The Quick Count and Election Observation

CHAPTER FIVE: STATISTICAL PRINCIPLES AND QUICK COUNTS
62 had a class of 10 or fewer students. More importantly, the grades of
exceptionally good, or exceptionally poor, students will have quite a
different impact on the average grade for the entire class. In a small
class, those “outlier” grades will have a big impact on the overall distribution
and on the class average; they will skew the results of the
grade curve. But in a larger class, the impact of any individual exceptional
grade will have a far smaller impact on the average mark for the
whole class.
The practical implication of the grade distribution example is simple: as the
amount of data (number of observation points) increases, the impact of any
one individual data point on the total result decreases.
A second statistical principle that is vital to quick count methodology is known
as the central limit theorem. This axiom holds that, the greater the number of
observations (sample points), the more likely it is that the distribution of the
data points will tend to conform to a known pattern. A class of 500 physics students
in Brazil will produce the same grade distribution as a class of 300 literature
students in France, even though the marks themselves may be different. In both
cases, most of the data points will cluster around the average grade.
These two statistical axioms – the law of large numbers and the central limit
theorem – work in conjunction with each other. Together they indicate that:
The greater the number
of observations we
have, the more likely
it is that we can make
reliable statistical predictions
about the
characteristics of the
population.
1. the larger the number of observations (sample points), the less likely it
is that any exceptional individual result will affect the average (law of
large numbers); and
2. the greater the number of observations, the more likely it is that the
dataset as a whole will produce a distribution of cases that corresponds
to a normal curve (central limit theorem).
A general principle follows from these statistical rules, one that has powerful
implications for quick counts: the greater the number of observations we have,
the more likely it is that we can make reliable statistical predictions about the
characteristics of the population. However, it is absolutely crucial to understand
that, for these two statistical principles to hold, the selection of the cases
in the sample must be chosen randomly.
Randomness
A sample can be thought of not just as a subset of a population, but as a miniature
replica of the population from which it is drawn. The population of every
country can be considered as unique in certain respects. No two countries are
the same when it comes to how such characteristics as language, religion, gender,
age, occupation and education are distributed in the population. Whether
an individual possesses a car, or lives in a city rather than a town, or has a job,
or owns a pet dog contributes to the uniqueness of personal experience. It is
impossible to produce a definitive and exhaustive list of every single feature