03-Sampling Technique (2)

8/16/2019 03-Sampling Technique (2)

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Sampling and

Sampling Distribution

Module-3

Types of Sampling


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Sampling : Introduction

A sample is a definite plan for obtaining a

data 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 angalore. The total of all households in R.T. Nagar is thepopulation.

Suppose a list of households is not available!each bloc" may be considered as sampling unit.

A #ist of such bloc"s will be used as thesampling frame.


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Types of Sampling :

$robability Sampling Method

Simple Random Sampling

Systematic Sampling

Stratified Sampling Cluster Sampling

Non-$robability Sampling Method

Convenience Sampling

udgment Sampling

!uota Sampling


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Probability Sampling Methods

%t is based on the theory of probability. %t is also

"nown as random sampling or chance sampling.

%n probability sampling every population has a

chance of being selected. Such chance is "nown

as probability.

&.g. %f a sampling frame is a list of '(( students of

a specific course of study! in a simple random

sample! each student has ')'((th chance of being

selected

$robability 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.

n independent chance means that the dra! of one

element !ill not affect the chances of other element

being selected.

"here some element are purposely e#cluded from the

sample $ the resulting sample is not a random one.

%ence all the element should be included in the sample

frame to dra! a random sample.


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Procedure:

Enumeration of all element in the

population.

Dra!ing sample number by using :'ottery method

table of random numbers


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Lottery Method:-

This is the simplest and most familiar procedure of

random sampling.

E.g. (f a sample of )* students is to be dra!n out of +* in a

section$ "rite the no,s )+* in a slips and pic- )* slips $

the units bearing the numbers of slips dra!n constitutethe random sample.

They are two alternatives:

fter a number is selected by dra!$ 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

dra!s$ 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$

ne should start selecting the number from a

table of /andom number at any randomly

selected point & !ith in the range of frame. The table of random numbers is ideal for

obtaining a random sample from relatively

small populations. "hen population are quite

large say la-hs$ dra!ing number from the table

becomes tedious.


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Example:-

'et us suppose that the random sample of +* is toselected from a college population of +** commercestudents.

Sample of random numbers

)** 012 22+ 110 032 +22 104 ))* 245 160 254 103

*54 55+ 660 *)6 *25 316

*6* +05 44+ 12* **) *)2

)25 4+* 05* +4* 444 *06

ll the numbers !ithin the range of )+** may be pic-edup for the study.


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Suitability:-

The simple random sampling is suitable only for a

small homogenous population7 group !ith reference to

the specified characteristics.

"here the population is relatively small. "here a complete list of all elements is available or can

be prepared.

The simple random sampling is not suitable for dra!ing 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 dra!n from each stratum.

(n simple !ords$ !hen the population is very much heterogeneous

& it is divided into different strata on the basis of age$ socioeco

status$ occupation$ educational bac-ground$ /esidence 8urban$

suburban$ /ural9 in this case stratified random sampling !ill be

the best choice.

(t is the process of selecting a sample in such a !ay that$ identified

subgroup in the population are represented in the sample.


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Steps for random sampling

(dentify and define the population

Determine the desired sample sie

(dentify the variable & subgroup 8strata9 for !hich

you !ant to guarantee appropriate representation.

;lassify all members of the population as member of

one of the identified subgroups.

/andomly select an appropriate number of individuals

from each of the subgroup.


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Example:-

Population 4**

)*th grade student

0*%igh (< Students 23* vg (< Students 0* 'o! (< Students

1* %igh (< boys 4* %igh (< girls

/andomly Selected

)+ %igh (< boys & girls


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Need for Stratification

(ncreasing a sample,s statistical efficiency

Providing adequate data for analying the

various subpopulation.

Stratification is essential !hen the researcher

!ants to study the characteristics of population

subgroup.

Suitability: is appropriate for a large

heterogeneous population


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Representation of the subgroups can be proportionate or

disproportionate

!or example" if you #anted to sample $%% farmers from a

population of farmers in #hich &%' are male and $%' are

female" a proportionate stratified sample #ould select &%

males and $% females

(ut you may #ant to )no# more about the #omen farmers

then is possible in a sample

So you can select a disproportionate stratified sample" for

example" you could select *% males and *% females


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;ase Study )+.1 Stratified sampling of households

+ sur,ey is conducted on household #ater supply in a

district comprising "%%% households" of #hich .%% /or

%'0 are urban and $"1%% /or 2%'0 are rural

It is suspected that in urban areas the access to safe #ater

sources is much more satisfactory than in rural areas

+ decision is made to sample %% households altogether"

but to include $%% urban households and $%% rural

households

Is this sample a proportionate or a disproportionate stratified

sample3


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Systematic Sampling

This method of sampling is an alternative to random

sampling. (t consists of ta-ing every - th item in the

population after a random start !ith an item from ) to

-.

E. g. suppose it is desired to select a sample of 2*

students$ from a list of 1** students $ divide the

population total of 1** by 2*$ the quotient is )+.

select a number at random bet!een ) & )+$ using

lottery method. Suppose the selected number is 6$ then

the students numbered 6 $ 2486=)+9$ 16 824=)+9$

+4816=)+9$ 36$54>.. re selected as sample.


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;luster 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 !ants to select a random sample of )***households out of 4**** estimated households in a city for asurvey. direct sample of individual household !ould be difficultto select $ because a list of households does not e#ist and !ould beto costly to prepare.

(nstead he can select a random sample of a fe! bloc-s7!ards. The

no of bloc-s to be selected depends upon the average no ofestimated households per bloc-. Suppose the average no ofhouseholds per bloc- is 2**$ then + bloc-s comprises the sample$& from each sample bloc-s a certain number of households maybe selected by systematic sampling.


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Some illustration of cluster are:

Population Elements ;luster or sampling

unit

;ity %ouseholds ?loc-s

;ity (ndividuals %ouseholds

ffiliating @A(B Students ffiliated ;olleges

/ural areas %ouseholds Billages


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4luster 5s Stratified

Cluster Sampling

"hen natural groupings are evident in a statistical population# this

technique is used.

It can be opted if the group consists of homogeneous members.

Its advantages are that it is cheaper as compared to the other

methods.

The main disadvantage is that it introduces higher errors.


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Stratified Sampling

In this method# the members are grouped into

relatively homogeneous groups.

It is a good option for heterogeneous members.

The advantages are that this method ignores

the irrelevant ones and focuses on the crucial

sub populations. Another advantage is that

for different sub populations# you can opt for

different techniques.


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Stratified Sampling

This also helps in improving the efficiency and

accuracy of the estimation. This allows

greater balancing of statistical power of tests.

"hen there are homogeneous subgroups# it is

not much useful. Its implementation is

e$pensive. If not provided with accurate

information about the population# then anerror may be introduced.


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4ontd:-

;onvenience Sampling : The selection of the sample is left to theresearcher !ho is to select the sample unit in a Cust hit and missfashion. Most suitable in e#ploratory research,.

E.g. (ntervie!ing the people !hom !e happen to meet.

udgment Sampling :This involves selection of cases !hich !e Cudge as the most appropriate ones for the given study. (t is basedon the Cudgment of the researcher and some e#perts. (t does notaim at securing a cross section of the population.


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;haracteristics of a Food Sample Design

Foal rientation

Measurability

@sability

;ost Gactor


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Sampling and AonSampling Errors

Starting from data collection to inferring results" t#o )inds of errorsmay come:

Sampling Errors : arise due to studying only a part of the total population 6hese may arise due to non-representati,e ness of thesample and the inade7uacy of sample si8e

9hen se,eral samples are dra#n from a population" their results#ould not be identical 6he degree of ,ariation of sample result is)no#n as standard error

AonSampling Errors : arise due to technically faulty obser,ation orcalculations during the processing of data

Methods of data collection Incomplete co,erage of the population

Inaccurate information pro,ided by the participants

Error during tabulation" editing etc


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4oncept of measurement Scaling

Measurement in research consists of assigning numbers

to empirical events in compliance !ith 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.

pplying the mapping rule to each observation of that

event.


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Example:

8)9 Do you feel respected by your colleagues7 co!or-ersH

Bery desirable + 4 1 2 ) Bery undesirable

Sample element : ;olleagues7 ;o!or-ers or (ndividuals

Empirical bservation : /espected

Mapping rules : /ating Scale

829 (s there employee turnover in your organiationH

8a9 Ies b9 Ao


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Scaling 6echni7ues

%ominal Scale & In this scale# numbers are used to

identify the ob'ects.

(g.) & university registration numbers assigned to

students.

(g.* & +ave u ever visited ,angalore -

es / )

%o / *

The idea of using nominal scale is to make sure that notwo persons or ob'ect receive the same no.

Statistical implication & It is possible to e$press mode.


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Scaling 6echni7ues

0rdinal Scale & is an ranking scale. This scale are used

to ascertain the consumer perception# preferences etc.

(g& Respondents may be given a list of brands which

may be suitable 1 were asked to rank on the basis of

ordinal scale.

Statistical implication& It is possible to calculate the mode

1 the median.


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4ontd

Ran" rand No. of Respondents

I Cinthol )23

II 4iril 533

III +amam *23

I6 4u$ *33

6 4ifebuoy )33

Total )333


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;ifference bet#een Nominal


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Inter,al Scale

Interval scale is more powerful than the

nominal 1 ordinal scale.

The distance given on the scale represents

equal distance on the property beingmeasured.

Interval scale may tell us : +ow far the

ob'ects are apart with respect to an

attribute-;


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4ontd:

This means that the difference can be

compared. The difference between ) 1 * is

equal to the difference between * 1 5.

(g& Suppose we want to measure the rating ofa refrigerator using interval scale# it may

appear as follows &

). ,rand name ood

*.


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4ontd :

(g& +ow important is price to you while buying a

car -

4east important / )

?nimportant / *

%eutral / 5

Important / @

ost important / 2


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4ontd :

(g& The counter=clerks at ICICI bank are very

friendly.

). Strongly disagree

*. 8isagree

5. %either agree nor disagree

@. Agree

2. Strongly agree

Statistical implication& range# mean# S.8# t=test.


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;ifference bet#een inter,al ordinal scale

0rdinal scale gives only the ranking of the

alternatives& one is greater than the other#

but wonBt give the differencedistance

between one and the other. Interval scale provides information about the

difference between one and the other.


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Ratio Scale

Ratio scale is a special kind of interval scale#

with this scale income# sales or distance can

be measured.

In this scale# it is possible to say / how manytimes greater or smaller one ob'ect is being

compared to other.

(g& Sales this yr for product A are twice the

sales of the same product last yr.


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6ypes of measurement data=scales

Types ofdata7scales

;haracteristics of data ?asic empiricaloperation

E#amples

Aominal ;lassification but noorder$ distance ororigin

Determination ofequality

Fenders$

rdinal ;lassification & orderbut no distance orunique origin

Determination ofgreater or lesservalue

Superior to$happier than$poorer than

(nterval ;lassification order &distance but no unique

origin

Determination ofequality of

intervals ordifferences

Temperature indegrees

/atio ;lassification orderdistance & uniqueorigin

Determination ofEquality of ratio

reas$ distance$

number of

customers$

costs$ age


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Properties of scales

$ ;lassification : a measure that can be used to classify obCects or

their characteristics into distinctive classes7categories. this is a

minimum requirement for any measure.

2. rder: a measure is said to have an order if the obCects or their

characteristics can be arranged in a meaningful order.

1. equal distance : if for a measure$ the difference bet!een any t!o

consecutive category 8 generally termed as values for numeric

variable9 of a measured attribute$ are equal $ then the measure is

said to have equal distance .

4. origin : a measurement scale for measuring a characteristic issaid to have a fi#ed origin if there is a meaningful ero or absence

of the characteristic.


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6ypes of scales

$ nominal scales : a 7ualitati,e scale #ithout order is

called nominal scale 6his scale can only be categori8ed

ordinal : is the scale that does not measure ,alues of the

characteristic" but indicates only the order or ran)

>ualitati,e scale #ith order is called ordinal scale

? inter,al : inter,al data is 7uantitati,e data that can be

measured on a numerical scale

. Ratio :


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4haracteristics of sound measurement

6alidity &= refers to the e$tend to which a test

measures what we actually wish to measure.

Reliability &= has to do with the accuracy andprecision of a measurement procedure.


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9hat is Scaling3

Scaling :

is a procedure for the assigning of numbers to

indicants of the properties of obCects.

Types of /esponse Scales&=

Rating Scales

Ranking Scales


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4ontd:-

Rating Scales :- is used !hen respondents score an

obCect !ithout ma-ing any comparison to other obCect.

Ranking Scales :- constraints the studyparticipants to ma-e comparison among t!o or more

indicants or obCects .


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6ypes of Rating Scales

Simple category

Multiple choice :single response

Multiple choice :multiple response

'i-ert scale

Semantic differential

Aumerical

Multiple rating

Fraphic rating


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6ypes of Ran)ing Scales


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6ypes of Rating Scales:

Simple category : also called dichotomous scale.

(t offers t!o mutually e#clusive response choice. They

are yes & no$ agree & disagree etc

E.g. Does compensation leads to motivation directlyH

8a9 Ies b9 Ao


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4ontd:-

Multiple choice single response 7 multiple

response: llo!s the rater to select one or several

alternatives.

E.g. "hat sort of nonmonetary benefits !ould you prefer

in your ;ompanyH

a9 Training facilities d9 Gle#ible !or- hoursb9 /e!ards for referrals e9 verseas assignment

c9 Fifting of leave f9 /ecognitions


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4ontd:-

'i-ert scale : The 'i-ert Scales consists of a number ofstatements !hich either a favorable or unfavorable attitude

to!ards the given obCect to !hich the respondent is as-ed to

react.

E.g. n advertisement helps my decision in choosing the brandH

Strongly gree J K

Moderately gree J K

Aeither gree nor Disagree J KModerately Disagree J K

Strongly Disagree J K


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4ontd:-

Semantic differential : This method consists of aset of bipolar rating scale$ usually !ith seven points$ by

!hich one or more respondents rate one or more

concept on scale item.

E.g. ther than brand attributes li-e quality$ value for

money$ ho! much do you thin- celebrity endorsement

is importantH

Most important :L: L :L :L :L :L :L : Aot at all important

Severe :L: L :L :L :L :L :L : 'enient

1 2 ) * ) 2 1


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4ontd:-

Aumerical Scales : are +points scale. Therespondent !rites a number from the scale ne#t to

each item.

E.g. Do you receive timely information relating to your !or-H

+ 4 1 2 )


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4ontd:-

Multiple rating Scale: is similar to the numericalscale but differs in t!o !ays:

)9 (t accepts a circled response from the rater

29 The layout allo!s visualiation of the results.E.g. Please indicate ho! important or unimportant each

service characteristic is.N

(mportant unimportant

Gast reliable repair 0 3 + 4 1 2 )Services at my location 0 3 + 4 1 2 )

Ono!ledgeable technicians 0 3 + 4 1 2 )


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4ontd:-

Fraphic rating Scale: This scale uses pictures$ icons$other visuals to communicate !ith the rater and

represent a variety of data types.

E.g. %o! li-ely are you to recommend complete care to

others HN 8 place an # at the position along the line that

best reflects your Cudgment 9

Bery li-ely LLLLLLLLLLLLLLLLLLLLL Bery @nli-ely


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6ypes of Ran)ing Scales

Pairedcomparison Scale &= the respondents can

e#press attitude unambiguously by choosing bet!een

t!o obCects.

(.g. Gor each pair of sports car listed$ place a chec-beside the one you !ould prefer if you had to choose

bet!een the t!o.

a9LLLLLLLL ?M" 1 LLLLLLLL ;hevrolet

b9LLLLLLLLPorsche ?o#ster LLLLLLLL Porsch?o#ster


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!orced ran)ing scale

This method is faster than paired comparisons and is usually

easier and more motivating to the respondents. (n this scale

attributes are given7listed$ respondents are as-ed to ran- relative

to each other.

Eg +cc to your preference ran) the folg non-monetary benefits pro,ided in your 4ompany3

a0 6raining facilities d0 !lexible #or) hours

b0 Re#ards for referrals e0


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4omparati,e Scales:-

(s ideal for comparison of attributes using ran-ing scale$

if the respondents are familiar !ith the standard.

(.g. ;ompared to your previous mutual fund,sperformance$ the ne! one is.N

Superior Same (nferior

LLLLL LLLLL LLLL LLLL LLLLL

) 2 1 4 +


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Scale ;esign 6echni7ues

Arbitrary scaling &= A scale is custom=designed to

measure a property or indicant.

*onsensus scaling &= Requires items to be selected

by a panel of 'udges and then evaluated.

%tem 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 4ikert scale.

*umulative scaling +- Scales are chosen for theirconformity to a ranking of items with ascending and

descending discriminating power.

03-Sampling Technique (2)

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