Statistical Methods in Medical Research 4ed

104 Analysing means and proportions
Table 4.2 Anxiety scores recorded for 10 patients receiving
a new drug and a placebo in random order.
Anxiety score Difference
di
Patient Drug Placebo (drug placebo)
1 19 22 3
2 11 18 7
3 14 17 3
4 17 19 2
5 23 22 1
6 11 12 1
7 15 14 1
8 19 11 8
9 11 19 8
10 8 7 1
basis of which he or she was given an `anxiety score' (with possible values from 0 to 30),
high scores corresponding to states of anxiety. The results are shown in Table 4.2.
The last column of Table 4.2 shows the difference, di, between the anxiety score for the
ith subject on the drug and on the placebo. A t test on the 10 values of di gives
P
di ˆ 13,
P 2
di ˆ 203,
P
…di d† 2 ˆ 186 1:
Therefore,
d ˆ 1 30:
s 2 ˆ 186 1=9 ˆ 20 68,
…s2 p p
=n† ˆ …20 68=10† ˆ 2
p 068 ˆ 1 438,
and, to test the null hypothesis that E…di† ˆ0,
1 30
t ˆ ˆ 0 90 on 9DF:
1 438
The difference is clearly not significant …P ˆ 0 39†.
The 95% confidence limits for the mean difference are
1 30 …2 262†…1 438†
ˆ 4 55 and 1 95:
To conclude, this trial provided no convincing evidence that the new tranquillizer
reduced anxiety when compared with a placebo …P ˆ 0 39†. The 95% confidence interval
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