Week 7:

Sampling

Lessons of Life

Slide 1

Learning Objectives

Understand . . .

• The two premises on which sampling theory is based.

• The accuracy and precision for measuring sample validity.

• The five questions that must be answered to develop a sampling

plan.

• The two categories of sampling techniques and the variety of

sampling techniques within each category.

• The various sampling techniques and when each is used.

Slide 2

Idea of Sampling

The basic idea of sampling is that

by selecting several elements

from a population, we can make

an inference about the entire

population.

Slide 3

Population and Sampling

Slide 4

Population and Sampling

Slide 5

The Nature of Sampling

• Population

• Population Element

• Sample

• Sample subject

• Sampling frame

• Census

• Parameter

• Statistics

Slide 6

Statistics

Slide 7

Inference Process

Population

Sample

Sample

Statistics

Estimation &

Hypothesis

Testing

),( spX

Slide 8

Parameter and Statistics: Example

“Average height of 2nd year students is

150 centimeters”

Parameter

“Average height of 2nd year students in

Mr Ali’s class is 150 centimeters”

Statistic

Population

Sample

Slide 9

Inference

Slide 10

Why Sampling is Needed?

• Cost

• Time

• Destruction of Test unit

• More accurate

▪ Better interviewing

▪ Checking for missing, suspicious

information

▪ Better supervision

▪ Better processing

Slide 11

When Is a Census Appropriate?

NecessaryFeasible

Slide 12

What Is a Valid Sample?

Accurate Precise

Slide 13

Accuracy (Unbiased)

Presidential poll In 1936, 2 million people participated,

Alfred Landon was predicted to defeat Franklin Roosevelt.

Problem was they drew the sample from telephone owners

who were mostly middle and upper class.

True Mean

2.5 3 3.5 4 4.5

S1

S2

Slide 14

Sampling Design within the Research Process

Slide 15

Types of Sampling Designs

Element Selection Probability Nonprobability

Unrestricted Simple random Convenience

Restricted Complex random Purposive

Systematic Judgment

Cluster Quota

Stratified Snowball

Double

Slide 16

Some basic terms

• Representativeness

• Probability Sampling

▪ Randomly selected, each element has a known probability of

being chosen which is not equal to 0

• Non-Probability Sampling

▪ Non-random, unknown probability of being chosen

Slide 17

14-105

Steps in Sampling Design

1. What is the target population?

2. What are the parameters of interest?

4. What is the appropriate sampling method?

5. What size sample is needed?

3. What is the sampling frame?

Slide 18

Formula – Infinite Population

Where:

n = Sample Size for infinite population

Z = Z value (e.g. 1.96 for 95% confidence level)

p = population proportion (expressed as decimal)

(assumed to be 0.5 (50%)

M = Margin of Error at 5% (0.05)

n =൯z2 ∗ p(1 − p

M2

Slide 19

Formula – Finite Population

Where:

S = Required Sample size

X = Z value (e.g. 1.96 for 95% confidence level)

N = Population Size

P = Population proportion (expressed as decimal)

(assumed to be 0.5 (50%)d = Degree of accuracy (5%), expressed as a

proportion (.05); It is margin of error

S =൯X2NP(1 − p

ሻd2 N − 1 + X2P(1 − P

Slide 20

Sample Sizes – Rules of Thumb

• Rules of Thumb

▪ 5 sample per item

▪ 10 sample per item

Slide 21

Sample Sizes – Krejcie & Morgan

Slide 22

Sample Sizes – Gpower http://gpower.hhu.de/

Slide 23

Gpower

Slide 24

Gpower

14-25 Slide 25

Power

Slide 26

Sales Profit

Gender Grades

Ethnicity Grades

Slide 27

Sample Sizes – Raosofthttp://www.raosoft.com/samplesize.html

Slide 28

When to Use Larger Sample Sizes?

Population variance

Small error range

Desired Precision

Number of Subgroups

Confidence Level

Slide 29

Selecting a random sample

• Numbered paper/ball

• Random number tables

• Computer generated

Slide 30

Numbered paper/ball

Slide 31

Random Number Tables

57613 55089 10233 28076 57112 50531

85765 78648 49879 69624 64138 91376

91297 12918 71506 21698 10908 34550

77602 13397 52530 77171 42623 76675

5215 36596 1273 30562 73009 59435

40421 19973 75608 1754 91815 78997

1625 85425 55401 41762 68540 25339

71816 15535 77156 98915 95654 70585

64313 47684 63308 80079 54648 13211

87164 13605 30983 77390 57604 54092

68575 38111 95346 24386 59240 44034Slide 32

Random Number Tables

57613 55089 10233 28076 57112 50531

85765 78648 49879 69624 64138 91376

91297 12918 71506 21698 10908 34550

77602 13397 52535 77171 42623 76675

15215 36596 11273 30562 73009 59435

40421 19973 75608 11754 91815 78997

11625 85425 55401 41762 68540 25339

71816 15535 77156 98915 95654 70585

64313 47684 63308 80079 54648 13211

87164 13596 30983 77390 57604 54092

68575 38111 95346 24386 59240 44034Slide 33

Computer Generated

Slide 34

Computer Generated

Slide 35

Computer Generated

Slide 36

Computer Generated

Slide 37

Simple Random

• In the unrestricted probability sampling design, more commonly

known as simple random sampling, every element in the population

has a known and equal chance of being selected as a subject.

• If we have 1000 elements in the population, and we need a sample

of 100. The probability would be 100/1000 = 0.1.

Slide 38

Simple Random

Advantages

• Easy to implement with random

dialing

Disadvantages

• Requires list of population elements

• Time consuming

• Uses larger sample sizes

• Produces larger errors

• High cost

Slide 39

Systematic Sampling

• The systematic sampling design involves drawing every nth element

(denoted as k) in the population starting with a randomly chosen element

between 1 and n.

• Let’s say we want to sample n = 10 from a population of N = 30.

• First, we will calculate the: k = N/n = 30/10 = 3

• Then we will need to select the first respondent randomly from 1-3, then

the subsequent respondent will follow the step number k which is +3.

• Let’s say we selected the first number as 2, then the next number will be 5

and the next number will be 8 and so on until we get the 10 samples.

Slide 40

Systematic Sampling

Slide 41

Systematic Sampling

Advantages

• Simple to design

• Easier than simple random

• Easy to determine sampling

distribution of mean or proportion

Disadvantages

• Periodicity within population may

skew sample and results

• Trends in list may bias results

• Moderate cost

Slide 42

Stratified Random Sampling

Slide 43

Stratified Sampling

• Population is divided into sub-

population or stratum and the

subjects selected randomly.

▪ Proportionate

▪ Disproportionate

All Students

Off Campus On Campus

Sample

Slide 44

Stratified Sampling

• Population is N = 10,000

• Sample size needed is n = 500

Stratum Population % Proportionate Disproportionate (%) Selected

Small 95 475 50 250

Medium 3 15 25 124

Large 2 10 25 125

Total 100 500 100 500

Slide 45

Stratified Sampling

Advantages

• Control of sample size in strata

• Increased statistical efficiency

• Provides data to represent and

analyze subgroups

• Enables use of different

methods in strata

Disadvantages

• Increased error will result if

subgroups are selected at different

rates

• Especially expensive if strata on

population must be created

• High cost

Slide 46

Cluster Sampling

Population is divided

into clusters, the cluster

is randomly selected

All Students in

Malaysia

Kuala Lumpur Johor

Sample

Malacca

Slide 47

Cluster Sampling

Advantages

• Provides an unbiased estimate of

population parameters if properly

done

• Economically more efficient than

simple random

• Lowest cost per sample

• Easy to do without list

Disadvantages

• Often lower statistical efficiency

due to subgroups being

homogeneous rather than

heterogeneous

• Moderate cost

Slide 48

Comparing Stratified and Cluster Sampling

Stratified

• Population divided into few

subgroups

• Homogeneity within subgroups

• Heterogeneity between subgroups

• Choice of elements from within

each subgroup

Cluster

• Population divided into many

subgroups

• Heterogeneity within subgroups

• Homogeneity between subgroups

• Random choice of subgroups

Slide 49

Area Sampling

• Area sampling is a method of sampling used when no complete frame of

reference is available. The total area under investigation is divided into

small sub-areas which are sampled at random or according to a restricted

process (stratification of sampling).

• Clusters consist of geographic areas such as counties, city blocks, or

particular boundaries within a locality.

• It is a low-cost and frequently used method.

Slide 50

Area Sampling

Slide 51

Double Sampling

Advantages

• May reduce costs if first stage

results in enough data to stratify

or cluster the population

Disadvantages

• Increased costs if indiscriminately

used

Slide 52

Nonprobability Samples

• In nonprobability sampling designs, the elements in the population

do not have any probabilities attached to their being chosen as

sample subjects.

• This means that the findings from the study of the sample cannot be

confidently generalized to the population.

Slide 53

When to be Used

Cost

No need to generalize

Limited Objectives

Time

Feasibility

Slide 54

Nonprobability Sampling Methods

Convenience

Snowball

Quota

Judgement

Slide 55

Convenience Sampling

• Convenience sampling refers to the collection of information from

members of the population who are conveniently available to provide it.

• Convenience sampling is most often used during the exploratory phase

of a research project and is perhaps the best way of getting some basic

information quickly and efficiently.

Slide 56

Convenience Sampling

Slide 57

Advantages

1. Collect data quickly: In situations where time is a constraint, many researchers choose

this method for quick data collection.

2. Inexpensive to create samples: The money and time invested in other probability

sampling methods are quite large compared to convenience sampling. It allows

researchers to generate more samples with less or no investment and in a brief period.

3. Easy to do research: The name of this surveying technique clarifies how samples are

formed. Elements are easily accessible by the researchers and so, collecting members

for the sample becomes easy.

4. Low cost: Low cost is one of the main reasons why researchers adopt this technique.

When on a small budget, researchers – especially students, can use the budget in other

areas of the project.

5. Readily available sample: Data collection is easy and accessible. Most convenience

sampling considers the population at hand. Samples are readily available to the

researcher. They do not have to move around too much for data collection. Slide 58

Disadvantages

1. Convenience samples do not produce representative results. If you need to

extrapolate to the target population, convenience samples aren't going to

get you there.

2. The natural tendency is to extrapolate from convenience samples.

3. The results of convenience samples are hard to replicate.

4. Highly vulnerable to selection bias and influences beyond the control of

the researcher

5. High level of sampling error.Slide 59

Purposive Sampling

• Instead of obtaining information from those who are most readily or

conveniently available, it might sometimes become necessary to obtain

information from specific target groups.

• The sampling here is confined to specific types of people who can

provide the desired information, either because they are the only ones who

have it, or they conform to some criteria set by the researcher.

Slide 60

Purposive - Judgement Sampling

• Judgment sampling involves the choice of subjects who are most

advantageously placed or in the best position to provide the

information required.

• For instance, if a researcher wants to find out what it takes for women

managers to make it to the top, the only people who can give first‐hand

information are the women who have risen to the positions of presidents,

vice presidents, and important top‐level executives in work

organizations.

Slide 61

Purposive - Quota

• Quota sampling, a second type of purposive sampling, ensures that

certain groups are adequately represented in the study through the

assignment of a quota.

• The population is first subdivided into stratum.

• Then from each stratum and % is selected.

• Reason to ensure representativeness or numbers in each group.

• Useful if you want to do sub-group analysis.

Slide 62

Purposive - Quota

• Population is N = 1,000

• Sample size needed is n = 200

Stratum Population % Selected Selection Quota Selected Quota

Malay 60 120 30 60

Chinese 25 50 30 60

Indian 10 20 20 40

Others 5 10 20 40

Total 100 200 100 200

Slide 63

Advantages

1. Saves time: Because of the involvement of a quota for sample creation, this sampling

process is quick and straightforward.

2. Research convenience: By using quota sampling and appropriate research questions,

interpreting information and responses to the survey is a much convenient process for a

researcher.

3. Accurate representation of the population of interest: Researchers effectively

represent a population using this sampling technique. There is no room for over-

representation as this sampling technique helps researchers to study the population using

specific quotas.

4. Saves money: The budget required for executing this sampling method is minimalistic.Slide 64

Disadvantage

• Vulnerability to errors in judgment by researcher.

• Low level of reliability and high levels of bias.

• Inability to generalize research findings.

Slide 65

Snowball Sampling

Slide 66

When to be Used

1. No official list of names of the members: This sampling technique can be used for a

population, where there is no easily available data like their demographic information. For

example, homeless or list of members of an elite club, whose personal details cannot be

obtained easily.

2. Difficulty to locate people: People with rare diseases are quite difficult to locate. However, if

a researcher is carrying out a research study similar in nature, finding the primary data source

can be a challenge. Once he/she is identified, they usually have information about more such

similar individuals.

3. People who are not willing to be identified: If a researcher is carrying out a study which

involves collecting information/data from sex workers or victims of sexual assault or

individuals who don’t want to disclose their sexual orientations, these individuals will fall

under this category.

4. Secretiveness about their identity: People who belong to a cult or are religious extremists or

hackers usually fall under this category. A researcher will have to use snowball sampling to

identify these individuals and extract information from them.

Slide 67

Advantages

1. It’s quicker to find samples: Referrals make it easy and quick to find subjects as they come

from reliable sources. An additional task is saved for a researcher, this time can be used in

conducting the study.

2. Cost effective: This method is cost effective as the referrals are obtained from a primary data

source. It’s is convenient and not so expensive as compared to other methods.

3. Sample hesitant subjects: Some people do not want to come forward and participate in

research studies, because they don’t want their identity to be exposed. There are some sections

of the target population which are hard to contact. For example, if a researcher intends to

understand the difficulties faced by HIV patients, other sampling methods will not be able to

provide these sensitive samples. Slide 68

Disadvantages

1. Sampling bias and margin of error: Since people refer those whom they know and

have similar traits this sampling method can have a potential sampling bias and margin

of error. This means a researcher might only be able to reach out to a small group of

people and may not be able to complete the study with conclusive results.

2. Lack of cooperation: There are fair chances even after referrals, people might not be

cooperative and refuse to participate in the research studies. Oversampling can be

done; respondents may be hesitant to answer all questions.

3. It is not possible to determine the actual pattern of distribution of population.

4. It is not possible to determine the sampling error

Slide 69

What is Important in this chapter?

• Basic terms

• Why sampling is needed?

• Characteristics of a good sample

• Probability and nonprobability samples

• When each should be used

Slide 70

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