

Statistics

Sampling (questions 1–7)
1. What is
population size? 
The population size includes all the individuals in the
identified group to be studied. This may be the number of people in a city,
or the number of people who buy new cars. Often you may not know the exact
population size, which is not a problem. The mathematics of probability
proves that 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.
For this reason, The Survey System ignores the population size when it is "large"
or unknown. A large population is referred to as infinite, while a small
population is considered finite. Population size is only likely to be a
factor when you work with a relatively small, known, finite group of people
(e.g., the members of an association). 
The sample size is the number of individuals included
in a study and represents only a subset of the population. This subset
is selected in a way that gives every member of the population an equal
chance of being chosen. The larger your sample, the more sure you can
be that it truly reflects the population. 
3. Why is
sample size important? 
It is essential to use the correct sample size to accurately
represent the population. Choosing a sample size that is too small may
not give an accurate representation of the population distribution. Too
large a sample size is wasteful and sometimes impossible to complete.
For example, you want to change something in a school with a population
of 500 students, and decide to survey the school but ask only ten people.
Is this truly representative of the school community? No. Ten people are
not enough to accurately represent the school. Suppose you tried to ask
every person in the school. Sometimes this is not easily accomplished
and can be unnecessary. In this case, a sample of 23 should be enough
to represent the population. Reasonable sample size is dependent on population
size and how much sampling error is tolerated. 
4. What is
simple random sampling? 
Simple random sampling is the basic sampling technique
in which a group of subjects, i.e., a sample, is selected for study from
a larger group, i.e., a population. Each individual is chosen entirely
by chance and each member of the population has an equal chance of being
included in the sample. Every possible sample of a given size has the
same chance of selection; i.e., each member of the population is equally
likely to be chosen at any stage in the sampling process. 
5. How do
you organize a simple random sample? 
A simple random sample is formed by assigning each member
of the population a number and then indiscriminately selecting from these
numbers. One way to make the selection random is to use a random number
table or let a computer generate a series of random numbers.
Each member of the population is assigned a unique number, or perhaps a number is
already assigned to each member, such as a social security number or telephone
number. The members of the population chosen for the sample will be those
whose numbers are identical to the ones extracted from the random number
table (or computer), in succession, until the desired sample size is reached.

6. What are
the strengths and weaknesses of using simple random sampling? 
>The simple random sample requires less knowledge about
the population than other techniques, but it does have two major drawbacks.
One is the fact that if the population is large, a great deal of time
must be spent listing and numbering the members. The other is the fact
that a simple random sample will not adequately represent many population
attributes (characteristics) unless the sample is relatively large.
That is, if you are interested in choosing a sample to be representative
of a population on the basis of the distribution in the population of
gender, age, and economic status, a simple random sample will need to
be very large to ensure that all of these distributions are equivalent
to (or representative of) the population. 
7. What are
some other types of sampling? 
Systematic sampling — Similar to simple random sampling, but instead of selecting random numbers from tables, you move through
a list (sample frame) picking every nth name. For example, pick every
10th name from an alphabetical list of students enrolled in a school.
Random route sampling — Used in market
research surveys, mainly for sampling households, shops, garages, and
other premises in urban areas. A starting address is randomly selected
and, taking alternate left and righthand turns at road junctions,
every nth address is selected.
Stratified sampling — All people in
the sampling frame are divided into "strata" (groups or categories).
Within each stratum, a simple random sample or systematic sample is
selected. For example, a politician wishes to poll his/her constituents
regarding taxation. The constituents are broken into income brackets
and then each bracket is polled.
Cluster or area random sampling — In
cluster sampling, the population is divided into clusters (usually along
geographic boundaries), the clusters are randomly sampled, and all units
within the sampled cluster are measured. For example, a survey of town
governments that will require going to the towns personally could be
done by using county boundaries as the clusters and randomly selecting
five counties. All the town governments in these selected counties would
then be measured.
Multistage cluster sampling — As the
name implies, this involves drawing several different samples. The first
stage would be a cluster sample (as described above) but then another
sample is taken from these samples. For example, a facetoface survey
of the residents of a state could be done by first selecting a sample
of counties and then doing another sample, such as systemic sampling,
of the residents of those selected counties. Thus the cost of interviewing
is minimized.
There are many other methods of sampling that are more advanced.


