Introductory Statistics and Analytics: A Resampling Perspective

7

CONFIDENCE INTERVALS

In this chapter, we take the simulation procedures that we have been working on and put them in a more formal (traditional) statistics framework. After completing this chapter, you should be able to:

• distinguish between the appropriate uses of point estimates and interval estimates,
• calculate confidence intervals (via resampling or formulas),
• explain the relationship between the Central Limit Theorem and the applicability of Normal approximations for confidence intervals,
• calculate standard error and explain the difference between it and standard deviation,
• calculate the confidence interval for a mean or proportion,
• calculate the confidence interval for a difference in means or proportions.

This material, particularly the vocabulary and definitions, is most relevant for the research community. Data scientists, however, will encounter confidence intervals in their work and will benefit from a solid understanding, via resampling, of how they work.

7.1 POINT ESTIMATES

The procedures we have discussed all involve establishing the possible error that occurs when we measure some parameter in a population by taking a sample from that population. The technical term for this procedure of establishing the possible error is a confidence interval. It is one way to measure the accuracy of a measurement. The statistic or the measurement itself is often called a point estimate.

Definition: Point estimate

A point estimate is a statistic, such as a mean, median, and percentile ...