Transcript Proposition 1.1 De Moargan’s Laws

Example 8.1.1: Paired Design
Doctors 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 Testing
A 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
Difference
Line
1
2
3
y1
24
41
44
y2
25
40
46
d = y1 – y2
4
5
6
30
28
43
31
31
43
mean
s
SE
Example: Paired Hypothesis Testing
(cont)
Cold Warm
Difference
Line
1
2
3
y1
24
41
44
y2
25
40
46
d = y1 – y2
-1
1
-2
4
5
6
30
28
43
31
31
43
-1
-3
0
mean
s
SE
Example: Paired Hypothesis Testing
(cont)
Cold Warm
Difference
Line
1
2
3
y1
24
41
44
y2
25
40
46
d = y1 – y2
-1
1
-2
4
5
6
30
28
43
31
31
43
-1
-3
0
mean
s
35
36
8.67 8.19
-1
1.41
SE
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