Sampling methods and sample size

Sampling methods and
Sample size
in Quantitative Researches
Sampling methods and Sample size -Dr Mahmoud Danaee

Outlines
Introduction
Statistical inference
Population and sample
Types of Sampling Methods
Sample size calculation
G-Power ( Power Analysis)

Introduction

Research
• The systematic investigation into and study of materials
and sources in order to establish facts
and reach new conclusions
• In the broadest sense of the word, the research includes gathering
of data, information and facts for the advancement of
knowledge.

• Research must be systematic and follow a series of steps and a standard
protocol.
• These rules are broadly similar but may vary slightly between the
different fields of science.
• Scientific research must be organized and undergo planning, including
performing literature reviews of past research and evaluating
what questions need to be answered

Quantitative Research (data collection) Techniques
Existing Statistics
ExperimentsSurveysContent Analysis

Quantitative research is generally made using scientific methods,
which can include:
• The generation of models, theories and hypotheses.
• The development of instruments and methods for measurement.
• Experimental control and manipulation of variables.
• Collection of empirical data.
• Modeling and analysis of data.

● Step I: Define the research problem
● Step 2: Developing a research plan & research Design
● Step 3: Define the Variables & Instrument (validity & Reliability)
● Step 4: Sampling & Collecting data
● Step 5: Analysing data
● Step 6: Presenting the findings

Why do sampling?
•Sampling is done because you usually cannot gather
data from the entire population.
•Even in relatively small populations, the data may be
needed urgently, and including everyone in the
population in your data collection may take too long.

information about
Malaysian people
population
High Cost & time
Results 100%
accurate
Unbiased
Sample
Low cost & fast
Results but not
100% accurate
Biased
Statistical
inference
Statistical inference

What is Sampling?
• Sampling is the process of selecting observations (a sample) to provide an
adequate description and robust inferences of the population
• The sample is representative of the population.
Population:
a set which includes all measurements of interest
to the researcher
Sample:
A subset of the population

What is Sampling?
Population Sample
Using data to say something (make an inference) with confidence,
about a whole (population) based on the study of a only a few
(sample).
Sampling
Frame
What you
want to talk
about
What you
actually
observe in
the data

Target Population:
• The population to be studied/ to which the investigator wants
to generalize his results
• A population can be defined as including all people or items
with the characteristic one wishes to understand.
Sampling Unit:
• Smallest unit from which sample can be selected
Sampling frame
• List of all the sampling units from which sample is drawn
Sampling scheme
• Method of selecting sampling units from sampling frame

Developing a Sampling Plan
1. Define the Population of Interest
2. Identify a Sampling Frame (if possible)
3. Select a Sampling Method
4. Determine Sample Size( power analysis)
5. Execute the Sampling Plan

Factors to Consider in Sample Design
Research objectives Degree of accuracy
Resources Time frame
Knowledge of
target population
Research scope
Statistical analysis needs
Research objectives Degree of accuracy
Resources Time frame
Knowledge of
target population
Research scope

Classification of Sampling Methods
Sampling
Methods
Probability
Samples
Simple
Random
Cluster
Systematic Stratified
Non-
probability
QuotaJudgment
Convenience Snowball

Non probability sampling
17
• Any sampling method where some elements of population have no chance
of selection
• It involves the selection of elements based on assumptions regarding the
population of interest, which forms the criteria for selection.
• Hence, because the selection of elements is nonrandom, nonprobability
sampling not allows the estimation of sampling errors..

Non probability samples
Convenience (ease of access)
Snowball (friend of friend….etc.)
Purposive (judgemental)
Quota

Convenience or Accidental
• Members of the population are chosen based on their
relative ease of access.
• To sample friends, co-workers, or shoppers at a
single mall, are all examples of convenience sampling.
• Such samples are biased because researchers may
unconsciously approach some kinds of respondents
and avoid others
Advantages
• Easy Method
• Represents class of data pollster is familiar with
• Less time consuming
• Economic way of sampling
No Yellow and Orange in sample !!!

• The first respondent refers a friend. The friend also refers a friend,
and so on.
• Such samples are biased because they give people with more social
connections an unknown but higher chance of selection
• The process of snowball sampling is much like asking your subjects to
nominate another person with the same trait as your next subject.
• The researcher then observes the nominated subjects and continues in
the same way until the obtaining sufficient number of subjects
Snowball sampling
For some populations, snowball sampling is the only sampling
strategy because the study group is secretive or hard to reach
because of social stigma, illegality of their work or lack of data
Homeless people, People suffering from rare diseases, Victims of
sexual assault, Terrorists, Hackers

Types of Snowball Sampling
 Linear Snowball Sampling
Subject refers only one other subject
 Exponential Non-Discriminative Snowball Sampling
Subject gives multiple referrals and each referral gives some more until
required sample size is reached.
 Exponential discriminative Snowball Sampling
Subject refers multiple people but only one is chosen as sample
Advantages
 Referral system helps find samples quickly
 Low cost solution
 Works for hesitant subjects
 Secretive groups can be identified easily

Judgmental sampling or Purposive sampling
• The researcher chooses the sample based on who they
think would be appropriate ( based on knowledge and
experience ,…) for the study.
• This is used primarily when there is a limited number of
people that have expertise in the area being researched.
• This type of sampling technique is also known as
authoritative sampling.
•

Quota Sampling
• The researcher sets the proportions of levels or
strata within the sample.
• This is generally done to insure the inclusion
of a particular segment of the population.
• The researcher sets a quota, independent of
population characteristics.

Methods used in probability samples
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
Multi-stage sampling

Simple random sampling
• Each member of the population has an
equal chance of being selected as subject.
• The entire process of sampling is done in a
single step with each subject selected
independently of the other members of the
population.
• One of the best things about simple random
sampling is the ease of assembling the
sample.

• If the sample is not representative of the population, the random
variation is called sampling error.
• One of the most obvious limitations of simple random sampling method
is its need of a complete list of all the members of the population.
• Please keep in mind that the list of the population must be complete and
up-to-date.
•
• This list is usually not available for large populations. In cases as such,
it is wiser to use other sampling techniques.

Online Random Generators
https://www.random.org/
Random Integer Set Generator

Random numbers using Excel
To get a random number that
doesn't change when the
worksheet is calculated, enter
=RAND() in the formulas bar
and then press F9 to convert
the formula into its result. To
generate a set of random
numbers in multiple cells,
select the cells, enter RAND()
and press control + enter.

Other Online Random Number Generator
• https://www.randomizer.org/
• https://www.mathgoodies.com/calculators/random_no_custom
• https://andrew.hedges.name/experiments/random/
• http://www.miraclesalad.com/webtools/random.php
• http://stattrek.com/statistics/random-number-generator.aspx

Systematic sampling
• Relies on arranging the target population according to some ordering
scheme and then selecting elements at regular intervals through
that ordered list.
• Involves a random start and then proceeds with the selection of
every kth element from then onwards.
• k=(population size/sample size).=Sampling fraction

Stratified sampling
 Divide the population by certain characteristics into homogeneous subgroups
(strata) ( PhD students, Masters, Bachelors).
 Elements within each strata are homogeneous, but are heterogeneous across
strata.
 A simple random or a systematic sample is taken from each strata relative to the
proportion of that stratum to each of the others.
When a stratum of interest is a
small percentage of a
population and random
processes could miss the
stratum by chance.

https://dzone.com/articles/statistics-for-rookies-learn-data-driven-decision

Cluster sampling
• First, the researcher selects groups or clusters, and
then from each cluster, the researcher selects the
individual subjects by either simple random or
systematic random sampling.
• The researcher can include the entire cluster and
not just a subset from it.
• The most common cluster used in research is a
geographical cluster. For example, a researcher
wants to survey academic performance of high
school students in a city.

Section 4
Section 5
Section 3
Section 2Section 1

Difference Between Strata and Clusters
• Although strata and clusters are both non-overlapping subsets of the
population, they differ in several ways.
• All strata are represented in the sample; but only a subset of clusters
are in the sample.
• With stratified sampling, the best survey results occur when elements
within strata are internally homogeneous.
• However, with cluster sampling, the best results occur when elements
within clusters are internally heterogeneous

Multi-stage sampling method
• Multistage sampling is the taking of samples in stages using smaller
and smaller sampling units at each stage.
• Multistage sampling can be a complex form of cluster sampling
because it is a type of sampling which involves dividing the
population into groups (or clusters).
• The number of stages can be numerous, although it is rare to have
more than 3 stages.

Stage 1
• Selecting five state
Stage 2
• Selecting 5 area in each state
Stage 3
• Selecting both Rural and urban
Stage 4
• Selecting 3 schools in each area
Stage 5
• Simple Random ( Students )
we select the clusters at the first stage. selected clusters are called first stage units
(FSUs) or primary stage units (PSUs).
Then select a sample of units from within each selected cluster – selected units are called
second stage units (SSUs).

Determining Sample Size
One of the most common questions any
statistician gets asked is
“How large a sample size do I
need?”
• Researchers are often surprised to
find out that the answer depends on a
number of factors and they have to
give the statistician some information
before they can get an answer!

Sample Size depends on :
•Budget/time available
•Executive decision
•Statistical methods
•Historical data/guidelines

Classical Method on determining sample size
• Rule of Thumb
( Exp : minimum 30 per each group, 5 to 10 for each item in
questionnaire ,……..)
• Literature
• Formula ( Cochran is the most common)
• e is the desired level of precision (i.e. the margin of error),
• p is the (estimated) proportion of the population which has the attribute in
question (ie : Prevalance )
• q is 1 – p.

Factors Affecting Sample Size for Probability Designs
• Variability of the population characteristic under investigation.
• Level of confidence desired in the estimate.
• Degree of precision desired in estimating the population characteristic
(sampling error which is the deviation of the selected sample from the true
characteristics, traits, behaviors, qualities or figures of the entire population)

Type I error (alpha error)
• Occurs when an experimenter thinks she/he has a significant result, but it
is really due to chance
• Risk of a Type I error is the same as the significance level, e.g., p < .05
• Solutions:
 Avoid internal validity errors (such as confounding variables),
 Use a more stringent significance level,
 Use replication

Type II error (beta error)
• Occurs when a researcher fails to find a significant result when, in
fact, there was something significant going on.
• Must be calculated with a test of statistical “power,” e.g., given the
sample size, how big would an effect have to be in order to detect it?
• Solutions:
Increase sample size,
 Use more sensitive precise measures,
 Use replication

Determining sample size Using Power
Analysis
• Power analysis allows us to determine the sample size required to
detect an effect of a given size with a given degree of confidence.
• . Power = 1−β = the probability of correctly rejecting a false null
hypothesis
• Power analysis is normally conducted before the data collection.
• Most recommendations for power fall between 0.8 and 0.9.

Effect size
• The effect size is the minimum deviation from the null hypothesis that
you hope to detect.
• Effect size is a quantitative measure of the magnitude of a phenomenon
• Examples of effect sizes are the correlation between two variables, the
regression coefficient in a regression, the mean difference, or even the
risk with which something happens
• Effect size is a simple way of quantifying the difference between two
groups that has many advantages over the use of tests of statistical
significance alone.

Types of effect size
Correlation family: Effect sizes
based on "variance explained"
Difference family: Effect sizes
based on differences between
means
Categorical family: Effect sizes for
associations among categorical
variables
Pearson r or correlation coefficient Cohen's d Cohen's w
Coefficient of determination Glass' Δ Odds ratio
Eta-squared (η2) Hedges' g Relative risk
Omega-squared (ω2)
Ψ, root-mean-square
standardized effect Risk difference
Cohen's ƒ2
Distribution of effect sizes based
on means
Cohen's h
Cohen's q

https://www.uccs.edu/lbecker/

Effect size Convertor

G*Power: Statistical Power Analyses for
Windows and Mac
G*Power is a tool to compute statistical power
analyses for many different t tests, F tests, χ2
tests, z tests and some exact tests. G*Power can
also be used to compute effect sizes and to display
graphically the results of power analyses.
http://www.gpower.hhu.de/fileadmin/redaktion/Fak
ultaeten/Mathematisch-
Naturwissenschaftliche_Fakultaet/Psychologie/AAP/g
power/GPowerWin_3.1.9.2.zip
Download it
free at

G.power provides
sample size
calculation based on
different statistical
test

https://www.ncss.com/software/pass/

http://www.surveysystem.com/sscalc.htm
http://www.nss.gov.au/nss/home.nsf/pages/S
ample+size+calculator
http://www.calculator.net/sample-size-
calculator.html
http://www.sample-size.net/

Thank you
• Dr. Mahmoud Danaee
• mdanaee@um.edu.my
Senior Visiting Research Fellow
• Academic Enhancement and Leadership Development Center ( ADeC)
Academic Networkin By Dr Mahmoud Danaee

Sampling methods and sample size

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