from Stats, published by the American Statistical Association
Fall 1998, Number 23, page 22-25

Statistics in Marketing: An Analysis of the Arizona Lottery

by Kathryn DeBoer, WestGroup Marketing Research

Introduction

Market segmentation is a marketing tool used to direct products and services to targeted groups of consumers. The objective of market segmentation is to identify characteristics of the consumers who will most likely have an interest in a product or service. This information is then used to design a marketing strategy. Information obtained from a market segmentation study can be used to define the market of an existing product, provide information for introducing a new product, or help find new opportunities in a market. A complete market segmentation study requires the use of two well known statistical methods-factor analysis and cluster analysis. Much of the work is descriptive and requires both mathematical models and subjective decision making.

In this article, we present the results of a market segmentation analysis conducted in 1996 for the Arizona Lottery. The purpose of this article is to show the wonderful way statistics combines with psychology in providing insightful and useful information about the people who play Lottery games. We begin by giving you some background for this study, and then discuss the statistical methods employed in the study.

The Arizona Lottery

The Arizona Lottery consists of many games of chance - Powerball (a high-jackpot, multi-state draw game), Lotto (a high-jackpot, in-state draw game), Fantasy Five (a lower level jackpot, in-state draw game) and Instant Scratcher games. The odds of winning are best with the Instant Scratcher games which have lower payoffs (highest prizes range between $1,000 and $10,000). The odds of winning are greatest for the high jackpot games which have jackpots that routinely reach more than $20 million (for Powerball).

In 1994, the Lottery saw a slip in sales from $259 million to $249 million with the influx of casinos on the Indian reservations. In 1995, Powerball was introduced to the State of Arizona and sales increased to record levels ($286 million). In 1996, however, sales declined to $258 million. As a result, the Arizona Lottery decided that they should conduct a statewide survey to gain insights into what was happening with Lottery play. The goal of the survey was to define the nature of their target market of customers and identify their motivations for playing Lottery games. The ultimate objective of the project was to help the Lottery design an effective marketing strategy to maximize the return on their marketing dollars. I was fortunate to be the project director in charge of the research. For a psychologist with a background in research and statistics, this was a dream project.

Data Collection

More than 3,000 Arizona residents age 18 and older were interviewed for this project. Respondents were contacted through the use of a random digit dial sample of phone numbers across the state. Quotas were set by county as well as for Hispanic participants because of the high representation of Hispanics in Arizona. Residents who were either morally opposed to the lottery, or who felt the state of Arizona would be better off without a lottery, were asked demographic questions only, and screened out of the remainder of the survey.

Our interviewers asked respondents an extensive battery of questions including both attitudinal and behavioral aspects (e.g., frequency of play, types of games played) for both general gaming and the Arizona lottery. Questions were also asked concerning general attitudes about life, advertising media, and leisure activities. The survey took approximately 25 minutes to complete and respondents were not paid for their participation.

Steps in a Market Segmentation Analysis

The data analysis in a market segmentation study employs both factor analysis and cluster analysis. Factor analysis is used to define factor scores for each individual that describe characteristics that can be used for grouping consumers into homogeneous groups. Cluster analysis is used to perform the grouping. Once the groups are identified, the groups most likely to have interest in a product are identified and targeted in the marketing plan. We now discuss this general process in more detail.

1. Factor Analysis

Factor analysis is a statistical tool used to represent information contained in a large set of variables with a smaller set of variables. The smaller set of variables are often referred to as latent (or underlying) factors. The larger set of variables are often described as the manifest (observable) variables. That is, an underlying assumption of factor analysis is that there are a few latent factors that are manifest in the values of many observable variables. For example, the desire for wealth might be a latent factor in our lottery example. This latent factor might be responsible for values we observe on such variables as the amount of money wagered in a given time period or the frequency with which a person purchases a lottery ticket. Factor analysis is conducted in an effort to determine possible latent factors. This process involves the formulation of a mathematical model that describes the relationship between the latent and manifest variables, as well as subjective evaluations to recognize and describe the latent factors.

Once latent factors have been determined, cluster analysis is used to separate or segment a population of items into groups with similar values for the latent factors. The underlying belief is that individuals with similar latent traits will react in a similar manner to a marketing campaign.

In our Arizona Lottery example, we first conducted a factor analysis of the responses of all 3,084 respondents to a list of 45 statements about their attitudes toward the lottery and general gaming. Respondents were asked to indicate their level of agreement or disagreement (on a 1 to 7 scale) with each of the 45 statements (such as those shown below).

As noted previously, identification of latent factors requires both mathematical models and subjective decision making. If you are not familiar with factor analysis, you can find information about the topic in most multivariate analysis text books. In this particular study, we used a maximum likelihood method to estimate the relationship between the latent factors and the manifest (observable) variables. The numbers that describe the relationship are called factor loadings. Factor loadings are coefficients of the latent factors in a linear model thought to describe the observable variables. In order to interpret the latent factors, it is necessary to focus on the loadings that have the greatest magnitudes (absolute values). This process is often made easier by rotating the original factor structure. In our situation, we applied the varimax rotating method (see, e.g., Johnson and Wichern (1992), pages 419-429). We then used our experience and knowledge to subjectively identify six latent factors. That is, we identified six underlying constructs that can be used to explain attitudes of our respondents toward the lottery and general gaming.

The six latent factors identified are listed below.

Winning the Lottery
This is the fun and anticipation of the possibility of winning. Playing the Lottery represents the only way to make your fortune, and, it's an inexpensive way to make an investment in your future.

Futility of Gambling
Gambling or taking risks when you have no control or influence on the outcome is a waste of time and money. There is little or no excitement in playing the Lottery because of the unpredictability and perceived futility in playing.

The Odds of Winning
I have as good of a chance of winning as anybody else because every ticket has an equal chance of winning.

The Effect of Winning on My Life
Winning one of the big Lottery jackpots would significantly improve my life.

The Effect of Winning on Me
Winning one of the big Lottery jackpots would change who I am as a person.

Gambling is Fun
It is the fun and excitement of gambling, or the possibility of winning, that keeps me playing, not necessarily whether or not I win.

2. Cluster Analysis

Each respondent in the sample can now be assigned a factor score based on the factor loadings and the responses to the 45 questions (see, e.g., Johnson and Wichern (1992), pages 429-434). People with similar factor scores a latent factor such as Gambling is Fun, have similar attitudes about the fun of gambling. Now recall that the factor analysis identified six such latent factors. Ideally, to find people with similar attitudes, we would like them to have similar scores on all six latent factors. This desire to group people using six scores instead of only one score leads us to the use of cluster analysis.

As with factor analysis, there are many well written descriptions of cluster analysis. Mathematical rules are established for grouping individuals, and subjective decisions are made to determine the number of clusters. In our study, we used a K-Means cluster analysis to provide the rules for grouping (see, e.g., Johnson and Wichern (1992), pages 597-601). The notion here is to form clusters of similar individuals in a six dimensional space. The number of clusters to form is subjective, but numerous references are available that provide guidelines for making this decision. In our situation, we evaluated several cluster configurations before deciding on a final solution. Such decisions require knowledge of the industry, an understanding of the product, and an understanding of human behavior. In addition to mathematical criteria for identifying good solutions, we also had to look at the clusters to make sure they were meaningful and interpretable. After much investigation, it was decided to separate the market into six segments.

After each respondent was placed in his or her appropriate segment using their factor scores, descriptive statistics were computed for each segment. The summary statistics included both the summaries of the factor scores, and the original 45 questions. With this summary information, we were able to add "flesh" or "personality" to the structure that had been identified. It continues to amaze me how we can set the foundation with a "cold" statistical analysis of a set of responses and then watch it "come alive" as we look at the general characteristics of our market groups.

Market Segments in the Lottery Study

The six segments of the population were identified as Optimists, Critics, Dreamers, Managers, Analysts, and Pessimists.

The largest groups were the Optimists (23%) followed by the Critics (18%) and the Dreamers (15%). Managers comprised approximately 11% of the population, Analysts - 9%, and Pessimists - 6%. Those opposed to the Lottery represent approximately 18% of the total population. (See Chart).

The following table displays demographic characteristics of each group in addition to the average factor scores for each group (higher average scores = agreement or positive outlook; lower average scores = disagreement or negative outlook).

Optimists:
For the Optimists, playing the Lottery, and gambling in general, is a fun and exciting part of their lives. They feel that they have as good of a chance of winning the Lottery as anyone else and they believe they have a good chance of winning a large prize. They also enjoy fantasizing and daydreaming about the day they will win one of the big jackpots.

Dreamers:
For Dreamers, playing the Lottery represents their best chance to improve the quality of their life and change who they are as a person. Many believe that the only way they will ever become rich is through playing the Lottery and they love to dream and fantasize about what their life will be like after they win the big Powerball or Lotto jackpot. They feel that winning the Lottery has a lot of prestige and if they won, it would prove to their critics that they were not foolish for playing.

Managers:
Managers appear to like having more control over their destiny than playing the Lottery would allow. On one hand, they feel that their chances of winning the Lottery are as good as anyone else's and their lives would be better if they would win a big jackpot; but "deep down," they do not believe that they could win the Lottery. They are concerned that if they would win a large jackpot, the sudden change would make them a different person and perhaps ruin their life.

Pessimists:
Although Pessimists enjoy playing the Lottery and other games of chance as well as dream about how different their lives would be if they won, they do not feel that they have much chance of winning at all, even if they were to play the Lottery more often. In fact, they feel that their chances of winning are not as good as other people's. They are somewhat embarrassed when they are seen buying Lottery tickets and, occasionally, they will have someone buy their tickets for them.

Analysts:
The foundation of the relatively negative view of the Lottery and gaming, in general, among the Analysts is the belief that the odds of winning are stacked against them. In their view, it is highly unlikely that they, or anyone else who is a player, will win a significant amount of money in the Lottery.

Critics:
Unlike the Analysts, the negative attitudes of the Critics are not driven by the perception that the odds of winning are low, but rather by their belief that there are better ways to invest their money and be successful. They acknowledge that they would have a better life if they were to win one of the big jackpots, but they feel that even if they would play the Arizona Lottery more often, they would never win a big prize.

Among the six segments, the Optimists and the Dreamers had the greatest frequency of play in the lottery. In fact, 69% of the "core" Lottery players are in one of these two groups. Thus, based on the demographic information we collected for each group, the Arizona Lottery made a concerted effort to direct their advertising campaigns to members of these segments. Information from the segmentation study helped provide direction for constructing campaign messages, purchasing media that will reach the demographic groups found in the target segments, as well as identifying the most appropriate media to use.

There you have it. An insightful, detailed picture of the Arizona Lottery market. The information from this study is currently being used to develop new advertising campaigns and marketing strategies.

Reference
Johnson, Richard A., and Wichern, Dean W. (1992). Applied Multivariate Statistical Analysis (3rd edition). Prentice Hall, Englewood Cliffs, NJ.

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