Paired Data

1
Unit 18

• Paired Data
• Dependent Samples

2
Example

• A company changed from a five day work week to
  a four day work week. To see if employees drove
  less after the switch they recorded the annual
  miles driven fro 11 employees.

3
Question

• Did the mileage change?
• Two sample t-test says No .
  p-value .4
• But the samples are not independent. Data is
  matched pairs
• Analyze pairwise differences

4
Analyze Differences

• Its the differences we care about
• Treat the differences as the data
• Ignore the original data
• Paired t-test is really a one sample t-test on
  the difference data
• In general the null hypothesis will test for no
  difference

5
On the TI-83/84

• Enter the data in L1 and L2 on your calculator
• Clear L3 and with L3 highlighted type L1
  L2 then enter
• The difference data is now in L3
• We will analyze the difference data using a one
  sample t-test and a one sample t-interval.

6
Analysis of Mileage Data

• Reject Ho. There is a significant reduction in
  the average number of miles driven annually
  (plt.02)
• 95 CI
• With 95 confidence state that on average
  employees drove between 216 and 1747 less miles
  per year following the change to a 4 day week.

7

• Husbands and Wives
• In America, do husbands tend to be older than
  their wives? If so, how much?

8
Strive for Mostly Positive Differences

• A casual glance of the ages of husbands and wives
  reveals that more often than not, husbands in
  this experiment were older than wives.
• So we compute the difference
• Husbands age Wifes age
• Positive differences are easier to interpret

9
Analysis

• Keep Ho. There is no evidence from this data that
  husbands tend to be older than their wives
• 95 CI
• Since the CI includes zero we cannot, with 95
  confidence, conclude there is a difference in the
  average age of husbands and wives