MATH 111-01, Introduction to Statistics, Fall 2010

Abstract

Statistics is widely considered an exciting, dynamic, and intrinsically interdisciplinary science. The work of statisticians powers search engines like Google, has proven critical to the exploration of the human genome, and is used by hedge fund managers to detect arbitrage opportunities (risk-free trading strategies that yield profit with positive probability) that are profitable only on average (called statistical arbitrage). The New York Times recently declared that, over the next decade, statisticians will enjoy one of the highest-paying, highly-coveted careers. Statistics is often considered a mathematical science quite distinct from mathematics itself. It arguably began in the 17th century with the development of probability theory by Blaise Pascal and Pierre de Fermat. Probability theory itself arose due to interest in games of chance. In contrast to probability theorists (who propose probability models and then study those models with somewhat less regard for the particular random realizations generated by those models), statisticians are interested in the random realizations themselves (called data), and what those random realizations suggest about the parameters that govern the underlying probability models. A critical development in the history of statistics was the method of least squares, which was probably first described by Carl Friedrich Gauss in 1794. Early applications of statistical thinking revolved around the needs of states to base public policy on demographic, economic, and public health data. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and the natural and social sciences. Computers are transforming the field at a breathtaking pace. In fact, this semester, our approach to the two main tasks of statistical inference—constructing confidence intervals and executing hypothesis tests—will be motivated by simulations and visualizations in a software environment. Please be aware that there can ultimately be no escape from approaching statistics in this fashion. Because hard drive space is becoming much cheaper (i.e., it is easy to collect and store vast quantities of data) and processing speeds are becoming much faster (i.e., it is easy to do more things with data than ever before), the world of tomorrow will be dominated by the computer-driven data analysis we will undertake this semester!