Estimation Method for Media Audience Duplication - IBOPE Time Chile

7/25/2019 Estimation Method for Media Audience Duplication - IBOPE Time Chile

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Estimation method for media audience duplication

Patricio Moyano Galdames and Orlando Muoz BalmacedaTime Ibope, Chile

Elias Selman CarranzaIbope Time Pacific, Chile

OVERVIEW

Modeling the duplication of vehicles audiences has a long history in our field, both successful and unsuccessful, from Agostini's method,1with its

controversial K constant, to the more broadly accepted Metheringham Method (Beta Binomial Distribution).2But this outstanding pioneer in the study of

audience duplication phenomena left us with a serious problem: the decline of reach in the case of the addition of a spot with a lower average rating tha

the previous average.3The discussion of this problem has not advanced significantly. This undesirable effectthe decline of reachled many of our

colleagues to improve their estimations using proprietary models of a similar type. 4However, these experiences are all linked principally to readership

estimations used to solve the problem of advertising in print media.

In television, the considerations are somewhat different, as people's exposure depends on day parts and programming schedules. Therefore, it is

necessary to analyze intra- and inter-channel duplication. Initial investigations assumed constant duplication5in the set of media outlets analyzed.

One approach that simplifies the analysis, and which has been used for a long time, is to assume that duplication is a random event and thatconsumption of a media outlet, program, etc., is an independent phenomenon. But this solution is questionable with respect to the estimation of mediareach.

With the rise of personal computers, there has been an explosive growth in the analysis of media plans and of software used for this purpose with

evaluation functionalities6that provide statistics on reach, average frequency, exposure distributions, etc. It should be pointed out that these systems

work by calculating real duplication using a raw database produced by research, especially using the People Meter system. In some cases a finaladjustment is performed in order to match the published GRPs (daily) with those calculated using a constant sample panel that is generally formed on th

middle day7of the period being evaluated.

The need for combined media assessments has led market researchers to design a methodology generically known as single source.8When inquiring

about the consumption of different media in a single interview, it is possible to use this same data to perform multimedia evaluations using the samesample. This is unquestionably an adequate solution, but the information it provides is more for media strategy (long-term), while the purchase of spacin vehicles is more closely related to media tactics (short-term), particularly in television, where the fight for audience occurs on a daily basis andspecialized studies, such as those of readership or those using the People Meter system, provide more accurate and detailed data.

Another alternative, which is both new and promising, is data fusion. This interesting technique uses common elements to match up the contents ofvarious databases, thereby creating one single database. It is also possible to assume that a multimedia estimation is an adequate approximation,except that the complexity involved in matching more than two databases requires the additional assumption that the matching variables are sufficient establish a consistent fusion.

In short, there are different approaches to the problem of evaluating media plans, especially when they are mixed, e.g. based on the different needs ocommunication campaigns for products and services.

Our approach takes into account the fact that specialized studies for audience measurement provide the highest-quality and most detailed data, and thathey are used intensively in the purchase of spaces. What is lacking is a consistent link that would allow consolidation of the results of globally-viewedadvertising media plans with high precision and low information loss.

THE MODEL

We define f(x)as the distribution of the frequency of a certain schedule for a media outlet, A, and g(y)as the distribution of the frequency of another

schedule for a media outlet, B. Thus, the problem is creating a new intermediate distribution that we will call h(x,y)and which describes the joint effecof the two schedules on the campaign's target group. Then, in the following stage, it consolidates this in a new distribution that we will call T(z).

Thus, the distributionsXand Yshall be the marginal distributions of the joint distribution obtained from the algorithm that we will describe below.

The expected value E(X)of the distributions is equal to the GRPs of each schedule (see Equation 1).

Then, the condition that must be satisfied by the new distribution T(z) final is that the GRPs be equal to the sum of the two distributions and that thetotal reach be equal to or greater than the largest of the two reaches and less than the one produced under the hypothesis of independence.

Conditions:

1. Grps(T)= Grps(X)+ Grps(Y)

2. Reach(T) Max(Reach(X),Reach(Y))

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3. Reach(T) Reach(X)+ Reach(Y) (Reach(X)) (Reach(Y))

Where Reach= l-f(0), that is, 1 minus those who do not see the schedule.

This procedure begins by calculating the new total reach, which is assumed to be within the interval of the conditions described above.

The Limits of the Reach from the Point of View of Set Theory

1. The maximum reach of both schedules (see Figure 4)

For the minimum level, we are assuming that the reach of schedule A is contained in or is a subset of B, which means that A does not exceed the reach(see Equation 2).

This means that when consolidating both schedules, the total reach is equal to the reach of B.

2. The schedule B is independent from A (see Equation 3)

This means that the intersection of schedules A and B is the product of their probabilities (see Equation 4).

This means that the maximum level is equal to random duplication.

CREATING THE FACTORS

First, the factors that determine the maximum and minimum levels of reach are calculated; the interval of the solution of the total reach (the result ofconsolidating both schedules) is defined here.

Factor: Maximum Reach of Both Schedules. This corresponds to the factor with which the reach of the lower limit of the consolidated schedule is obtaine(see Equation 5).

Factor: Random Reach (Independence). This corresponds to the factor with which the reach of the upper limit of the consolidated schedule is obtained(see Equation 6).

New Factor or Probabilistic Factor. The factor most likely to occur (see Equation 7).

The new total reach or mixed reach of the consolidated model is determined using the probabilistic factor (see Equation 8).

Figure 1depicts the curves of the three factors as a function of increases in the GRPs. They make the reach increase, but with decreasing returns. The

factor acts to decelerate the reach as a function of increases in the GRPs, as they are basically the OTS minus the GRPs.

The step that follows the estimation of the mixed reach of the schedules being consolidated is to calculate the ratio that allows the joint distribution of thdistributions to be created.

Estimation of the Ratio: This Ratio will make it possible to distribute the joint proportions of the schedule distributions that are being consolidated (see

Equation 9).9

Where random duplication (Duprdm

) is: (see Equation 10)

Within the concept of probabilities, this duplication involves independence between the media that are being consolidated. In other words, theconsumption of one media outlet has no influence on the consumption of the other.

Where actual duplication is: (see Equation 11)

In the following section we present an example that illustrates the application of this method.

ILLUSTRATION

In order to illustrate the methodology that consolidates the frequency distributions of various media, two schedules were created: a television scheduleand a print media schedule. The schedules were then evaluated using the software currently available in the Chilean market, TVdata and PrintPlan, whicare used for television and print media schedules, respectively.

The target group used here is the total number of people (in Chile) between the ages of 25 and 54; this universe comprised of 2,149,519 people. Figureshows the output of the software when applied to the two schedules being studied.

The frequency distributions of individual media are presented in Table 1(also see Table 2).

Estimation of Maximum Factor. This is the factor that corresponds to the lower limit of the consolidated schedule. In this case it is the minimum reachpossible in the new distribution, which is to say the maximum reach of the media evaluations, independently. Let Reach

maxbe the maximum reach of th

two schedules, let GRPtv

be the GRP obtained in the television schedule, let GRPpr

be the GRP obtained in the print media schedule, and let GRPmix

be

GRPtv

+ GRPpr

(see Equation 12).

Estimation of the Random Factor. This is the factor that corresponds to the upper limit of the consolidated schedule. In this case, it corresponds to therandom duplication, which means assuming independence between the media. Let Reach

rdmbe the reach when assuming random duplication (Dup

rdm)

(see Equation 13).


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Estimation of the Probabilistic Factor. This is an average of the Maximum and Random factors, weighted according to their respective reaches (seeEquation 14).

Estimation of the Reach of the Consolidated Schedule: The weighted factor is used to determine the reach of the consolidated schedule (Reachmix

). It is

calculated as follows in Equation 15.

Calculation of Actual Duplication. Once the reach of the consolidated schedule has been determined, the actual duplication of the television and printmedia schedules can be determined. We label designate duplication as Dup

act. We know that the reach of the consolidated schedule (Reach

mix) is the

sum of the reaches of the television schedule (Reachtv

) and the print media schedule (Reachpr

), minus their duplication (Dupact

), that is: (See Equation 1

This produces: (see Equation 17)

Estimation of the Frequency Distribution of the Consolidated Schedule:In order to estimate the consolidated frequency distribution, the proportion of thenon-impacted ones (zero frequency) of both distributions (television and print media) must be recalculated.

1. Estimation of the Ratio: (see Equation 18)

2. Re-estimation of the proportion of individuals not reached by each schedule: (see Equation 19)

Where:

P*,0

: Re-estimation of the proportion of people not reached by the television schedule.

Pj=0

: Original proportion of people not reached by the television schedule.

P*0,

: Re-estimation of the proportion of people not reached by the print media schedule.

Pi=0

: Original proportion of people not reached by the print media schedule (see Tables 3and 4).

The distribution of the consolidated frequency is obtained from the matrix in which the frequency distributions of the media are combined with their recalculated zero frequency.

Let

Be

Pi,j

: Matrix cell i,j contains the proportion of individuals exposed i times to the print media model and j times to the television model, where i=0,1,...,11+

and j=0,l,...,9+.

P,j

: Frequency distribution of television with the recalculated zero frequency.

Pi,

: Frequency distribution of print media with recalculated zero frequency.

Matrix cell 0,0 contains the proportion of individuals not exposed to either of the two schedules, meaning the people who are not exposed to theconsolidated schedule. The method of calculating this is as follows in Equation 20.

The remaining cells in the matrix are calculated the same way. To exemplify our methodology, the calculation of cell (1,0) is shown (see Equation 21).

Cell (i,j) indicates the proportion of individuals who were impacted i times by the print media schedule and j times by the television schedule. Adding upthe diagonals of the matrix produces the respective frequencies of the consolidated schedule. By way of illustration, Table 4shows the diagonal that

corresponds to frequency 4 of the consolidated distribution (0.0056 + 0.0284 + 0.0387 + 0.0349 + 0.0145 = 0.1221).

Table 5shows the frequency distribution after consolidating the television and print media distributions, which produces a reach of 75.04 (100 24.96)

and a GRP of 247. This coincides with the sum of the GRPs obtained by the television and print schedule. Figure 3shows a graph of the consolidated

frequency distribution.

Table 6summarizes different evaluations of combined schedules, comparing the proposed method with the results obtained by treating the data as asingle source.

CONCLUSION

This model incorporates a methodology which allows consistent evaluations to be performed using diverse data sources, especially those fromspecialized media studies, due to the fact that it uses the final data of each distribution.

The table above compares the results of this method with those obtained by processing the data as a single source.

This confirms that the differences are not statistically significant, which validates the model.

FOOTNOTES

1. Agostini, J.M. How to Estimate Unduplicated Audiences.JAR,March 1963.


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2. Metheringham, R. A. Measuring the Net Cumulative Coverage of a Print Campaign.JAR, December 1964.

3. Leckenby, J.D. and M.D. Rice. The Declining Reach Phenomenon in Exposure Distribution Models.Journal of Advertising(15), 1986.

4. Metrex, TruCume and MetherPlus are a few examples of improved estimation models.

5. See Goodhart and Ehrenberg's 1969 papers.

6. Time Ibope provides the TV data software that was used to carry out these evaluations.

7. This adjustment generally uses probabilistic negative binomial distributions.

8. For example, TGI (Target Group Index) and EGM (Estudio General de Medios, General Media Study).

9. For more information, see Katz, Lancaster. Strategic Media Planning.

NOTES & EXHIBITS

EQUATION 1

FIGURE 4

EQUATION 2

EQUATION 3

EQUATION 4


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EQUATION 5

EQUATION 6

EQUATION 7

EQUATION 8

FIGURE 1: SOLUTION OF THE REACH COMBINED


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EQUATION 9

EQUATION 10

EQUATION 11

FIGURE 2: RESULTS PRODUCED BY TVDATA AND PRINTPLAN SOFTWARE


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TABLE 1: DISTRIBUTION OF TELEVISION AND PRINT MEDIA FREQUENCY

TABLE 2: SUMMARY OF THE RESULTS OF EVALUATIONS OF A TELEVISION SCHEDULE AND A PRINT MEDIA SCHEDULE


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EQUATION 12

EQUATION 13

EQUATION 14

EQUATION 15

EQUATION 16

EQUATION 17


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EQUATION 18

EQUATION 19

TABLE 3: FREQUENCY DISTRIBUTIONS OF TELEVISION AND PRINT MEDIA WITH RECALCULATED ZERO FREQUENCIES

TABLE 4: COMBINATION OF THE FREQUENCY DISTRIBUTIONS OF TELEVISION AND PRINT MEDIA


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EQUATION 20

EQUATION 21

TABLE 5: FREQUENCY DISTRIBUTION AFTER CONSOLIDATING TELEVISION AND PRINT MEDIA DISTRIBUTIONS


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FIGURE 3: CONSOLIDATED FREQUENCY DISTRIBUTION

TABLE 6: SUMMARY OF EVALUATIONS OF COMBINED SCHEDULES

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Estimation Method for Media Audience Duplication - IBOPE Time Chile

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