Block Design
A block design is the experimental counterpart to a stratified sample. A block design recognizes
inherent differences in groups of experimental units. The random assignment of experimental
units is carried out separately for each block.
Matched Pairs Design
A matched pairs design begins with pairs of experimental units that are matched to be as similar
within a pair as possible. The members of each pair are then randomly assigned to one or the
other of two treatments. The matched pairs design is essentially a two treatment block design
with each pair being a block.
Statistical Inference
Statistical inference is concerned with extending the results of a survey or an experiment to the
population. Since sample results and experimental results typically have inherent variation, the
population level conclusions will be open to question. The particular observed outcomes may be
an artifact of the sample or experiment. In statistics, we claim that an effect is statistically
significant if it is an effect that is so large that it would rarely occur just by chance.
On the other hand, the lack of
‘design’ associated with anecdotal evidence provides no basis for
drawing conclusions. The observed patterns may be the result of biased samples, inadequate
coverage, o
r poorly designed experiments. With anecdotal evidence, you just don’t know.
Sampling Distributions
This introduction to sampling distributions uses a simulation to reveal the main elements of a
sampling distribution. It is intended as a preview to the material that will come later in the
course. In Chapter 4, the mathematical tools of probability will be developed. These tools will be
used to provide an alternative development of sampling distributions that are not dependent on
simulations.
Consider the fo
llowing ‘thought experiment’.
A sample
of ‘n’ observations
provides a single
value for a statistic. In class, the statistic represented the proportion of the people in the survey
that supported getting rid of the long gun registration. Figure 1 displays the result of the first 10

respondents in a single simulated survey. The statistic, the proportion of 100 respondents that
are not in favour of maintaining the long gun registry, has a value of 0.39 or 39%. This statistic
can be used as an estimate of the proportion of the population that support getting rid of the
long gun registration. This represents one large area of statistics, statistical estimation. A sample
is taken from a population. A statistic is calculated from the sample. The value of the statistic is
used to estimate a parameter of the population. The estimate will depend on the size, n, of the
sample, and it is expected to be different (ie vary) if the survey or sample is repeated (with a
new random sample from the population.) This variation between one sample and other
possible samples is referred to as sampling variability. Part of the statistical design such as
blocking or stratifying reduces the variability within a block or strata. Larger sample sizes also
tend to reduce the sampling variability of the computed statistics.