Example 8.1.1: Paired DesignDoctors studying healthy subjects measured myocardial blood flow (MBF) during bicycle exercise before and after giving the subjects a dose of caffeine that was equivalent to drinking two cups of coffee.

Example: Paired Hypothesis TestingA researcher wants to know how the temperature

affects the number of bristles on each fruit flies. The difficulty is that she has 12 fruit flies from 6 different lines (2 of each) and there is no reason to expect that the different lines of fruit flies will have the same number of bristles. She thinks that the bristle number has approximately a normal distribution, but the flies from the same line should have similar bristle numbers.

Example: Paired Hypothesis Testing (cont)

Cold Warm DifferenceLine y1 y2 d = y1 – y2

1 24 252 41 403 44 464 30 315 28 316 43 43meansSE

Example: Paired Hypothesis Testing (cont)

Cold Warm DifferenceLine y1 y2 d = y1 – y2

1 24 25 -12 41 40 13 44 46 -24 30 31 -15 28 31 -36 43 43 0meansSE

Example: Paired Hypothesis Testing (cont)

Cold Warm DifferenceLine y1 y2 d = y1 – y2

1 24 25 -12 41 40 13 44 46 -24 30 31 -15 28 31 -36 43 43 0mean 35 36 -1s 8.67 8.19 1.41SE 3.54 3.34 0.58

Paired tests: Summary

Table 7: Critical values for Sign Test

Example 8.4.1*: Sign Test

Skin grafts are applied to both sides of the body in 11 recipients. One graft has a close HL-A match with the recipient; the other does not. Observe the time it takes to reject each skin graft. Does a good HL-A match increase graft survival time with a significance of a = 0.05?

Example 8.4.1*: Sign Test (cont)HL-A Compatibility

Close Poor Sign of

Patient Y1 Y2 d = Y1 – Y2

1 37 29

2 19 13

3 57+ 15

4 93 26

5 16 11

6 23 18

7 20 26

8 63 43

9 29 18

10 60+ 42

11 18 19

Example 8.4.1*: Sign Test (cont)HLA Compatibility

Close Poor Sign of

Patient Y1 Y2 d = Y1 – Y2

1 37 29 +

2 19 13 +

3 57+ 15 +

4 93 26 +

5 16 11 +

6 23 18 +

7 20 26 -

8 63 43 +

9 29 18 +

10 60+ 42 +

11 18 19 -

Example: Before-after studies vs. Control