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How to ensure your simple random sampling is really
random?
What is a random sampling process?
When we carry out a discrete sampling exercise, we want to pick up a
predetermined number of objects from a much larger population. The
sampling methodology depends on the type of statistical analysis being
performed, but it is suffice to consider simple random sampling or
systematic sampling methods.
Simple random sampling is the process of selecting a random sample from a
finite or infinite population. As the word “random” in statistics suggests, we
must collect a number of samples from the population without definite aim
or pattern. It has two important properties that make it outstanding from
other methods, i.e.
Unbiased: each unit has the same chance of being chosen
Independence: selection of one unit has no influence on the selection of
other units.
If there is a finite population of n units and we want to take r unit samples
each time, we can then draw a total combination of nCr different samples
from these n units.
By mathematical definition, a combination is a selection of all or part of a set
of objects, without regard to the order in which objects are selected. The
number of combination of n objects taken r at a time is given by the
following formula:
!)!(!
!
!
)1)...(2)(1(
r
P
rnr
n
r
rnnnn
Crn
rn
… Eq [1]
In mathematics, the factorial of a non-negative integer n, denoted by n! is the
product of all positive integers less than or equal to n. For example, if n =5, then,
5! = 5 x 4 x 3 x 2 x 1.
The equation [1] also tells us that each random sample has an equal
rnC
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probability of being selected.
Let’s say hypothetically there are 100 drums of chemicals for a shipment,
how many ways that 4 different drums can be randomly selected to form a
sample from them for testing?
