Matched Pairs Design

1
Matched Pairs Design

• Sec 9.3

2
Review

• Last time we studied inference for the difference
  in means of two populations when the two samples
  are independent of each other.
• Use z when sigmas are known.
• Use z when sample sizes are large.
• Use Welshs t test when sigmas are unknown.
• Use pooled t test when sigmas are unknown and
  there is strong justification that both are equal.

3
Example 1

• Makers of generic drugs must show that they do
  not differ significantly from the reference drug
  that they imitate. One aspect they might differ
  in is their extent of absorption in the blood.
  To study this, 10 subjects are randomly divided
  into two groups. The first group is given only
  the reference drug. The second group is given
  only the generic drug. The absorption of the
  given drug was measured.

4
Data
5
Confidence Interval

• Find 95 interval for the difference between mean
  absorption rate of the reference drug and the
  mean absorption rate of the generic drug.
• Find a 95 interval for the mean absorption rate
  of the generic drug.

6
Hypothesis test

• Use two sample t-procedures to test

7
Assumptions for 2 sample t.

• We have two SRSs, from two distinct populations.
  The samples are independent. That is, one
  sample has no influence on the other.
• Both populations are normally distributed. The
  means and standard deviations of the two
  populations are unknown.
• Robustness. The t procedures are robust against
  non-normality, especially if the sample sizes are
  large.
• If both samples are the same size and both
  populations have similar shapes, the 2 sample t
  procedures can safely be used.

8
2nd example

• The same thing is being studied, but this time 10
  subjects are randomly divided into two groups.
  The first group was given the generic drug first,
  the second group was given the reference drug
  first. In all cases, a washout period separated
  the two drugs so that the first had disappeared
  from the blood before the subject took the
  second. The absorption of each drug was
  measured.

9
Data
10
Confidence Interval.

• The procedures presented here are used for all
  matched paired experiments.
• Turn the data into single sample data by taking
  the difference in each pair.
• Use one sample t-procedures to construct a
  confidence interval for mD which is equal to
  mR-mG.

11
Hypothesis test

• Use one sample t-procedures to test the
  equivalent hypothesis .

12
Assumptions for matched pairs

• The data is collected in matched pairs.
• The list of pairs is a SRS from all pairs in the
  population.
• The differences in the population are normally
  distributed with unknown mean and standard
  deviation.
• The procedure is robust against non normality,
  especially when the sample size is large.

13
Comment on Matched Pairs

• In our example, the same subject was subjected to
  both treatments. When this cannot be done,
  paired data can be obtained by matching subjects.
  For example, divide 10 subjects into 5 pairs
  according to blood pressure. In each pair, one
  person is given reference drug and one generic
  drug.
• In a paired design you have half the degrees of
  freedom as in a two sample design. Pairing is
  still useful when enough variability in the
  response to the two treatments is controlled by
  the pairing to overcome the loss of degrees of
  freedom.