The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

9.6 Exercises 157

Table 9.9

Aggressiveness Scores for 12 Sets of Identical Twins Based on

Birth Order

Twin set 1st born

aggressiveness

score (rank) x

2nd born

aggressiveness

score (rank) y

Ranked

pair ( x. y )

Term r ( x i ) r ( y i )

1 85 (8) 88 (10) (8, 10) 80
2 71 (3.5) 78 (7) (3.5, 7) 24.5
3 79 (6.5) 75 (5.5) (6.5, 5.5) 35.75
4 69 (1) 64 (2.5) (1, 2.5) 2.5

5 92 (12) 96 (12) (12, 12) 144
6 72 (5) 72 (4) (5, 4) 20
7 79 (6.5) 64 (2.5) (6.5, 2.5) 16.25
8 91 (11) 89 (11) (11, 11) 121
9 70 (2) 62 (1) (2, 1) 2
10 71 (3.5) 80 (9) (3.5, 9) 31.5
11 89 (10) 79 (8) (10, 8) 80
12 87 (9) 75 (5.5) (9, 5.5) 49.5

5. Given the aggressiveness scores for the twins shown in Table 9.8 , apply
   the sign test to see of the there is a difference depending on order of birth.
   Remember that when the paired difference is 0, we ignore the case. So
   in this case, we treat the 11 sets without ties (8 pluses and 3 minuses). Are
   the results statistically signifi cant at the 5% level (two - sided)? What is the
   two - sided p - value? What is the p - value for the one - sided alternative that
   the fi rst born is more aggressive?


6. Using Table 9.9 , compute the Spearman rank correlation coeffi cient for the
   aggressiveness scores. Does this suggest that both twins tend to be similar
   in degree of aggressiveness?