THE CASE FOR UNDERGRADUATE STATISTICS

Richard L. Scheaffer, University of Florida
and Carl Lee, Central Michigan University

The following is written to help students at the high school and undergraduate level see the value in studying statistics either as their major field or as a quantitative supplement to their college major. A desired secondary goal is that it might also prove useful for teachers and academic advisors at the high school and college levels. Additional information on academic programs and careers in statistics can be found on the Web site of the American Statistical Association (ASA) at www.amstat.org.

Everyone is fascinated with numbers – at least some numbers, some of the time. Data (numbers in context) are sought out for guidance, studied for unusualness, and compared for possible trends. Where can I get the best buy on a CD? Wow, that many wins in a row must be really rare! Gas mileage on my car seems to fluctuate a lot; I wonder what the causes might be? The modern world of technology produces numbers faster than we can grasp them, and we appear to be at their mercy in terms of the TV shows we watch, the products that are available for us to buy, the credit rating we have (or will have) as consumers, and many other areas of life. In fact, data is so important in so many aspects of society that many find a formal study of the collection and analysis of data – statistics - an indispensable, exciting, and even fun part of their educational experience. Let’s look at a few stories along these lines. (The quotes below are taken from the longer career profiles that are available in Appendix I.

You may think that statistics would be relatively useless in law -- and criminal law, in particular -- but you’d be surprised. The logic of statistics is useful in developing legal arguments, and the methods of statistics are often directly applicable to data pertinent to a case.

Carlton F. Gunn, Attorney

The lament "When are we ever going to use this?" is never uttered when you teach statistics to high school students. From the first class where they gather data about themselves, students see that studying statistics is useful and interesting. And all those activities that involve food is another element that captures student attention. Whether we are measuring fish crackers, counting Skittles to construct confidence intervals, catapulting gummy bears in a unit on design of experiments, or comparing the color counts of M&M’s, students are engaged in the gathering, analyzing and thinking about data.

At a time when colleagues are retiring, it is too much fun watching students feel the power and excitement as their understanding of statistics grows.

Gretchen Davis, High School Mathematics Teacher

I decided to major in nursing in college. This decision derailed an earlier plan to consider a career in mathematics, and for many years I wondered whether I would ever "use" the high school math courses (5 years worth) that I had enjoyed so much. …

When I consult with nurse-scientists and other researchers, I draw on both my clinical experience in nursing and my formal preparation in measurement and statistics. The clinical experience gives me insight into the research questions and helps to establish rapport with persons asking for my advice. My quantitative training gives me the knowledge and information needed to answer questions about research design, measurement of variables, and analysis of data.

Susan J. Henly, Nurse

At that time (graduation from high school), despite my growing interest in math, my goal to become a doctor was stronger than ever. I immediately declared a chemistry major because it seemed a more logical route to medical school. But during my sophomore year, after completing all of my premedical requirements (organic chemistry, biology, etc.), I started to miss my math classes and realized that the next two years would be my last chance to continue my mathematical education before medical school. So I decided to major in statistics, knowing that would allow me to apply my mathematical aptitude directly to medical research.

Last year when I began applying to medical schools, the fact that I majored in statistics was always a good conversation point in interviews and made me more unique as an applicant.

Amy Elise Derrow, Medical Student

Statistical models are fascinating in the sense that sometimes characteristics you least expect to have any relevance as to what you are trying to predict, truly do affect your outcome. For example, your zip code may determine how risky you are to a bank or retailer. It is also interesting to analyze the probability of an event to occur, such as will the check you write at Wal-Mart be accepted. Every time another data set comes in, it’s always fun for me to find out what type of oddity or normality is going to show up this time.

Tischa Agnessi, Financial Data Specialist

I found that statistics used more reasoning and logic skills than the mathematics courses I had previously taken. The more I did statistics, the more I liked the "alternative" application of mathematics that it provided. I especially liked being able to use a lot of data and a little common sense to figure out problems. I graduated with a Bachelor of Science in Statistics. Following graduation I was able to find the perfect use for my skill in the aerospace industry.

Tiffany T. Sundelin, Quality Control Engineering

I love that statistics is very multi-disciplinary. It involves problem solving in a group environment and it involves many skills and talents. I love the ability to be a mathematician, computer scientist, teacher, quizmaster, sleuth, and devil’s advocate all rolled into one.

QED (Quod Erat Demonstandum) which was to be proved is the classic end to a mathematics proof and sometimes the end to a statistical analysis, proving and disproving research questions, and an appropriate name for a statistical consulting company of one.

Linda Quinn, Private Industrial Consultant

…it became clear that while advanced statistical tools are important, a first step which must be taken is to ask the basic question of ‘statistical thinking,’ "Do the data provide any evidence of a real change or does there appear to be only what statisticians call random (or chance) variation?" This question can frequently be answered with the simplest of statistical tools. Indeed, companies are training employees in statistical methods that could have been learned in high school.

David Fluharty, Statistical Consultant

My expertise in statistics allows me to play a pivotal role in the design and analysis of … studies and my medical experience allows me to see relationships, form hypotheses, and become an integral member of many research teams. The ability to work on complex problems has provided me a unique niche in the medical school. Statistics and medicine have been a perfect combination for me.

Michael Beach, Physician

As the quotes above indicate, modern statistics is more than looking carefully at data that may come your way – much more. Statistics can be thought of as the science of collecting and analyzing data for the purpose of making decisions under uncertainty. These decisions are being made about processes, such as planning to buy a new CD, playing a baseball game, or operating an automobile. Since all processes are subject to variation, statistics can also be thought of as the measurement and reduction of variation in processes or systems. Now, let’s take a look at a few broad areas in which statistics is playing a key role. (These abbreviated stories have been excerpted from the complete stories found in Appendix II.)

NEVER A DULL DAY: THE LIFE OF AN INDUSTRIAL STATISTICIAN!

Gerry Hahn

Manager, Applied Statistics

GE Corporate Research and Development

Schenectady, NY 12309

Looking for a career with an exciting new challenge each day? Then consider becoming an industrial statistician. Today's industrial statisticians are in the thick of their company's initiatives to build products that delight customers-and to increase market share and profitability. Their involvement is holistic and runs from product conception to field deployment.

All of this provides great new opportunities to industrial statisticians to serve as statistical leaders—a term popularized by the late and great Ed Deming. Statistical leaders engage principally in leveraging statistical concepts and thinking, and focus their activities on mentoring and supporting the most business-vital and technically challenging problems dealing with getting the right data, and converting such data into actionable information.

See below for more about this!

WHY CAN YOU TRUST THE DRUGS YOU TAKE?
(and how statisticians contribute)

James A Bolognese

Biostatistician

Merck Research Laboratories

Rahway, NJ

Suppose you go to your doctor because you sometimes have difficulty breathing. Your doctor tells you that you have asthma, and that there is a new drug that can help you breathe better. How do you know the new drug will work and will be safe for you to take? You might also wonder where this new drug comes from. You can trust the drugs you take because current drug approval regulations require extensive, extremely accurate testing to demonstrate the safety and efficacy (i.e., effectiveness) of drugs before marketing. Statisticians enable scientists and reviewers to establish the accuracy and validity of these tests.

Returning to the title question, you can trust the safety and efficacy of the drugs you take because they are extensively tested according to strict guidelines. The results of this testing are carefully reviewed by the world’s leading medical and statistical experts prior to approval for marketing. Without extensive statistical analysis, the implications of scientific data would be less clear, and important information might be lost. Statisticians are essential in the drug development process because they ensure the validity and accuracy of findings at all stages of drug discovery, development, approval, and marketing.

See below for more about this!

IT’S ALL IN THE GENES! - STATISTICS AS A TOOL IN MODERN GENETICS

Mark Yang

University of Florida

Gainesville, FL

Everyone has heard of the human genome project. It is to lay out the 3,000,000,000 DNA codes in the whole human genome. We may say that the blue print of constructing a human being from a fertilized egg to a full-grown person is there. But to understand how it works is a challenge of the 21st century. How do these codes work together? We hope that one day we can decipher the whole genome function. Without this full understanding, any genetic engineering on human genome would be too risky. Now we know that the genome contains not only useful genes, but also a lot of useless codes called junk DNA. At this moment, we still have no sure method to identify the gene portion in the genome. There are rules to identify genes and there are exceptions to the rules. Due to this type of uncertainty, statistics plays a key role in human genome research.

See below for more about this!

MINING PLATINUM AND GOLD: USING STATISTICS FOR CREDIT DECISIONS

Tim K. Keyes, Ph.D.

VP. GE Capital Commercial Finance

If you have a credit card, you may be aware that information about you is being used at the point of sale by someone who wants to loan you money. If you are in good credit standing (whatever that means) and can afford the new item, you get "approved," otherwise, you get "denied" (too bad, so sad). Sometimes, and often for no apparent reason, the clerk may ask you to surrender your card and then stare at you as you walk away nonplussed. Luckily, more often you'll receive a bonus for having successfully managed the card, e.g., a discount on your desired purchase, or a coupon for other purchases.

You've probably guessed that a statistician or data miner is working somewhere behind the scenes, making mathematical guesses about your future payment behavior. You're right! The talents embodied by these people are a necessary ingredient to the effective management the millions of credit applications, and billions of purchase requests annually in the United States and abroad. From a statistician's point of view, this application is extremely exciting and gratifying: billions of dollars worth of credit decisions are made each year from the integration of statistical models into practical business solutions. The Federal Reserve Board estimated that credit cards in 1998 carried $550 billion of debt in the U.S. alone. In few other ways can a statistician or data miner have so much impact!

See below for more about this!

Data and chance are now becoming core strands in school mathematics. The Principles and Standards for School Mathematics produced by the National Council of Teachers of Mathematics (NCTM) state the following:

• formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them;
• select and use appropriate statistical methods to analyze data;
• develop and evaluate inferences and predictions that are based on data;
• understand and apply basic concepts of probability

Many now realize that statistical thinking and statistical concepts are essential skills for all academic disciplines as well as for life-long learning. As a result of this thinking, spurred on by the influx of freshmen who have already seen basic statistics by the time they arrive at the college door, statistics is receiving more attention at two-year colleges, four-year colleges, and universities. The American Mathematical Association of Two-Year Colleges (AMATYC) also has a standards document, Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus (1995). The Standard on Probability and Statistics reads as follows:

Students will analyze data and use probability and statistical models to make inferences about real-world situations. The basic concepts of probability and descriptive and inferential statistics should be integrated throughout the introductory college mathematics curriculum at an intuitive level. Students will gather, organize, display, and summarize data. They will draw conclusions or make predictions from the data and assess the relative chances for certain events happening. Suggested topics include basic sampling techniques, tabulation techniques, creating and interpreting charts and graphs, data transformation, curve fitting, measures of center and dispersion, simulations, probability laws, and sampling distributions.

Introductory statistics courses in four-year colleges and universities are improving as they are modernized to follow the ASA-MAA Joint Committee recommendations:

• Emphasize statistical thinking
• More data and concepts: Less theory, Fewer recipes.
• Foster active learning.

Taken together, these school and college efforts exemplify the positive movement of statistics education towards more lively and meaningful learning.

Students may have the opportunity to study some statistics in high school, either as part of algebra or as a separate course, perhaps even an AP Statistics course. (The latter is becoming quite popular, as seen by the fact that around 35,000 students took the AP Statistics exam in 2000.) There are many additional opportunities for using statistical tools in other courses that involve data collection and analysis, such as projects in science, social science, and business.

Beyond the introductory course, educational opportunities in statistics at the undergraduate level are expanding rapidly to meet the need of the information society of today. Many colleges and universities offer a major in statistics as part of a mathematical sciences or statistics department. Many more offer a minor or concentration in statistics that can be paired with other majors in the sciences, social sciences, engineering, or business.

Those desiring to study statistics as either a major or a minor should have a strong background in mathematics, at least through calculus, and have some facility with computing. The Occupational Outlook Handbook from the Bureau of Labor Statistics, found at http://stats.bls.gov/oco/ocos045.htm, offers the following advice on academic preparation for work in statistics.

Because computers are used extensively for statistical applications, a strong background in computer science is highly recommended. For positions involving quality and productivity improvement, training in engineering or physical science is useful. A background in biological, chemical, or health science is important for positions involving the preparation and testing of pharmaceutical or agricultural products. Courses in economics and business administration are helpful for many jobs in market research, business analysis, and forecasting.

Good communications skills are important for prospective statisticians, in order to qualify for many positions in industry, where the need to explain technical matters to laymen is common. A solid understanding of business and the economy is important for those who plan to work in private industry.

In short, statistics is an intellectually attractive field for people with broad quantitative interests.

Further educational opportunities abound for those with bachelor’s degrees, concentrations, or interdisciplinary programs in statistics. Each year, statistics departments have more openings for graduate students than they can fill. Graduate programs in other fields (health sciences, physical sciences, social sciences, business, engineering, journalism - even sports journalism) look favorably on students with strong quantitative backgrounds and some experience in statistics. As seen in the opening vignettes, professional schools (law, medicine) also count it as advantageous for students to have a working knowledge of statistics.

Statistics seems especially attractive to women interested in a career in a quantitative area, and many graduate programs offer special benefits for women and minorities.

The workplace in 2000 and beyond will require workers with improved quantitative skills. Graduates with strong statistics backgrounds will have available to them excellent job prospects in business (marketing, finance, management), industry (automotive, pharmaceutical, health), or government (Census Bureau, Environmental Protection Agency, Food and Drug Administration) at competitive salaries and with opportunities for advancement. When looking for new employees, regardless of area of specialty, employers often are interested in the unique niche a prospective employee can fill. Statistical skill is certainly one such niche of high interest. Academic careers in colleges and universities will also be open to those with advanced degrees in statistics and related fields. In addition, there are increasing numbers of attractive positions open for teaching statistics in high schools and at two-year colleges.

Again, the Occupational Outlook Handbook from the Bureau of Labor Statistics: http://stats.bls.gov/oco/ocos045.htm offers some specifics.

Job opportunities should remain favorable for individuals with statistical degrees, although many of these positions will not carry an explicit job title of statistician. This is especially true for those involved in analyzing and interpreting data from other disciplines such as economics, biological science, psychology, or engineering. Among graduates with a bachelor’s degree in statistics, those with a strong background in an allied field, such as finance, engineering, or computer science, should have the best prospects of finding jobs related to their field of study. Federal agencies will hire statisticians in many fields, including demography, agriculture, consumer and producer surveys, Social Security, health care, and environmental quality... Those who meet State certification requirements may become high school statistics teachers. (For additional information, see the statement on kindergarten, elementary, and secondary school teachers elsewhere in the Handbook.)

Manufacturing firms will hire statisticians at the master’s and doctoral degree levels for quality control of various products, including pharmaceuticals, motor vehicles, chemicals, and food. For example, pharmaceutical firms employ statisticians to assess the safety and effectiveness of new drugs. To address global product competition, motor vehicle manufacturers will need statisticians to improve the quality of automobiles, trucks, and their components by developing and testing new designs. Statisticians with knowledge of engineering and the physical sciences will find jobs in research and development, working with teams of scientists and engineers to help improve design and production processes to ensure consistent quality of newly developed products. Business firms will rely heavily on workers with a background in statistics, to forecast sales, analyze business conditions, and help solve management problems in order to maximize profits. In addition, sophisticated statistical services will increasingly be offered to other businesses by consulting firms.

One final note. In a recent report on the 10 hottest jobs of 2000 (Time, 5/22/00) number 5 was "data miners," those who "attract useful tidbits from mountains of data." Data mining involves statistical and computer skills, and is another example of a great opportunity in statistics for those with broad quantitative skills!