Title: Confidence Intervals
Headings: 
Introduction
Learning Objectives
Parameter Estimation
Confidence Intervals
Table - Z-Scores for Commonly Used Confidence Intervals
Confidence Interval Estimates for Smaller Samples
Confidence Intervals for One Sample: Continuous Outcome
Confidence Intervals for μ
(126.7,127.9)
Answer
Answer
Confidence Interval for One Sample, Dichotomous Outcome
p̂= x/n
Confidence Interval for the Population Proportion
Answer
Confidence Interval for Two Independent Samples, Continuous Outcome
Computing the Confidence Interval for a Difference Between Two Means
Large Sample Example:
Small Sample Example:
Confidence Intervals for Matched Samples, Continuous Outcome
The Unit of Analysis
Computing the Confidence Intervals for μ d
Example:
Interpretation:
Crossover Trials
Example:
Confidence Interval for Two Independent Samples, Dichotomous Outcome
A. Confidence Interval for a Risk Difference or Prevalence Difference
Computing the Confidence Interval for A Difference in Proportions ( p 1 -p 2 )
Example:
Answer
B. Confidence Intervals for the Risk Ratio (Relative Risk)
Computation of a Confidence Interval for a Risk Ratio
Example:
exp (-1.50193) = 0.2227 and exp (-0.14003) = 0.869331
Answer
C. Confidence Intervals for the Odds Ratio
The Difference Between "Probability" and "Odds"
Odds of event = Y / (1-Y)
OR= (7/10) / (5/57) = 6.65
OR = (a/b) / (c/d)
Computing the Confidence Interval for an Odds Ratio
Example:
OR= (7/10) / (5/57) = 6.6
Answer
Summary
References
Solutions to Selected Problems
Answer to first problems on page 3
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Answer to BMI Problem on page 3
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Answer to Problem at Bottom of Page 4
Answer to Problem on Confidence Interval for Risk Difference on Page 7
Answer to Problem on Confidence Interval for Relative Risk - Page 8
Answer to Odds Ratio Problem on Page 10
Answer to Pain Reliever Problem - Page 8

Content: Confidence Intervals
Confidence Intervals
Author: Lisa Sullivan, PhD
Professor of Biostatistics
Boston University School of Public Health
Introduction
As noted in earlier modules a key goal in applied biostatistics is to make inferences about unknown population parameters based on sample statistics. There are two broad areas of statistical inference, estimation and hypothesis testing. Estimation is the process of determining a likely value for a population parameter (e.g., the true population mean or population proportion) based on a random sample. In practice, we select a sample from the target population and use sample statistics (e.g., the sample mean or sample proportion) as estimates of the unknown parameter. The sample should be representative of the population, with participants selected at random from the population. In generating estimates, it is also important to quantify the precision of estimates from different samples. Learning Objectives
After completing this module, the student will be able to: Define point estimate, standard error, confidence level and margin of error
Compare and contrast standard error and margin of error
Compute and interpret confidence intervals for means and proportions
Differentiate independent and matched or paired samples
Compute confidence intervals for the difference in means and proportions in independent samples and for the mean difference in paired samples
Identify the appropriate confidence interval formula based on type of outcome variable and number of samples
Parameter Estimation
There are a number of population parameters of potential interest when one is estimating health outcomes (or "endpoints"). Many of the outcomes we are interested in estimating are either continuous or dichotomous variables, although there are other types which are discussed in a later module.