PROBABILITY SAMPLING TECHNIQUES

1.6 PROBABILITY SAMPLING
TECHNIQUES
Outcome 1:
Use a variety of sources for the
collection of data, both primary and
secondary

1.2 Describe and justify the survey
methodology and frame used

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
More convenience,
Possibility of selecting the
more precise result
same item as a sample twice

• 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.

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.

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.

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.
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)

Eg: solution
No. Students ID Gender
Name
3 digits
001 Aaaab F
002 Aabbb F
003 Abbbc M
004 Baaaa M
005 Bbbaa M
006 Bcaab F
… …
… …
499 Mmnnr M
500 Zzwrnn M

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.


Random Number
Tables

Prepared by: Mdm. Nor Azian Abu Asan
Dept. of Maths & Stats Unit 6: Business Decision Making

2. Systematic (Random) Sampling
• there is a gap, or interval, between each selected unit
in the sample.
• Selection of units is based on sample interval, k starting
from a determined point, where k = N/n
Steps:
i. Number the units on your frame from 1 to N and the
population are arranged in some way
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.

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

No. Students ID Gender
Name **You will need to
001 Aaaab F select one unit
Select 1 of 8
randomly

002 Aabbb F
(student) of every
8th units to end up
003 Abbbc M
with a total of 70
… … …
students as your
008 Dddbb M
sample.
… F
016 Fffaaa M c. Select a number
… … … between 1 and 8 at
499 Mmnnr M random (random
500 Zzwrnn M start)

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

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

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.

Systematic (Random) Sampling
You wanted to survey your employees about their thoughts
on their work environment.

Would you used Systematic Sampling Techniques?

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.

3. Stratified (Random) Sampling
• 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).

Stratified (Random) Sampling
• can be stratified by any variable that is available
e.g Gender (Male & Female), edu. Level (SPM, diploma, 1st
degree,…),etc.

• Number of sample from each stratum – select randomly
= no. of element in the stratum x no. samples
no. of population require

Example 5: Stratified (Random) Sampling
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).

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

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).

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

4. Cluster (Random) Sampling
• 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.
- By the luck of the draw you will wind up with
respondents who come from all over the state

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

Example 5: Cluster (Random) Sampling
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

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.

5. Multi-stage Sampling
• 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

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

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

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

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

PROBABILITY SAMPLING TECHNIQUES

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PROBABILITY SAMPLING TECHNIQUES