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3 - Confidence Intervals

Published online by Cambridge University Press:  03 February 2022

Timothy DelSole
Affiliation:
George Mason University, Virginia
Michael Tippett
Affiliation:
Columbia University, New York
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Summary

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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Publisher: Cambridge University Press
Print publication year: 2022

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  • Confidence Intervals
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.004
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  • Confidence Intervals
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.004
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Confidence Intervals
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.004
Available formats
×