) where: AF = average frequency
GRP = gross rating points
Ap. tom.1 #
spots/total #
programs.
Fit by regression to some tabulated schedules, reach can subsequently be calculated as in (2) below:
R= GRP/AF (2) where: R = reach.
Another curve fitting approach involves the application of simultarmus linear equations to two data points available from the syndicated measurement senices such as Arbitron. This involves the following formulation, ordinarily, as shown in (3) below:
R = b * S where: R = reach
S = number of spots.
(3)
Two equations in two unknowns (actually one if the constant or intercept is assumed to be zero as would be the case in reality) can be developed in the fwst equation one spot is assumed to produce the rating of the spt as reach while in the second the maximum number of spots to be bought in a daypartin a market, say 132 for example, is assumed to produce the weekly cume or maximum reach reported by the data service. Reach can then be predicted for any sehedttle as a function of the number of spots contained in the schedule, awuming a linear relation between these two variables.
The fwst of these two approaches is undesirable since it is dependent upon the data set at hand; such curves must be recalculated each time the data set is renewed to ensure represcmmiveness. This is a time-consuming and possibly expen-
.~ive prcxxiure. The exposure theory behind this approach is
Unappealing.
103
The seeond approach is dangerous since it is based upon two extreme data points of the distribution. It is known to produce inaccurate results at the midpoint for certain types of schedules.
Of course, the non-linearity assumption of this approach could be relaxed through the application of some theory such as a logistic or concave model. Whether or not this would improve empirical results is unknown. Work of this type is largely proprietary and not publicly available. Since a great deal of applications in practice employ one or the other of the above approaches, it would seem desirable to explore these approaches publicly (Leckenby and Boyd, 1984).
Probability Models. The primary disrnbution to find application in the broadcast area television in particular, has ken the univariate beta binomial disrnbution (BBD). In an indirect estimation approach called the BBD-IE, Headen, Klompmaker and Ted (Headen et. al., 1976) developed a procedure using regression analysis of schedule chruacteristics such as number of SpOtS, grp’s and the like to predict the vfi~ce of tie BBD.
This is subsequently utilized with the grp’s to predict the two parameters of the BBD using the method of moments as described by Rice (1985).
This approach suffers from the same cbawbaeks as the curve fitting approaches, namely, the requirement of tabulated schedules upon which to conduct the regressions. This needs to be conducted periodically to insure representat.ivenes.s of the sample of schedules used to serve as the basis for the regressions.
In an approach called the BBD-LD, Rice (Rice 1985) developed a procedure using only the single audience ratings of spots and the number of spots to estimate the upper and lower bound on reach as the basis for retro-fitting a BBD using the method of means and zeros (Anscombe 1950). The lower bound of this method uses binomial reach of one insertion in each vehicle in the schedule. This lower bound can exeeed the true reach of a schedule, a theoretically as well as practically unpleasing result. In addition, the use of averaging an upper and a lower reach lacks a theoretical basis. Fhm.lly, estimating the reach independently of the probability distribution employed obscures the theoretical assumptions regarding the nature of the media exposure process.
Another approach to broadcast employing anexaet univariate distribution, the Poisson binomial, was developed by Ju (Ju
1991). It requires only single audience ratings of the spots in the schedule as well as the number of spots as input. It was found to perform as well as the BBD on magazine schedules but is as yet to be tested on broadcast schedules so that the results here are inconclusive.
In summary, the reach/frquency model development in broadcast has been relatively more dominated by practitioners and involves proprietary research for the most part than has that in the case of magazines. In the available literature only one example exists of the application of multivariate methods to television (Rust and Leone, 1984), and this was to address the problem of combining television and magazine schedules rather than estimating bro~dcast schedules only. Unresolved, then, is the development of true muhivariate probability disrnbutions
7(?:,

104 to model television and broadcast exposure processes generally.
Once a model has keen developed either by practitioners or academician, it is important, if not critical, to obtain some information on the performance of the model as a predictor of actual, delivered reach and frequency of a media schedule.
There are three important issues involved in model testing (1)
Criterion data sets employed (2) Error definitions as a means of assessing model accuracy; and (3) Test sample sizes employed.
Cn’#en”on Data Sets
Histon”ccd Precedence. The testing of reach/frequency models stems from tie early work by practitioners in the magazine field. The basic notion has historically been that
“prototypical” media schedules are conmucted to represent the universe of all media schedules which might be used in practice.
The data base upon which the average results for audience projections of individual vehicies is derived is then “head counted” to see, perhaps over multiple interviews of the same people, how many individuals in the database would be reached by the combination of media insertions in one or more vehicles.
These same averages must then necessarily serve as input to the models which “predict” these head-counted reach projections.
Alfred Polit,z was one of the first audience researchers to utilize this technique to predict and measure the cumulative audience ofLife magazine (Poli(,z 1950). Much later, using this basic approach, Greene and Stock (1967) showed in a study for
Readers’_Digest magazine that the BBD could accurately predict the multiple cumulative audiences of that magazine very accurately. But initially, tabulation of the ,actual data base
(head counting) was used by Politz to calculate the cumulative reach of magazines, and it is this precedent which set the stage for the notion of model estimate testing (Politz 1958). William
Simmons carried on this approach through the W.R. Simmons and Associates studies (1977). But eventually, even the data services provided estimates of cumulative audiences beyond two insertions in the published “books” of their audience surveys using the BBD as opposed to head counting (Simmons
Market Research Bureau, 1979).
In summary, whether this is d~irable or not, to&y model testing procedure has come to mean that syndicated audience data will serve as the benchmark to assess the accuracy of any model. This has certain implications. For example,
United States, Simmons Mwket Research Bureau (SMRB) collects data on two subsequent interviews with the same sampling uni~ this means that for the input data to match the tabulated data from this service, models may be tested only using two insetions per vehicle, an obvious limitation of fu]lrange model perfo~~ce xsessment. It may be desirable to collect pnm~ data specific~ly for the purpose of testing the full-range performance of models independently of the syndicated measurement services.
Proceedimm of the 1992 Conference
AudienceMearuremetiMethodology. There are few, ifany, published studies of the tests of mcxiels which employ data other than that of syndicated services. This means that model builders who wish to assess the validity and reliability of their models must choose among those services available to them. In the magazine field in the United States, this means a choice essentially between SMRB and MRI (Media Research, Inc.) fm general interest publications. SMRB utiiizes “through- thebook” method and MRI, on the other hand, utilizes “recent reading” method for all publications. Which serviee should be used as the benchmark?
Comparability of Findings. Ideally, whenevera new reaeh/ frequency model is developed, it would be desimble to be able to compare its likely performance with that of existing models which may have bcxm previously tested so that exact one-to-one comparisons em be made. This would require that the same data set, say 1988 SMRB data would be used to test a model developed in 1989 and one, say, in 1992. Or, perhaps the old model would be retested with the new model on 1991 SMRB data. Frequently, however, models must be compartxi in the magazine field which have been tested on different yearly data sets. In reality data sets do change from year toy= and the models should be able to account for this. Ideally the models should be tested on multiple year data sets to assess the generalizability of the process. Therefore, if the rtxdity of media consumption has variance, then the models must be able to adjust for this instead of “assuming the problem away” by using one standard data se~ However, most models were tested on one year’s data set partl y because of availability of data sets, and partly because of time consumption in data tabulation. So if it is not practical or possible to use multiple year data to test individual’s model, then it is helpful to have a standard data set that everyone tests their media models on.
This situation is not quite as discouraging as that which occurs when different syndicated benchmarks altogether are used by researchers to test their models. For example, theDMD for magazines has been shown to be the best in performance on
SMRB data sets of any magazine model publicly available
(Leckenby et. al., 1990). But when the DMD was tested on magazine data from New Zealand along with the approximate loglinear model, the loglinear model was found superior on some error definitions but not all of those error definitions employed in that study (Danaher 1988). The authors are currently testing the loglinear model on an SMRB data set along with the DMD and other models. This work would be unmxessary had the model builder had access to the SMRB data set.
Another problem which destroys comparability of results across studies, and prevents metatheoretical development in this area, is the lack of agreement on standard error definitions by which model performance is judged in the tests.
Error Definitions
Use of Error Definitions. Following is an incomplete list of error definitions which have mn used by various researchers in the published literature to assess model performance: Aver-
726

American Academy of Advertising age Emorin Reach, Chi-square, 95 pereent Confidence Interval,
Average Percentage Error in Distribution, +/-5 percent of
Actual Reach, Tots.lEmorin Distribution, Correlation of Actual and Estimated Distribution, Average Error in the Distribution,
Average Exposure Level Error, EffectiveReachError, Number of Over, Under and Within +/- 5 percent at each Exposure
Level, Maximum and Minimum Average Percentage Error in
Exposure Distribution,Mean SquaredErrorirt Exposure Distribution, Relative Error in Reach, Error in Exposme Probabilities over Reach, Absolute Error in Effective Reach, Sum of Square
Frequency Error, and Average Absolute Frequency Error.
Clearly, one study will not utilize all these error measurements to evaluate a given set of models. TypicaI1y, one study might use four of the above (Danaher 1988).
Non-Comparability of Findings. When an attempt is made to determine which of the models in the literature is superior in performance to another, this becomes extremely difficult because authors use different error criteria (Leckenby e~ al.,
1990). The use of different data sets across tests poses one set of problems, but the use of different error criteria across tests makes it imp.sible to make any comparison except on a rank order basis. This is a formidable roadblock to the development of any theQry of media exposure processes based upon cumulative knowledge development over studies. Clemly, some standards of examination are needed.
Error Definition Standards. It would be extremely beneficial if a seleetion of two or three error definitions in reach and two or three error definitions in the exposure dishibution could be agreed upon by those engaging in reach/frequency research.
Perhaps editors of academic journals could play a role in this as well as a media standards committee of the Advertising Research Foun&tion.
Perhaps what is needed initially is a study of the sensitivity of performance results of various models to the different error definitions toexarnine which provide the most precise indicator of mrxiel accuracy; this could be balanced with an evaluation of their intuitive importance in application work in practice.
Test Sample Size
Why So Large? The sample sizes of schedules used to test media reach/frequency models has varied from very small (n=4 in one proprietary test in which one of the authors was recently involved) to extremely Iarge (n of approximately 2000) in a television study by Headen, Klompmaker and Teel (Headen et.
al., 1976).
In the absence of any adjustments to inferential testing to minimize Type I Error, almost all models will be different on almost all error criteria using such statistical tests with sample sizes of approximately 2000 (Greene and S tock, 1967). Just as clearly, a sample size of four is not going to provide very convincing evidence of a model’s performance
wide range of schedule possibilities.
Some reasonable set of schedules needs to be tested and selected in a random fashion yet be representmive of the types of schedules actually encountered in practice. At minimum,
105 studies need to report the characteristics of the resulting test schedules in terms of GRP’s, number of insertions, number of vehicles and the like with maximum and minimum values of these noted so that a judgment can be made as to the reasonableness of the sample.
From the statistical inference point of view, little is to be gained by having a sample size over 300 schedules if subcategories (such as demographic or daypart) are not to be examined and compared.
This examination has shown some areas of reach/frequency model research needing attention. This survey has pointed out at least three problems which need some careful, concerted attention if progress is to be made in this field of advertising research.
FirsL if the field is to eseape from the predominant mode of ad hoe formulas which provide no expknation or insight into media exposure processes, a true multivariate probability distribution applicable to print and broadcast media schedules must be developed. The DMD provides a good starting point for study here.
Next, while it is not mandatory for progress in this area, it would be helpful if standard data sets which allow for a fullrange test of a model’s performance are developed and shared by the research community as abasis forcomparabletestingmd results. Perhaps the syndicated data serviees as well as reaeh/ frequency on-line services could cooperate with academicians through the Advertising Resetich Foundation to this end.
There is no reason to continue the overkill in sample size in this arm of work. It occurs in no other part of the advertising research field, and there appears to be little
for it to continue here other than tsadition. A sample size of 60-100 or
200 schedules randomly selected would provide for the intelligent application of inferential statistics.
Finally, it maybe desirable to examine all previous literature, say in the more highly developed magazine area with an eye toward theory development. There is no exwt m~ia reach/frequency theory which could guide further development of this area other than basic probability theory. While probability theory is extremely powerful, it could help to have mediaspecific theory in advertising.
It is hoped that this discussion will contribute to further beneficial development of media reach/frequency models.
Abernetiy, Avey M. ‘“I’elevision Exposure Programs vs. Advertising.” Current Issues and Research in Advertising, James H. Leigh and Claude R. Martin, Jr., eds., 1990, 61-77.
Anscombe, F.J. “Sampling Theory of the Negative Binomial and
Logarithmic Series Distributions.” Biornetrika Vol. 37, (December 1950), pp. 358-382.
Boyd, Marsha M. The Dirichlet Mulfiwriafe Mulfinornial Distribu-
tion as a Magazine Exposure Model. Unpublished doctorat dissertation, University ’of Illinois at Urbana-Chmptign. 1985.

.
.
106
Proceedings of the 1992 Conferenc e ChanciOR Jean-Imuis. A Comparative Study of Media Exposure
Models. Unpublished doctoral dissertuio~ Northwes~m University, 1976.
Danaher, Peter J.
“A Log-l,ineu Model for Predictig Magtie
Audiences,’’Jouml ofMmktkgResemch 25 (Novem& 1988),
356-362.
“~ Approximate Loglinear Model for Predicting Magazine
=diences,’’JomuIofMubthgResemch 26
(November 1989),
413419.
Leckenby, John D. and Wedding, Nug~t. Advert&kg M~gwm:
Criterk, Analysis and Decision Making, Columbus, Ohio: ~d
Publishing, hlC.,
1982.
Lee, Hae Kap. Sequtikl Aggreg&kn Advertiskg Me&a Mo&~.
Unpublished doctord disse~io~ The UniversiY of Texm at
Aust~ 1988.
Liebmq Leon and Lee, Edward. “Reach and Frequacy Estim~m
Services,” JournaIofAdvertiskg Research 14 (August 1974), 23.
—. “A C~OniCd Expansion Model for Multivzia~ Media Litd2~” Jo~ D C ~d ~dis~ ~wd M
Expsure Dis~ibutiom,”
JOUTM1 of Marke!ing Research 28
. .
(August 1991), 361-367.
“A Media Pl-
Calculus,’” in RtssL Roland T. Advertising Media Model: A
GenscL Dennis H. “A Computer Simulation Model for Selecting
PracticaIGti&. (Appendix 5A), Lexingtom Massachweti: Lex-
Advertising Schedules,’” Journal of Markting Research 6 (May
ington Books, 1986, 77-111.
1969), 203-214.
Merher-inghm, Richard A. ‘*Measuring the Net Cumulative Coverage
“Media Factors: A Review Article,”
JOIUM1
of Marketing of a Print Campaign,” Journal ofAdvertising Research 4 (kern.
=~arch 7 (May 1970),216-225.
Greene, J. and Stock J.S. Adverttiing Reach and Frequency in
Magazines. New York New York: Marketmath and Reader’s k 1964), 23-28.
Naples, Michael J. Effective Freqw: The Rekrtbmh@ B&em
Frequency andAdverti.ring
Effectiveness, Association of Nat.iond
Digest, 1967.
Advertisers, Inc., 1979.
Headen, R., KlompmAer, J. and Teel, J. “TV Audience Exposure,”
Politz, Alfred. A Study of the Accwul~ive Audkme of Life, con-
Journal of Advertising Research 16 (December 1976), 49-52.
ducted for L.jfe, New York, New York Tne, Inc., 1950.
Hyet4 G.P. ‘The Measuremmt of Readership,” paper read to the
Audiences Reuhed through Magazine Combtibm, CowleS statistics semina, London School of Economics, February, 1958.
=~gazines, Inc., 1958.
Jdmson, NormaI L. and Kotz Samuel. Discrete Distributions. New
Rice, Marshall D. Television Exposure Distrib~hnMode[s inAdver-
York: John Wiley & Sons, 1969.
/ising Media. Unpublished doctoral dissefitio~ University of
Ju. Kuen Hee. Simple
Approaches to Modeling Advertising Media
Illinois at Urbana-Chmpaign, 1985.
.!hposure.
Unpublished doctoral dissertatio~ The University of
Rust, Roland T. “Selecting Network Television Advtishg Schd-
Texas at AustiII, 1991. tsles,” Journal of Business Research 13 (1985), 483494.
Rust, Roland T. and Leone, Robert P. ‘The Mixed-Media Dirictiet
Kishi, Shizue. Exposure Distribution Models in Advertising Media.
Unpublishd doctoral dissertation, University of Illinois at Urbana-
Multinominal Distribution: A Model for Evaluatig Televkion-
Charnpaign, 1982.
Magazine Advertising Schedules,” Jourml of Martikg Re-
Kzeshel, Peggy J., Lancaster, Kent L., and Toomey, Maraget A.
search 21 (February 1984), 89-99.
“Advertistig Media Planning: How Leading Advertising Agen-
Rust, RolandT. and Stout, Pat. ‘~CarS Existing Media SelwtionModels
cies Estimate Effective Reach and Frequency, ” Journal of Adver-
Irtcorporate Qualitative Aspects of Television Viewing?” Pro- tising 14 (Summa 1985), 32-38.
ceedings of theAmricmAcademy ofAdvertiskg, San Diego, CA
Lancaster, Kent M. Kreshel, Peggy J., and Harris, Joys R. “Estimating
March, 1989, RC 99- RC 103.
the Impact of Advertiskg Media Plans: Media Executives De-
Schreiber, Robert J. ‘me Metherhghm Method for Media Mix: ASI scribe Weighting and Timing Factors,” Journal ofAdvertising 15
Evaluatio~” Jourml of Advertising Research 9 (June 1969), 54-
(September 1986), 21-29.
56.
Leckenby, John D. and Boyd, Marsha M. “How Media Directors View
Sirrtrnons, W.R. and Associates, Inc. Selective Markets and Media
ReachfFrequmcy Model Evaluation Stan&WCIS,” Journal of Ad-
Reaching Thm New York, New York, W.R. SirnmoIIS and
vertising Research 24 (OctobrNovembr 1984), 43-51.
Associates, Inc., 1977.
Leckenby, JohrI D. and Ju, Kuen Hee. “Advmc~ in Media Decision
Simmons Mazket Research Bureau, Inc. The 1979 Sttiy ofMediad
Models,” Curreti ISSUS and Research in Adverting, James H.
Markets, New York New York, Simmom Market Resmch Bu-
Leight and Claude R. Martin, Jr., eds., 1990,311-357.
reau, Inc., 1979.
~ckenby, John D. azsd Kishi, Shizue. “How Media Directors View
Sissors, Jack Z. “Confusions Atsouc Effective Frequmcy,’’Joum/of
Reac~requacy Estimatio~” Journal of Advertising Research
Advertising Research 22 (Decem&/Jmu~, 1982), 33-37.
22 (June/July 1982), 35-44.
Sissors, Jack Z. and Bumb~ Lincoh. Advertising Media Pltig.
Third Edition, Lirvdnwood, Illinois: NTC Business Book, 1989.
—. ‘The Dirichlet Multinomid Distribution as a Magazine
Exposure Model,” Jourml of Markting Research 21 (Febm~
1984), 100-106.
—
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