Biostatistics

13.3 THE SIGN TEST 677
EXAMPLE 13.3.2
Adentalresearchteamwishedtoknowifteachingpeoplehowtobrushtheirteethwould
be beneficial. Twelve pairs of patients seen in a dental clinic were obtained by carefully
matching on such factors as age, sex, intelligence, and initial oral hygiene scores. One
member of each pair received instruction on how to brush his or her teeth and on other
oral hygiene matters. Six months later all 24 subjects were examined and assigned an
oral hygiene score by a dental hygienist unaware of which subjects had received the
instruction. A low score indicates a high level of oral hygiene. The results are shown in
Table 13.3.3.
Solution:
1. Data. See problem statement.
2. Assumptions. We assume that the population of differences between
pairs of scores is a continuous variable.
3. Hypotheses. If the instruction produces a beneficial effect, this fact
would be reflected in the scores assigned to the members of each pair. If
we take the differences X i Y i , we would expect to observe more ’s
than þ’s if instruction had been beneficial, since a low score indicates a
higher level of oral hygiene. If, in fact, instruction is beneficial, the
median of the hypothetical population of all such differences would be
less than 0, that is, negative. If, on the other hand, instruction has no
effect, the median of this population would be zero. The null and
alternate hypotheses, then, are:
TABLE 13.3.3 Oral Hygiene Scores of 12
Subjects Receiving Oral Hygiene Instruction (X i )
and 12 Subjects Not Receiving Instruction (Y i )
Score
Pair Number Instructed (X i ) Not Instructed (Y i )
1 1.5 2.0
2 2.0 2.0
3 3.5 4.0
4 3.0 2.5
5 3.5 4.0
6 2.5 3.0
7 2.0 3.5
8 1.5 3.0
9 1.5 2.5
10 2.0 2.5
11 3.0 2.5
12 2.0 2.5