The scientist does not study nature because   it is useful;    he    studies   it because   he    delights in it, and he delights in it because it is beautiful.

If nature were not beautiful , it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.

HENRI POINCARÈ

EMATH 4–ENGINEERING DATA ANALYSIS 

Module 2- 3. Sampling Techniques

Properties of Random Sampling

Random Sampling Techniques

Non-Probabilistic sampling(non-random or judgment sampling)

Prepared by: Engr. R.P. Roselo Instructor

SAMPLING TECHNIQUES:

*Random Sampling ( Fair sampling) - is a method of selecting a sample size(n) from a universe (N) such that each member of the population has an equal chance of being included in the sample and all possible combinations of size (n) have an equal chance of being selected as the sample.

* Non-Random Sampling (Bias sampling) - a method of collecting a small portion of the population by which not all the members in the population are given the chance to be included in the sample.

Properties of Random Sampling

Equiprobability- each member of the population has equal chance of being selected and included in the sample.

Independence - the chance of one member being drawn does not affect the chance of the other member.

Kinds of Random Sampling

Restricted Random Sampling - involves certain restriction intended to improve the validity of the sampling. This is applicable only when population being investigated  requires homogeneity.

Ex. A study on effectiveness of a new drug can be tested to two groups of animals. The experimental group will be treated with the new drug; and the controlled group will not treated with the new drug. The selection of  sample paired animals should be with restrictions according to their degree of illness so that the significant difference between the two groups will be accepted.

Unrestricted Random Sampling - the best random sampling design because there were no restrictions imposed.

Random Sampling Techniques

1.Lottery or Fishbowl sampling - done by simply writing the names or number of all members of the population  in small rolled pieces of paper which are later placed in a container drum . The drum  must be shaken thoroughly then draws n out of N as desired for a sample.

2. Table of random Numbers - It is use if the population is large in which the selection of each member of population has an equal chance of being chosen.

a. Direct selection method - used when there are only few sample units to be selected right away.

Table of Random Numbers 

Example for Direct method:

Mang Paustino  has 5 complimentary tickets to a  music concert. However, he has 8 children and he would want to distribute the

5  tickets without being accused of favouritism. So what he does is to write the names  of his children (in their presence, of course, to avoid  bickering later on) in pieces of paper of the same size. He then folds the pieces of paper uniformly  and places them in a container.

Mang Paustino using Table of Random Numbers- direct method.

Procedure:

1. List  the 8 names of Mang Paustino’s children; and assigned a number per child.

Number	Name
1   ………………………	Jofel
2   ………………………	Annie
3   ………………………	Lucy
4   ………………………	Karla
5   ………………………	Jonie
6   ………………………	Karen
7 ………………………	Matt
8 ………………………	Jasmine

2.From column B  of the Table of Random

Numbers, let us take the first digits of each of the following numbers:

537658- get  number 5 …1^st ticket for Jonie 971282- not included 97820  - not included 918210 - not included 228904 - get  number 2…2^nd ticket for Annie 163802 - get number 1… 3^rd ticket for  Jofel 965725 - not included 536062 - skip 276676 - skip

187856 - skip

190606 - skip

344580 - get number 3… 4^th ticket for  Lucy

338874 - skip

6331- get number 6… 5^th /last ticket for  Karen

b. Remainder Method – is used whenever the direct selection method cannot be applied.

Example:  N=123 (population), n= 10 ( sample size)

Soln:

Since our N is three-digit number, we make use of numbers not exceeding  3digits. Thus 1-999.From table of Random Number-column A.

         1^st set   ---123x 1= 123---( 1-123)      7^th set--123x7=861--(739-861)

        2^nd set--- 123x2= 246---(124-246)      8^th set--123x8=984-(862-984)

         3^rd set---123x3=369---(247-369)    9^th set-- 123x9=1,170--rejected

4^th set---123x4=492---(370-492)

         5^th set---123X5=615---(493-615)             Exceeded- 3digits

6^th set---123x6=738---(616-738)

Then the sample units are:

from 2^nd set:(upper limit of the set- number obtained from table) 246-163 = 83…is the remainder, the first sample unit

from 8^th set:

984- 903 =  81….is the remainder, the 2^nd sample unit

from 8th  set: 984- 970= 14… the 3^rd sample

from 3^rd set: 369-327= 42… the 4^th sample

from 4^th set: 492-465= 27…the 5^th sample

from 5^th set: 615- 603= 12 … the 6^th sample

from 7^th set: 861- 813= 48… the 7^th sample •   from 4th set: 492- 479= 13 …the 8^th sample

from 5^th set: 615- 518 =97… the 9^th sample

from 2^nd set: 246-243= 3… the 10^th sample.

therefore the sample units: 83,81, 14, 42, 27,12,48, 13,97 & 3.

3. Systematic Sampling- involves selecting every k^th element of a series representing the population. A complete listing is required in this method.

Ex. N= 100 n= 10

Find k:       k= N/n     thus,  K= 100/10= 10

So the 10 samples are: 10,20,30,40,50,60,70,80,90, and 100

Ex. We put 100pcs of paper in the box or container and sake them thoroughly. If number 7 is picked as the random start, the ten sample are: 7,17,27,37,47,57,67,77,87,97.

Other Types of Sampling

Stratified  Sampling- a random sampling technique in which the population is divided into non-overlapping subpopulation called strata. Ideally, strata are homogenous groups of population units.

Cluster or Area Sampling- involves dividing the population into non-overlapping clusters.

Multi-stage Sampling-This consider different stages or phases. n1=( N1/N)n n= total size of the stratified random sample

N= total population

N1= no. of 1^st stratum elements

N2= no. of 2^nd stratum elements

N3= no. of 3^rd stratum elements

Note: To determine the appropriate sample size without resorting to your subjective decision. Using Sloven’s formula: n=N/1+Ne²  

where: n= sample size N= population size e=0.05( sampling)

• Stratified sampling

a.) Simple Stratified Random Sampling

Ex. Population of students taking Civil Engineering Course of size N= 800 , sample  size n= 200 is to be taken. The population can be group according to year level. Then  random sampling applied to take 50 students per year level.

Year Levels	Population	Sample
4th year	185	50
3rd year	200	50
2nd year	215	50
1st year	200	50
Total	N=800	n=200

b.) Stratified Proportional Random Sampling

Ex. At a state college, the student may be classified according to the following: Determine appropriate sample size AND NO. OF SAMPLE UNITS PER YEAR LEVEL.

Classification	Population	Sample UNITS
Senior	119	34
Junior	210	60
Sophomore	325	93
Freshmen	346	99
total	1000	286

By Sloven’s Formula n= 286

N3=(325/1000)*(286)= 93

N1=(119/1000)*(286)= 34

N4=(346/1000)*(286)= 99

N2=(210/1000)*(286)= 60

• Cluster sampling(Area sampling)-usually applied on a geographical basis. It is cost efficient when the population is widely scattered. The population is grouped into cluster or small units( blocks, districts, municipality or city), where clusters may be of heterogeneous characteristics or attributes.

Non-Probabilistic sampling(non-random or judgment sampling)

Purposive sampling - based on criteria laid down by the researcher.

Quota sampling - relatively quick and inexpensive method to operate since the choice of the number of persons or elements to be included in a sample is done at researcher’s own convince or preference and is not predetermined by some carefully operated randomizing plan.

Incidental Sampling- applied to those samples which are taken because they are the most available.

Convenience sampling- method widely used in television and radio programs to find out opinions of TV viewers or listeners regarding a controversial issue.

Activity 2

Please file this in your portfolio.

Using the third column of  the Table of Random Numbers, pick 10 sample units from a population of 1,150. Using Remainder Method

A sample units of 15 is to be taken from population of 90. Use Systematic sampling method

Determine a.)  the sample size if  5% margin of error (b.)  % share per strata (c.)  number of sample units per strata. Use Stratified Proportional

Random method

Departments	Employees	% share	# Samples units
Administrative	230
Manufacturing	130
Finance	95
Warehousing	25
Research and Development	10
Total	?

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Answer 1 Using the third column of the Table of Random Numbers pick 10 sample units from a population of 1150 Using Remainder Method Solution Step 1 C... View the full answer