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Sampling : Introduction
A sample is a definite plan for obtaining a
sample from a given population.
It refers to the technique or the procedure the
researcher would adopt in selecting items for
the sample.
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Meaning:-
It is the aggregate of element about which we
wish to make inferences. A member of the
population is an element. It is the unit of
study.
A part of population is known as a sample.
The process of drawing a sample from a
large population is called sampling . The list of sampling unit from which a sample
is taken is called the sampling frame.
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Example:-
A researcher wants to survey the brandpreference of households regardingpremium soaps in R.T. Nagar area of the
city of Bangalore. A house hold is the sampling unit
The total of all households in R.T. Nagar is thepopulation.
Suppose a list of households is not available,each block may be considered as sampling unit.
A List of such blocks will be used as thesampling frame.
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Types of Sampling :
Probability Sampling Method
Simple Random Sampling
Systematic Sampling
Stratified SamplingCluster Sampling
Non-Probability Sampling Method
Convenience Sampling
Judgment Sampling
Quota Sampling
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Sampling and
Sampling Distribution
Module-3
Types of Sampling
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Probability Sampling Methods
It is based on the theory of probability. It is also
known as random sampling or chance sampling.
In probability sampling every population has a
chance of being selected. Such chance is knownas probability.
E.g. If a sampling frame is a list of 100 students of
a specific course of study, in a simple random
sample, each student has 1/100th chance of being
selected
Probability sampling yields a representative
sample.
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Simple Random Sampling
This technique gives each element an equal &
independent chance of being selected.
Equal probability selection method is described as
Epsem sampling. An independent chance means that the draw of one
element will not affect the chances of other element
being selected.
Where some element are purposely excluded from thesample , the resulting sample is not a random one.
Hence all the element should be included in the sample
frame to draw a random sample.
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Procedur e:
Enumeration of all element in the
population.
Drawing sample number by using :-Lottery method
A table of random numbers
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Lottery Method:-
This is the simplest and most familiar procedure of
random sampling.
E.g. If a sample of 10 students is to be drawn out of 50 in a
section, Write the no¶s 1-50 in a slips and pick 10 slips ,
the units bearing the numbers of slips drawn constitute
the random sample.
They are two alternatives:-
After a number is selected by draw, it may be replaced
and consequently it has a chance of being selected again.
This is referred as unrestricted random sampling .
The Selected number is set aside, & in the subsequent
draws, it does not get a chance of being selected again.
This is referred as restricted random sampling.
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The table of random numbers
To select a random sample out of a given
frame, One should start selecting the number
from a table of Random number at any
randomly selected point & with in the range of frame.
The table of random numbers is ideal for
obtaining a random sample from relatively
small populations. When population are quite
large say lakhs, drawing number from the table
becomes tedious.
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Example:-
Let us suppose that the random sample of 50 is toselected from a college population of 500 commercestudents.
Sample of random numbers
100 732 225 337 762 522374 110 248 397 284 376
084 885 997 019 028 639
090 578 445 320 001 012
128 450 780 540 444 079
All the numbers within the range of 1-500 may be pickedup for the study.
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Suitability:-
The simple random sampling is suitable only for a
small homogenous population/ group with reference to
the specified characteristics.
Where the population is relatively small.
Where a complete list of all elements is available or can
be prepared.
The simple random sampling is not suitable for drawing a
sample from a large heterogeneous population, as it
may not yield a representative sample of such
population.
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Stratified Random Sampling
The members of the population are first assigned to strata or
groups and simple random sample is drawn from each stratum.
In simple words, when the population is very much heterogeneous
& it is divided into different strata on the basis of age, socio-ecostatus, occupation, educational background, Residence (urban,
sub-urban, Rural) in this case stratified random sampling will be
the best choice.
It is the process of selecting a sample in such a way that, identified
sub-group in the population are represented in the sample.
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Ste ps for random sampling
Identify and define the population
Determine the desired sample size
Identify the variable & sub-group (strata) for whichyou want to guarantee appropriate representation.
Classify all members of the population as member of
one of the identified sub-groups.
Randomly select an appropriate number of individuals
from each of the sub-group.
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Example:-
Population 400
10th grade student
70-High IQ Students 260 Avg IQ Students 70 Low IQ Students
30 High IQ boys 40 High IQ girls
Randomly Selected
15 High IQ boys & girls
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Need for Stratification
Increasing a sample¶s statistical efficiency
Providing adequate data for analyzing the
various sub-population. Stratification is essential when the researcher
wants to study the characteristics of population
sub-group.
Suitability:- is appropriate for a large
heterogeneous population
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Systematic Sampling
This method of sampling is an alternative to random
sampling. It consists of taking every k th item in the
population after a random start with an item from 1 to
k.
E. g. suppose it is desired to select a sample of 20
students, from a list of 300 students , divide the
population total of 300 by 20, the quotient is 15.
select a number at random between 1 & 15, using
lottery method. Suppose the selected number is 9, then
the students numbered 9 , 24(9+15), 39 (24+15),
54(39+15), 69,84«.. Are selected as sample.
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Cluster Sampling
Divide the entire population into clusters and select entire groupsor clusters at random to collect information from these clusters orgroups.
E.g. Suppose a researcher wants to select a random sample of 1000households out of 40000 estimated households in a city for asurvey. A direct sample of individual household would be difficultto select , because a list of households does not exist and would beto costly to prepare.
Instead he can select a random sample of a few blocks/wards. The
no of blocks to be selected depends upon the average no of estimated households per block. Suppose the average no of households per block is 200, then 5 blocks comprises the sample, &from each sample blocks a certain number of households may beselected by systematic sampling.
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Some illustration of cluster ar e:
Population Elements Cluster or sampling
unit
City Households Blocks
City Individuals Households
Affiliating UNIV Students Affiliated Colleges
Rural areas Households Villages
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Non-Probability Sampling Methods
The probability of inclusion of any unit
(of population) in a sample is not known. It
involve human judgment rather than
pure chance. The degree of accuracy is
also unknown.
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Contd:-
Convenience Sampling : The selection of the sample is left to theresearcher who is to select the sample unit in a just µhit and missµfashion. Most suitable in µexploratory research¶.
E.g. Interviewing the people whom we happen to meet.
Judgment Sampling :This involves selection of cases which we judge as the most appropriate ones for the given study. It is basedon the judgment of the researcher and some experts. It does notaim at securing a cross section of the population.
Quota Sampling : The population is stratified on the basis of age,sex, income, family size etc. More often compounded stratificationis used in groups with gender.
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Characteristics of a Good Sample Design
Goal Orientation
Measurability
Usability
Cost Factor
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Sampling and Non-Sampling Errors
Starting from data collection to inf erring r esults, two kinds of errorsmay come:
Sampling Errors : arise due to studying only a part of the total population. These may arise due to non-r e pr esentative ness of the sample and the inadequacy of sample size.
When several samples ar e drawn from a population, their r esults wouldnot be identical. The degr ee of variation of sample r esult is known asstandard error
Non-Sampling Errors : arise due to technically faulty observation or calculations during the processing of data.
Methods of data collection Incomplete coverage of the population
Inaccurate information provided by the participants
Error during tabulation, editing etc.
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Conce pt of measur ement & Scaling
Measurement in research consists of assigning numbers
to empirical events in compliance with a set of rules.
The definition implies the measurement in three part
process:- Selecting observable empirical events.
Developing a set of mapping rules: a scheme for
assigning numbers to represent aspects of the event
being measured.
Applying the mapping rule to each observation of that
event.
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Example:
(1) Do you feel respected by your colleagues/ coworkers?
Very desirable 5 4 3 2 1 Very undesirable
Sample element :- Colleagues/ Co-workers or Individuals
Empirical Observation :- Respected
Mapping rules :- Rating Scale
(2) Is there employee turnover in your organization?
(a) Yes b) No
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Characteristics of sound measur ement
Validity :- refers to the extend to which a test
measures what we actually wish to measure.
Reliability :- has to do with the accuracy and
precision of a measurement procedure.
Practicality :- is concerned with a wide range of factors of economy, convenience, and
interpretability.
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What is Scaling?
S caling :-
is a procedure for the assigning of numbers to
indicants of the properties of objects.Types of Response Scales:-
R ating Scales
R anking Scales
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Contd:-
R ating Scales :- is used when respondents score an
object without making any comparison to other object.
R anking Scales :- constraints the study
participants to make comparison among two or more
indicants or objects .
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Types of Rating Scales
Simple category
Multiple choice :single response
Multiple choice :multiple response
Likert scale
Semantic differential
Numerical
Multiple rating
Graphic rating
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Types of Ranking Scales
Paired-comparison
Forced Ranking
Comparative
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Types of Rating Scales:
Simple category : also called dichotomous scale.
It offers two mutually exclusive response choice. Theyare yes & no, agree & disagree etc
E.g. Does compensation leads to motivation directly?
(a) Yes b) No
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Contd:-
Multiple choice single response / multiple
response: Allows the rater to select one or several
alternatives.
E.g. What sort of non-monetary benefits would you prefer
in your Company?
a) Training facilities d) Flexible work hours
b) Rewards for referrals e) Overseas assignment
c) Gifting of leave f) Recognitions
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Contd:-
Likert scale :- The Likert Scales consists of a number of
statements which either a favorable or unfavorable attitude
towards the given object to which the respondent is asked to
react.
E.g. An advertisement helps my decision in choosing the brand?
Strongly Agree [ ]
Moderately Agree [ ]
Neither Agree nor Disagree [ ]
Moderately Disagree [ ]
Strongly Disagree [ ]
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Contd:-
Semantic differential :- This method consists of a
set of bipolar rating scale, usually with seven points, by
which one or more respondents rate one or more
concept on scale item.
E.g. Other than brand attributes like quality, value for
money, how much do you think celebrity endorsement
is important?
Most important :_: _ :_ :_ :_ :_ :_ : Not at all important
Severe :_: _ :_ :_ :_ :_ :_ : Lenient
3 2 1 0 -1 -2 -3
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Contd:-
Numerical Scales :- are 5-points scale. The
respondent writes a number from the scale next to
each item.
E.g. Do you receive timely information relating to your work?
5 4 3 2 1
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Contd:-
Multiple rating Scale:- is similar to the numerical
scale but differs in two ways:
1) It accepts a circled response from the rater
2) The layout allows visualization of the results.
E.g. ³Please indicate how important or unimportant each
service characteristic is.´
Important unimportant
Fast reliable repair 7 6 5 4 3 2 1
Services at my location 7 6 5 4 3 2 1
Knowledgeable technicians 7 6 5 4 3 2 1
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Contd:-
Graphic rating Scale:- This scale uses pictures, icons,
other visuals to communicate with the rater and
represent a variety of data types.
E.g. ³How likely are you to recommend complete care toothers ?´ ( place an x at the position along the line that
best reflects your judgment )
Very likely _____________________ Very Unlikely
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Types of Ranking Scales
Paired-comparison Scale :- the respondents can
express attitude unambiguously by choosing between
two objects.
E.g. For each pair of sports car listed, place a check
beside the one you would prefer if you had to choose
between the two.
a)________ BMW Z3 ________ Chevrolet
b)________ Porsche Boxster ________ PorschBoxster
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Forced ranking scale
This method is faster than paired comparisons and is usually
easier and more motivating to the respondents. In this scale
attributes are given/listed, respondents are asked to rank relative
to each other.
E.g. Acc to your pr ef er ence rank the folg non-monetary
benefits provided in your Company?
a) Training facilities d) Flexible work hours
b) R ewards for r ef errals e) Overseas assignment
c) Gifting of leave f) R ecognitions
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Comparative Scales:-
Is ideal for comparison of attributes using ranking scale,
if the respondents are familiar with the standard.
E.g. ³Compared to your previous mutual fund¶s
performance, the new one is.´
Superior Same Inferior
_____ _____ ____ ____ _____
1 2 3 4 5
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Scale Design Techniques
Arbitrary scaling :- A scale is custom-designed to
measure a property or indicant.
Consensus scaling :- Requires items to be selected
by
a panel of judges and then evaluated.
Item Analysis scaling :- is a procedure for
evaluating an item based on how well it discriminates
between those person. The most popular scale using
this approach is Likert scale.
Cumulative scaling :- Scales are chosen for their
conformity to a ranking of items with ascending and
descending discriminating power.