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4.4 Inference on Two Populations 133

(also called dependent or matched samples study), the main precaution is that we
pair truly comparable cases with respect to every important factor. Since this is an
important topic, not only for the comparison of two means but for other tests as
well, we present a few examples below.

Independent Samples:

i. We wish to compare the sugar content of two sugar-beet breeds, A and B.
For that purpose we collect random samples in a field of sugar-beet A and in
another field of sugar-beet B. Imagine that the fields were prepared in the
same way (e.g. same fertilizer, etc.) and the sugar content can only be
influenced by exposition to the sun. Then, in order for the samples to be
independent, we must make sure that the beets are drawn in a completely
random way in what concerns the sun exposition. We then perform an
“independent samples” test of variable “sugar content”, dependent on factor
“sugar-beet breed” with two categories, A and B.
ii. We are assessing the possible health benefit of a drug against a placebo.
Imagine that the possible benefit of the drug depends on sex and age. Then,
in an “independent samples” study, we must make sure that the samples for
the drug and for the placebo (the so-called control group) are indeed random
in what concerns sex and age. We then perform an “independent samples”
test of variable “health benefit”, dependent on factor “group” with two
categories, “drug” and “placebo”.

iii. We want to study whether men and women rate a TV program differently.
Firstly, in an “independent samples” study, we must make sure that the
samples are really random in what concerns other influential factors such as
degree of education, environment, family income, reading habits, etc. We
then perform an “independent samples” test of variable “TV program rate”,
dependent on factor “sex” with two categories, “man” and “woman”.

Paired Samples:

i. The comparison of sugar content of two breeds of sugar-beet, A and B,
could also be studied in a “paired samples” approach. For that purpose, we
would collect samples of beets A and B lying on nearby rows in the field,
and would pair the neighbour beets.
ii. The study of the possible health benefit of a drug against a placebo could
also be performed in a “paired samples” approach. For that purpose, the
same group of patients is evaluated after taking the placebo and after taking
the drug. Therefore, each patient is his/her own control. Of course, in
clinical studies, ethical considerations often determine which kind of study
must be performed.