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Confidence intervals

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Introduction

In this chapter we introduce the concept of a confidence interval, which can be used to infer the range of likely values of a population parameter given a sample statistic.

When the population standard deviation is known

The standard error of the mean

When the population standard deviation is unknown

Confidence intervals for proportions

Standard error of a proportion

Comparing confidence intervals for multiple groups

It is often tempting to look at the confidence intervals for two groups as a way to determine whether or not the two groups' means are the same. This approach is technically incorrect and can lead to erroneous inferences. The correct approach is to use the difference of means test discussed later in the book.

XXX Outline - delete when material integrated

I. Confidence intervals 1. Known sigma 1. Explain the logic here 1. Concept of the standard error of the mean (s.d. over sqrt sample size) 2. Formula 3. Examples? 2. Unknown sigma (using s) 1. Trick: sigma is usually unknown (and if we knew sigma, we'd probably know mu) 2. Formula (fancy transition in slide?) 3. Examples? 3. Confidence intervals for proportions 1. Standard error of a proportion 2. Formula 3. Examples with polls? 4. Use normal or t distribution here? Books seem to show normal even with small n? Maybe the approximation sqrt(p(1-p)) to s/sigma is only asymptotically true? 5. If not in the surveys material: Using the formula to find expected margin of error for polls, needed sample sizes for a given MoE? 4. Achtung! Don't use CIs to test whether or not two groups have equal means.


References

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Discussion questions

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Glossary