Quantitative Methods:
Module 6: Sampling Methods
|
Population |
Complete set of conceivable observations |
|
Sample |
Subset of population |
In practice information is nearly always collected form samples for a Wide variety of reasons
Ø
Economic Advantage
Ø
Timeliness
Ø
Size and accessibility
Ø
Observation and destruction
Ø Opinion
poll,
Ø Quality
control,
Ø Checking
invoices
Ø Sample
should be representative of product representation, Sampling Methods
|
Simple Random Sample: |
Each member of Population has an equal chance of being
selected. I.e. draw names from a
hat. |
Multi-stage sample
|
Population is split into groups, and then subgroups. A
random sample is taken at each stage of the breakdown. |
|
Cluster sample: |
Closely linking
with multi-stage sampling in that the population is divided into groups,
subgroups but, the difference is that at the final stage each individual of
the chosen groups is included in the final sample |
|
Stratified sample: |
Sample contains same
% of breakdown of subgroups as in population. Prior knowledge of this break
down is used to make the sample more representative. |
|
Weighting: |
Is a way of recognizing
the existence of stratification
in the population after the sampling has been carried out. The
measurements made on individual elements of the population are weighted so
that the net effect is as if the proportions of each stratum in the sample
had been the same as those in the population. |
|
Probability Sample |
In simple random sampling, each element of the population
has an equal chance of being selected for that sample. There are
circumstances when it is desirable for elements to have differing chances to
be selected. |
|
Variable Sample |
Some special sub-population
is over-sampled i.e. deliberately over-represented. |
|
Area Sample |
An artificial breaking down of the population to make
sampling easier. (The population is split into geographical areas). |
Ø Involves a
significant degree of personal judgment
|
Systematic
Sampling: |
The sample is taken at regular intervals from the
population. (Example: For a sample of 1000 out of a population of 50000,
every 50th on the list would be chosen.) |
|
Convenience
Sampling |
Sampling is taken the easiest way possible. (For instance,
medically, a blood sample is usually taken from the arm.) |
|
Quota
Sampling |
Frequently used in market research interviews in order to
overcome interview bias |
Stratified sampling improves accuracy, but in simple random sampling, the
accuracy can be calculated.
Sampling Frame |
The complete list from which the sample is selected. In practice,
this list is often different from the population at large. |
Non-Response |
Can bias the sample, because the input of the
non-responses may be atypical of the population, and other members of the
sample. Reducing non-response can be expensive. |
Bias |
The tendency to over or underrepresented elements of the
population. Other sources include Ø Inaccurate measurement i.e.
physical inaccuracy thermometer calibrated one degree to high Ø Interviewer bias – interviewer induces
bias answers from question asked Ø Interviewee bias – interviewee injects
the bias false claims Ø Instrument bias – means of collecting data such
as a questionnaire. |
Ø What level
of Accuracy is needed in the results?
Ø Use
Statistical Theory to calculate the sample size – which is related to accuracy
Ø Random
sample, it is possible to say, with 95% accuracy, how close the calculated
sample statistic is to the actual population.
Ø Accuracy
increases with the square root of the sample size. (Example: increasing the
sample from 100 to 400 --a factor of 4, halves the error [Ö4 =2]. )
Ø Collect
the largest sample that the available budget allows.
Ø Small population sizes impact accuracy of
samples, for instance, in a population of 50, the first selection has a 1/50
chance of being picked, the second has a 1/49, the third, 1/48. Random sampling
requires that each member of the population has an equal chance of being
selected. This is not true for small populations (for large populations, the
differences are negligible.)
Ø Sampling with replacement:
Downside--elements could be selected twice.
Ø Use a different theory for calculating
accuracy and sample size.
1) Sampling is a trade off between accuracy and expense.
2) The larger the sample size, the closer the accuracy will
be to maximum (but, possible that measurement errors could swamp sampling
errors.)
3) Applications:
a) Opinion polls
b) Market research of consumer
attitudes and preferences
c) Medical investigations
d) Agriculture
e) Accounting
f) Quality control
g) Information systems
4) Sample size is dependent upon objectives and required
accuracy, not related to population size.