The
Confidence Interval is the plus-or-minus
figure usually reported in newspaper or
television opinion poll results.
For
example, if you use a confidence interval of 4
and 47% percent of your sample picks an answer
you can be "sure" that if you had asked the
question of the entire relevant population
between 43% (47-4) and 51% (47+4) would have
picked that answer.
The
Confidence Level tells you how sure you
can be.
It is
expressed as a percentage and represents how
often the true percentage of the population who
would pick an answer lies within the confidence
interval.
The 95%
confidence level means you can be 95% certain;
the 99% confidence level means you can be 99%
certain. Most researchers use the 95%
confidence level.
When you
put the confidence level and the confidence
interval together, you can say that you are 95%
sure that the true percentage of the population
is between 43% and 51%.
The wider
the confidence interval you are willing to
accept, the more certain you can be that the
whole population answers would be within that
range.
For
example, if you asked a sample of 1000 people in
a city which brand of cola they preferred, and
60% said Brand A, you can be very certain that
between 40 and 80% of all the people in the city
actually do prefer that brand, but you cannot be
so sure that between 59 and 61% of the people in
the city prefer the brand.
There
are three factors that determine the size of the
confidence interval for a given confidence
level. These are: sample size, percentage and
population size.
Sample
Size:
The larger
your sample, the more sure you can be that their
answers truly reflect the population. This
indicates that for a given confidence level, the
larger your sample size, the smaller your
confidence interval. However, the relationship
is not linear (i.e., doubling the sample size
does not halve the confidence interval).
Percentage:
Your
accuracy also depends on the percentage of your
sample that picks a particular answer. If 99% of
your sample said "Yes" and 1% said "No" the
chances of error are remote, irrespective of
sample size. However, if the percentages are 51%
and 49% the chances of error are much greater.
It is easier to be sure of extreme answers than
of middle-of-the-road ones.
When
determining the sample size needed for a given
level of accuracy you must use the worst case
percentage (50%). You should also use this
percentage if you want to determine a general
level of accuracy for a sample you already have.
To determine the confidence interval for a
specific answer your sample has given, you can
use the percentage picking that answer and get a
smaller interval.
Population
Size:
How many
people are there in the group your sample
represents? This may be the number of people in
a city you are studying, the number of people
who buy new cars, etc.
Often you
may not know the exact population size. This is
not a problem. The mathematics of probability
proves the size of the population is irrelevant,
unless the size of the sample exceeds a few
percent of the total population you are
examining. This means that a sample of 500
people is equally useful in examining the
opinions of a state of 15,000,000 as it would a
city of 100,000. Population size is only likely
to be a factor when you work with a relatively
small and known group of people (e.g., the
members of an association).
The
confidence interval calculations assume you have
a genuine random sample of the relevant
population. If your sample is not truly random,
you cannot rely on the intervals. Non-random
samples usually result from some flaw in the
sampling procedure. An example of such a flaw is
to only call people during the day, and miss
almost everyone who works. For most purposes,
the non-working population cannot be assumed to
accurately represent the entire (working and
non-working) population.
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