Editor’s note: Michael Lieberman is founder and president of Princeton, N.J., research firm Multivariate Solutions.

The first point I make to apprehensive students at the initial lecture of my basic statistics course is that statistics, when you boil it down, is simply a numerical description of an event. The confusing and scary array of correlations, regressions, ANOVAs and null hypotheses is no more than a collection of techniques to get an idea of what is happening.

Good research is the same. Quality information, professionally gathered and well-presented, provides a clear story with actionable, marketable results that are easily understood by the supplier and the client.

In this article we explore the performance score, a technique that presents information in an easily understood format for use in executive decision-making. We compress data from complex mathematical analyses into one number that can be used to compare performance across an array of attributes. This technique has been applied in the fields of public relations, publishing, advertising, retail, restaurant chains and professional sports.

The performance score is created by a weighted measure of attributes as they relate to a key attribute, such as overall satisfaction with a store or intent to purchase an item. The weights are created by measuring association to the key attribute - the dependent variable.

Let’s use a restaurant chain as an example. This chain has regular visits from diners who rate the restaurant on, say, 10 attributes, as well as giving an overall rating. The attribute weights are derived using regression analysis to determine the importance of each attribute relative to overall rating. The importance - or weight - of each independent attribute is called a beta score.

Table 1 is the output from our restaurant chain’s regression presenting data compiled from over 20,000 records.

Examining Table 1, we see that meal preparation and quality are the most highly-weighted attributes, which should not be a surprise. Now we want to synthesize these results into one score for the restaurant. We do this by multiplying each beta by the diners’ combined overall rating and adding them up. We then combine the score of different restaurants into a grand mean for the chain’s restaurants as a whole.

We now have a score for each restaurant which can be directly compared to the chain’s grand mean to easily see each restaurant’s relative performance, resulting in a value called the index. This individual restaurant ratings performance index is calculated by dividing a restaurant’s score by the grand mean and multiplying it by 100.

In Table 2, a comparison of restaurant ratings performances, a look at Key West’s index shows that it is doing better than average with an index of 112.

To then calculate percentiles, the restaurants in the sample are sorted highest to lowest, and the top restaurant is given 100 and the bottom one is given a 0; the percentiles are then calculated for the ones in between. The percentile shows, at a glance, the relative position of a given restaurant. The percentile is particularly useful if the sample has tightly bunched scores, producing indexes that are similar.

Interpreting the percentile is straightforward. Miami has a percentile of 44, which means that 43 percent of the restaurants have lower scores, and 56 percent scored higher. I would say the manager of the Miami branch is not pleased.

This comparison system can be applied to any unit of choice such as market, state or region.

Application: publishing

There is a snap, crackle and pop formula to selling magazines. Cover choices are often determined by focus groups, though quantitative methods are becoming increasingly relevant. In fact, we have found that applying the performance score method gives a quick and easy winner when an editor wants to know which of, say, four covers to go with.

As an example, the performance score can be determined through an online survey which shows a magazine cover, then asks the invited participant to rate each of the factors (shown in Table 3), then give an overall score. Or, consumer views can be gathered through mall intercepts, where individuals in the target groups (e.g., twentysomething professional women) are shown a magazine cover. While an eye-tracking device measures the respondent’s eye movements, the participant is asked to rate each cover on a scale, say 1-to-7.

This technique is most effective when the results are applied to an analytical model derived from historical data - a publisher’s database containing measurements from publications over a specified time period. The model can then be applied as needed.

Table 3 shows the regression results of the historical model. The model gives us both descriptive results - we know that the photo and article content are the most persuasive - and the publisher now has the ability to easily analyze data comparing potential covers. Table 4 shows the index scores for several tested covers.

Which cover will the editor go with? Table 4 gives the answer: “Lives of the Rich and Infamous,” using photo two.

Application: retail

A major national retailer has a database of millions of customer surveys. These are fairly extensive, ranging across different sections of the store. The retailer (we’ll call it WorldMart) wants to benefit from this wealth of information.

Again the first step is the model. In this database WorldMart has cases where a given customer has rated cosmetics, another the pharmacy and others the menswear department. Within each category there is an overall score. Each respondent also rated their visit and the likelihood of returning to this store.

The regressions were run, accounting for the differences among the departments such as the greater frequency of visits to the pharmacy.

WorldMart requested modified output in order to assess units within its empire on different levels. It wanted a universal number that could be calculated as needed. We provided the ability to calculate a percentile for each filter, department and manager.

The equation is:

[[Tested Store Score-Minimum Store Score]/[Maximum Store Score-Minimum Store Score] multiplied by 100.

In this equation the maximum WorldMart score was 132, the minimum 88, and the store we are looking at 112.

((112-88)/(132-88))100=54.55, or 55

The benefit of this approach is that it allows WorldMart to shine a spotlight exactly where it wishes. Table 5 shows the output of a request for cosmetic store performance in one state. Table 6 shows pharmacy performance by region. And Table 7 shows performance by regional manager.

Overall, Smith is not doing too well. He is going to have to sit on some staff to improve customer service or his head might roll. Smith’s best manager, Potter, is only just above average. Managers Vase and Fleener had better improve their numbers or update their resumes.

Application: advertising

The performance score can be further simplified by creating a visual presentation. This is effective when presenting performance score results to senior management or pitching to a potential client.

After a two-day mall intercept in Las Vegas, the McMann-Bronfman advertising agency is presenting the results to product managers at cosmetics firm Face Parisian. Rather than present detailed multivariate analysis, the ad agency is able to present a clear summary chart, as shown in Figure 1. I think the Face Parisian team will go with Copy C.

See and compare

Decision-makers are interested in utilizing sophisticated data analysis to improve their market position. Our system gives managers with diverse backgrounds the ability to see and compare relevant information. It is cost-effective, has wide application and provides findings in a simple, graphical presentation, making it a valuable measurement tool.