Each day, we observe the high, low, and close of stock market indexes from around the world. Indexes such as the S&P 500 Index and the Nikkei-Dow Jones Average are samples of stocks. Although the S&P 500 and the Nikkei do not represent the populations of US or Japanese stocks, we view them as valid indicators of the whole population’s behavior. As analysts, we are accustomed to using this sample information to assess how various markets from around the world are performing. Any statistics that we compute with sample information, however, are only estimates of the underlying population parameters. A sample, then, is a subset of the population—a subset studied to infer conclusions about the population itself.
This reading explores how we sample and use sample information to estimate population parameters. In the next section, we discuss sampling—the process of obtaining a sample. In investments, we continually make use of the mean as a measure of central tendency of random variables, such as return and earnings per share. Even when the probability distribution of the random variable is unknown, we can make probability statements about the population mean using the central limit theorem. In Section 3, we discuss and illustrate this key result. Following that discussion, we turn to statistical estimation. Estimation seeks precise answers to the question “What is this parameter’s value?”
The central limit theorem and estimation are the core of the body of methods presented in this reading. In investments, we apply these and other statistical techniques to financial data; we often interpret the results for the purpose of deciding what works and what does not work in investments. We end this reading with a discussion of the interpretation of statistical results based on financial data and the possible pitfalls in this process.