Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic Concepts in Probability and Statistics
- 2 Hypothesis Tests
- 3 Confidence Intervals
- 4 Statistical Tests Based on Ranks
- 5 Introduction to Stochastic Processes
- 6 The Power Spectrum
- 7 Introduction to Multivariate Methods
- 8 Linear Regression: Least Squares Estimation
- 9 Linear Regression: Inference
- 10 Model Selection
- 11 Screening: A Pitfall in Statistics
- 12 Principal Component Analysis
- 13 Field Significance
- 14 Multivariate Linear Regression
- 15 Canonical Correlation Analysis
- 16 Covariance Discriminant Analysis
- 17 Analysis of Variance and Predictability
- 18 Predictable Component Analysis
- 19 Extreme Value Theory
- 20 Data Assimilation
- 21 Ensemble Square Root Filters
- Appendix
- References
- Index
3 - Confidence Intervals
Published online by Cambridge University Press: 03 February 2022
- Frontmatter
- Contents
- Preface
- 1 Basic Concepts in Probability and Statistics
- 2 Hypothesis Tests
- 3 Confidence Intervals
- 4 Statistical Tests Based on Ranks
- 5 Introduction to Stochastic Processes
- 6 The Power Spectrum
- 7 Introduction to Multivariate Methods
- 8 Linear Regression: Least Squares Estimation
- 9 Linear Regression: Inference
- 10 Model Selection
- 11 Screening: A Pitfall in Statistics
- 12 Principal Component Analysis
- 13 Field Significance
- 14 Multivariate Linear Regression
- 15 Canonical Correlation Analysis
- 16 Covariance Discriminant Analysis
- 17 Analysis of Variance and Predictability
- 18 Predictable Component Analysis
- 19 Extreme Value Theory
- 20 Data Assimilation
- 21 Ensemble Square Root Filters
- Appendix
- References
- Index
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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- Statistical Methods for Climate Scientists , pp. 52 - 68Publisher: Cambridge University PressPrint publication year: 2022