Supplementary Exercises 3.77 and 3.79 of IPS7e
----------------------------------------------

3.77
----
Out of 663 registered voters, 72% said they had voted in the election.
The number (72%) is a statistic, computed as the total number among
those questioned saying they had voted, divided by 663. Based on the sample
of 662 voters, this is our best guess at the proportion of members of the 
entire population who voted in the election.

Election records showed that only 56% of registered voters actually
voted. The number (56%) is a parameter, for the entire population of
registered voters.

In this (artificial?) example, the difference between the estimate (72%)
and the true population value (56%) is quite large. We would rarely find
that the estimate equals the population value exactly, but they should
be reasonably close, in particular when the estimate is based on a large
sample. If these numbers were real, the difference between the estimate
and the true population value is well beyond what could be explained by
random variation only (we will see in later sections how to assess
that).


3.79
----
The mean pushes per minute for the two groups of subjects (283 for
placebo and 311 for caffeine) are both statistics, computed from all the
measurements taken on the experimental subjects in the two groups.

The design is described as a matched pairs experiment, and while that is
correct it would have been more informative to call it a cross-over
design (or experiment). Each subject is subjected to both treatments
(caffeine and placebo) in different observation periods. The
treatments are the two pills, and because each subject undergoes both
treatments, the experimental unit for the design is the period (not the
subject). One would assume/hope that a suitable wash-out period between 
the two treatment periods was part of the design. Furthermore, the simple 
means for the two treatment groups do not account for the order of the
treatments. It can therefore be strongly misleading to look at simple
means if the treatment order was not balanced between the two groups,
meaning that the same number of subjects started with the caffeine pill
(and then had the placebo pill) as the number of subjects starting with
the placebo pill (and then moving on to the caffeine pill).

The selection of study subjects is not mentioned in the brief description 
of the study, but that would be crucial in order to assess whether the
results can be considered as representative for a suitable population.
Without knowing what population the results might be generalizable to, 
the actual findings might be of limited interest.