The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

68 CHAPTER 5 Estimating Means and Proportions

or from injury such as liver trauma. In the early stages, a small experi-
ment to be part of the proof of concept is conducted on pigs. In the
experiment, 10 pigs are in the treatment group, and 10 in the control
group. All 20 pigs have the same type of liver injury induced. The
control group gets a low dose of the drug, and the treatment group gets
a high dose. Blood loss is measured for each pig, and we are interested
in seeing if the high dose is signifi cantly more effective at reducing the
loss of blood. We will do the inference by generating 95% confi dence
intervals for the difference in blood loss. The sample size results are
given in Table 5.1.
Perusing the data, we see the appearance that there is signifi cantly
less blood loss in the treatment pigs. If we generate a two - sided 95%
confi dence interval for the mean difference, assuming normal distribu-
tions with the same variance, for simplicity, the pivotal quantity involves
a pooled estimate of variance, and it has a t - distribution with 18 degrees
of freedom. The 95% confi dence interval for the treatment mean — the
control mean is [ − 2082.07, − 120.93]. Since this does not contain 0, we
would conclude that the treatment mean is lower than the control mean.

Table 5.1

Pig Blood Loss Data (mL)

Control pig ID

number

Control group

blood loss

Treatment pig

ID number

Treatment group

blood loss

C1 786 T1 543

C2 375 T2 666

C3 4446 T3 455

C4 2886 T4 823

C5 478 T5 1716

C6 587 T6 797

C7 434 T7 2828

C8 4764 T8 1251

C9 3281 T9 702

C10 3837 T10 1078

Sample mean 2187.40 Sample mean 1085.90

Sample standard

deviation

1824.27 Sample standard

deviation

717.12