Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 23

Analyzing Paired Data

“Melts in your mouth, not in your hands” is a famous advertising slogan. How long does it take a chocolate chip to melt in your mouth? Does a peanut butter chip melt any faster or slower than a chocolate chip? How could you design a randomized experiment to find out? And how would you analyze the resulting data? Is there a better study design for answering this question? Does the study design affect how you analyze the results? The answer to these last two questions is yes, as you will see in this topic.

Overview

In the previous topic, you learned two-sample t-procedures that enable you to analyze the results of randomized experiments and independent random samples to determine whether the difference in means between two groups for a quantitative variable is statistically significant and to estimate the size of the difference. In this topic, you will study paired data, where the two-sample t-procedures are not appropriate. You will learn how to apply paired t-procedures and see the advantages of collecting data with a matched-pairs design.

Preliminaries

1. Guess a typical age difference between a husband and wife. (Activity 23-1)
2. Which would you expect to have more variability: individual ages of married people or differences in ages within a husband/wife couple? (Activity 23-1)
3. Would you expect a chocolate chip to melt faster, slower, or at the same speed as a peanut butter chip? (Activity 23-2)

Collect Data

1. Your instructor will randomly assign ...