PROBABILITY SAMPLING TECHNIQUES

Use a variety of sources for the collection of data, both primary and secondary

1. Outcome 1:
Use a variety of sources for the
collection of data, both primary and
secondary
1.2Describe and justify the survey
methodology and frame used
1.6PROBABILITY SAMPLING
TECHNIQUES

2. SAMPLING

3. PROBABILITY SAMPLING TECHNIQUES

4. 1.Simple Random Sampling (SRS)
• Assure that each element in the population has
an equal chance of being selected.
• Selection is free from bias
•Can calculate the probability –
sample size (n) and population size (N) Therefore,
the probability is = n/N
• can be done with or without replacement
Possibility of selecting the
same item as a sample twice
More convenience,
more precise result

5. 1.Simple Random Sampling (SRS)
•Several ways of selecting a simple random sample:
Humans have long practiced various forms of
random selection, such as picking a name out of a
hat, or choosing the short straw.
i.Lottery draw: The name or identifying
number of each item in the population is
recorded on a slip of paper and placed in a
box - shuffled – randomly choose required
sample size from the box.

6. 1.Simple Random Sampling (SRS)
Techniques of selecting a simple random sample:
ii.Each item is numbered and a table of
random numbers is used to select the
members of the sample.
iii.There are many software programs, such as
MINITAB and Excel that have routines that will
randomly select a given number of items from
the population.

7. Example 1: Simple Random Sampling (SRS)
Imagine that you own a movie theatre and you are offering a
special horror movie film festival next month. To decide which
horror movies to show, you survey moviegoers asking them
which of the listed movies are their favourites. To create the list
of movies needed for your survey, you decide to sample 100 of
the 1,000 best horror movies of all time.
a.Horror movie population is divided evenly into classic
movies (those filmed in or before 1969) and modern movies
(those filmed in or later than 1970).
b.Write out all of the movie titles on slips of paper and place
them in an empty box.
c.Draw out 100 titles and you will have your sample.
By using this approach, you will have ensured that each movie
had an equal chance of selection.

8. Example 2: Simple Random Sampling (SRS)
In order to get your sample, you;
a.Assign a number from 001 to
500 to each students,
b.use a table of randomly
generated numbers (Random
Number Tables)
Suppose your college has 500 students (population)
and you need to conduct a short survey on the
quality of the food served in the cafeteria. You
decide that a sample of 70 students (sample) should
be sufficient for your purposes.

9. Example 2: Simple Random Sampling (SRS)
No. Students
Name
IDGender
001Aaaab F
002Aabbb F
003Abbbc M
004Baaaa M
005Bbbaa M
006Bcaab F
… …
… …
499Mmnnr M
500Zzwrnn M
Eg: solution
3 digits

10. c. Randomly pick a starting point in the table, and look at
the random number appear there.
d. (In this case) The data run into three digits (500), the
random number would need to contain three digits as
well.
e. Ignore all random numbers greater than 500 because
they do not correspond to any of the students in the
college.
f. Remember !! Sample is without replacement, so if the
number recurs, skip over it and use the next random
number.
g. The first 70 different numbers between 001 to 500 make
up your sample.
Example 2: Simple Random Sampling (SRS)

11. Unit 6: Business Decision Making
Prepared by: Mdm. Nor Azian Abu Asan
Dept. of Maths & Stats
Example 2: Simple Random Sampling (SRS)
Random Number
Tables

12. •Selection of units is based on sample interval, k starting
from a determined point, where k = N/n
ii.First sample drawn between 1 and k randomly
(determine point/ the random start ).
iii.Afterwards, every k th must be drawn until the
total sample has been drawn.
2.Systematic (Random) Sampling
•there is a gap, or interval, between each selected unit
in the sample.
i.Number the units on your frame from 1 to N and the
population are arranged in some way
Steps:

13. Example 3: Systematic (Random) Sampling
• Using the same survey problem from Example (1): SRS
a. Number the units on
your frame
(students) from 1 to
N (population). In
this case, N = 500.
b. Determine the
sample interval, k =
N/n, k = 500/70,
k = 7.1, k = 8
(rounding up) .
No.Students
Name
IDGender
001Aaaab F
002Aabbb F
003Abbbc M
…… …
008Dddbb M
… F
016Fffaaa M
…… …
499Mmnnr M
500Zzwrnn M

14. Example 3: Systematic (Random) Sampling
**You will need to
select one unit
(student) of every
8
th
units to end up
with a total of 70
students as your
sample.
c.Select a number
between 1 and 8 at
random (random
start)
No.Students
Name
IDGender
001Aaaab F
002Aabbb F
003Abbbc M
…… …
008Dddbb M
… F
016Fffaaa M
…… …
499Mmnnr M
500Zzwrnn M
S
e
le
c
t

1
o
f
8

r
a
n
d
o
m
ly

15. Example 3: Systematic (Random) Sampling
Example, if you choose
number 5, then the 5
th

student on your frame
would be the first unit
included in your sample.
Select every k
th
unit after
that first number.
Eg: 5 (the random start),
13 (5+8), 21 (13+8), 29
(21+8),… up to 500,
(where the total sample
needed are obtain).
No.Students
Name
IDGender
001Aaaab F
002Aabbb F
…… …
005Ddaac F
…… …
008Dddbb M
…… …
013Eaaaf F
…… …
021Hhaat F
…… …
500Zzwrnn M
1st
2nd
3rd

16. •The market
researcher
might select
every 5th
person who
enters a
particular
store, after
selecting the
first person at
random.
Example 4: Systematic (Random) Sampling
•The surveyor may
interview the
occupants of every
fifth house on a
street, after
randomly selecting
one of the first five
houses.

17. Systematic (Random) Sampling
Suppose you run a large grocery store and have a list of the
employees in each section.
•The grocery store is divided into the following 10 sections:
deli counter, bakery, cashiers, stock, meat counter,
produce, pharmacy, photo shop, flower shop and dry
cleaning.
•Each section has 10 employees, including a manager
(making 100 employees in total).
•Your list is ordered by section, with the manager listed first
and then, the other employees by descending order of
seniority.

18. Systematic (Random) Sampling
If you use a systematic sampling approach and your sampling
interval, k = 10, then you could end up selecting only
managers or the newest employees in each section.
Possible error:
This type of sample would not give you a complete or
appropriate picture of your employees' thoughts.
You wanted to survey your employees about their thoughts
on their work environment.
Would you used Systematic Sampling Techniques?

19. •A population is divided into homogenous, mutually
exclusive subgroups, called strata and a sample is selected
from each stratum.
•Goal: To guarantee that all groups in the population are
adequately represented.
•Within stratum - uniformity (homogenous),
Between strata – differences (heterogeneous).
3.Stratified (Random) Sampling

20. • Number of sample from each stratum – select randomly
= no. of element in the stratum x no. samples
no. of population require
•can be stratified by any variable that is available
e.g Gender (Male & Female), edu. Level (SPM, diploma, 1
st

degree,…),etc.
Stratified (Random) Sampling

21. Using the same survey problem from Example (1): SRS
If you were select a simple random sample of 70 students
from the frame, you might be end up with just a little over
350 female students in your college, since they account for
more than half of a % of the whole college students
population).
Example 5: Stratified (Random) Sampling
a. Stratifying the population by gender. (Male and Female)
b. Calculate the exact sample size from each strata;
Male = (150/500)*70 = 21 male students
Female = (350/500)*70 = 49 female students
Give the total sample = 21 + 49 = 70 students

22. Using the same survey problem from Example (1): SRS
c.Each units (students) from each strata will be numbered,
then the sample from each strata will be selected at
random (as in SRS).
Example 5: Stratified (Random) Sampling

23. Example 5: Stratified (Random) Sampling
No.Students
Name
IDGender
001Aaaa F
002Bbbb F
003Cccc F
004Dddd F
005Eeee F
006Ffff F
…… F
350Yyyy F
No.Students
Name
IDGender
001Aabb M
002Bbcc M
003Ccdd M
004Ddee M
005Eeff M
006Ffgg M
… M
150Zzzz M
Strata (by Gender)
Female = 49 Male = 21

24. Extra Easy Sudoku Puzzle #3

25. •To reduce the cost of sampling a population scattered over
a large geographic area.
•To gather data quickly and cheaply at the expense of
possible over – or under representing certain groups of
people.
4.Cluster (Random) Sampling
- By the luck of the draw you will wind up with
respondents who come from all over the state

26. Cluster (Random) Sampling
Steps:
•divides the population into groups or clusters
- Within cluster- differences (heterogeneous)
- Between cluster– uniformity (homogenous)
•select clusters at random
- all units within selected clusters are included in the
sample
- No units from non-selected clusters are included in the
sample

27. Imagine that the municipal council of Perak Tengah wants
to investigate the use of health care services by residents.
a. Council requests for electoral subdivision maps that
identify and label each area block.
b. From this maps, the council creates a list of all area
blocks (e.g: Bota, Parit, Kg.Gajah, Manong,…). This area
will serve as the survey sampling frame.
c. Every household in that area belongs to a area block.
d. Each area block represents a cluster of households.
Example 5: Cluster (Random) Sampling

28. e.Council randomly picks a
number of area blocks
(cluster)
using SRS approach.
c. List all households in the
selected area blocks; these
households make up the
survey sample.
Example 5: Cluster (Random) Sampling

29. • Combination of all the methods described above.
• Involves selecting a sample in at least two stages.
e.g: i. Stage 1: Stratified Sampling
Stage 2: Systematic Sampling
e.g: ii. Stage 1: Cluster Sampling
Stage 2: Stratified Sampling
Stage 3: Simple Random Sampling
5.Multi-stage Sampling

30. Advantages & Disadvantages
Sampling
Techniques
Advantages Disadvantages
Simple Random
Sampling
i. Easiest method &
commonly used.
ii. Not require any
additional info. on the
frame (such as
gender, geographical
area etc), other than
complete list of
members along with
contact info.
iii. Analysis of data is
reasonably easy
and has a sound
mathematical basis.
i. Make no use of
auxiliary info.
ii. Can be
expensive and
unfeasible for
large population
(to identified and
reach) or if the
personal interview
required.
iii. not be
representative of
the whole
population

31. Sampling
Techniques
Advantages Disadvantages
Systematic
(Random)
Sampling
i. Easier to draw,
without mistakes.
ii. More precise than
SRS as more
evenly spread over
population.
i. If list has
periodic
arrangement
then sample
collected
may not be an
accurate
representation
of the entire
population.
Advantages & Disadvantages

32. Sampling
Techniques
Advantages Disadvantages
Stratified
(Random)
Sampling
i. Ensure an adequate
sample size for sub-
groups in the
population of interest.
ii. Almost certainly
produce a gain in
precision in the
estimates of the
whole population,
because a
heterogeneous
population is split
into fairly
homogeneous strata.
i.Problem if strata
not clearly defined.
ii.Analysis is (or can
be) quite
complicated.
Advantages & Disadvantages

33. Sampling
Techniques
Advantages Disadvantages
Cluster
Sampling
i. Reduced field costs
ii. Applicable where no
complete list of units
is available (special
lists only need be
formed for clusters).
i.Clusters may not
be representative
of whole
population but
may be too alike.
ii.Analysis more
complicated than
for SRS.
Advantages & Disadvantages