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Published online by Cambridge University Press: 03 February 2022
A goal in statistics is to make inferences about a population. Typically, such inferences are in the form of estimates of population parameters; for instance, the mean and variance of a normal distribution. Estimates of population parameters are imperfect because they are based on a finite amount of data. The uncertainty in a parameter estimate may be quantified using a confidence interval. A confidence interval is a random interval that encloses the population value with a specified probability. Confidence intervals are related to hypothesis tests about population parameters. Specifically, for a given hypothesis about the value of a parameter, a test at the 5% significance level would reject that value if the 95% confidence interval contained that hypothesized value. This chapter explains how to construct a confidence interval for a difference in means, a ratio of variances, and a correlation coefficient. These confidence intervals assume the samples come from normal distributions. If the distribution is not Gaussian, or the quantity being inferred is complicated, then bootstrap methods offer an important alternative approach, as discussed at the end of this chapter.
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