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MEASUREMENT AND
SCALING
Prof M. R. Suresh
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Measurement: dened as astandardied !ro"ess of assi#nin#
num$ers or other s%m$o&s to "ertain"hara"teristi"s of o$'e"ts of interesta""ordin# to !res!e"ied ru&es.
im!ortant as statisti"a& ana&%ses "an $edone
on a!!ro!riate s"a&es
t(o "hara"teristi"s:
one)to)one "orres!onden"e $et(een the
s%m$o& and the "hara"teristi" *in theo$'e"t+
$ein# measured
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S"a&in# is a !ro"ess of "reatin# a"ontinuum on (hi"h o$'e"ts are &o"ated
a""ordin# to the amount of measured"hara"teristi" the% !ossess
T%!e of S"a&e Statisti"a& Tests
Nomina& Per"enta#e- mode- "hi)suare
/rdina& Per"enti&e- median Ran0)/rderCorre&ation 1riedman2s
AN/3A
Inter,a& Mean- - t)test- AN/3A-
Re#ression ana&%sis
"orre&ation
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Nomina& S"a&e
o$'e"ts are assi#ned to mutua&&%
e6"&usi,e- &a$e&ed "ate#oriesE.#. Ma&e- fema&e-Geo#ra!hi"a& area
if one entit% is assi#ned the same num$eras another- the% are identi"a& (ithres!e"t to a nomina& ,aria$&e
/rdina& S"a&e
o$tained $% ran0in# o$'e"ts or arran#in#
them in order (ith res!e"t to some"ommon ,aria$&e
E.#. Ran0s of students- seniors- 'uniors ina "o&&e#e
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Inter,a& S"a&ein this the num$ers used to ran0 the o$'e"ts
re!resent eua& in"rements of attri$ute$ein#
measured
di7eren"es "an $e "om!ared
di7eren"e $et(een 8 9 same as ; 9 . ?a&an"in#
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Sin#&e Item S"a&es
on&% one item to measure a "onstru"t
@. Itemied "ate#or% s"a&e
Satisfa"tion (ith !resent hea&thinsuran"e !&an
) ,er% satised
) uite satised
) some(hat satised
) not at a&& satised
3er% satised 3er%dissatised
8 @ B )@ )8
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8. Com!arati,e s"a&es
E.g.
Ran0)/rder S"a&es
reuire res!ondents to arran#e aset of o$'e"ts (ith res!e"t to
"ommon "riterionT(o !ro$&ems = for"ed to ma0e a"hoi"e- undi7erentiated midd&e
Constant sum s"a&eLimitation = on&% a fe( "ate#ories
= sort s"a&in#
Paired = "om!arison
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Mu&ti!&e Item S"a&es
/$'e"ts ha,e man% fa"ets
Likert scale a&so 0no(n as summateds"a&e de#ree of a#reementdisa#reementon a ,ariet% of statements
t(o !arts : item !art- e,a&uati,e !art
im!ortant assum!tion: sin#&e "ommonfa"tor
Thurstone scale a&so "a&&ed eua&
a!!earin# inter,a&s #rou! of 'ud#es are#i,en to @BB items de#ree offa,oura$&eness *@@ "ate#or% $i!o&ar+
s"a&e ,a&ue of ea"h items is the median
,a&ue assi#ned $% 'ud#es "om!&i"ated
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Semantic Diferential widely used
e.#. ima#es of "om!etin# $rands !referen"e of
$i!o&ar s"a&es !airs of o$'e"ts!hrases"orres!ond to !rodu"tser,i"e attri$utes ),e orunfa,ora$&e !o&e rotated treated as inter,a&s"a&es- #rou! mean ,a&ues "a&"u&ated
s!e"i" information "an $e &ost
Prole analysis a ,ariation
Stapel scales
Uni!o&ar 8 @
Tan#% )@ )@ )@
Associative scaling
A!!ro!riate for "hoi"e situation in aseuentia& de"ision !ro"ess trade = o7s not"a!tured redu"ed ,a&idit%
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Guide&ines for de,e&o!in# mu&ti)items"a&e
@. Determine (hat %ou (ant tomeasure
8. Generate as man% items as !ossi$&e
. E6!erts e,a&uation of initia& !oo& ofitems
. Determine t%!e of attitudina& s"a&eto $e
used
>. In"&ude ,a&idation items
;. Administer items to an initia&
sam!&e
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Choi"e of an attitudina&s"a&e
s!e"i" info reuired tosatisf% resear"h o$'e"ti,es
ada!ta$i&it% of s"a&e to data"o&&e"tion method- $ud#et
"om!ati$i&it% to res!ondent
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A""ura"% of attitude
measurementsTrue S"ore Mode&
/ H T S *a7e"ts in a "onstant
(a%+ R *transient fa"torsituationa&J+
3a&idit%
Contentfa"e ,a&idit%: su$'e"ti,e$ut s%stemati" e,a&uation of ho((e&& the "ontent of a s"a&ere!resents the measurement tas0
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Different types of validity
Content validity: Also called face validity. Measures all the relevant
dimensions
Criterion validity: examines whether measurement scale performs as
expected in relation to other variables selected as meaningful criteria
Predicted and actual behaviour should be same
Concurrent validity is a measure of how well a particular test correlates with a
previously validated measure.
This is the degree to which a test corresponds to an external criterion that is known
concurrently (i.e. occurring at the same time). If the new test is validated by a
comparison with a currently existing criterion (benchmark test), we have
concurrent validity. Very often, a new ! or personality test might be compared
with an older but similar test "nown to have good validity already.
Predictive validity: Pertains to #$ow best a researcher can guess the future
performance from the "nowledge of the attitude measurement score% An example
say there is a &uestionnaire that measures demand for a product. 'irst measure the
attitude to purchase a product and then predict future behaviour. (his is followed by
measurement of future behaviour at an appropriate time. )ompare the two results
*past and future+. f the two scores are closely associated then the scale is supposed
to have predictive validity.
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Validity contd..
Construct validity: A sales manager believes that there is clear relationbetween -ob satisfaction for a person and the degree to which a person is an
extrovert and the wor" performance *of his sales force+. (herefore those who
en-oy high -ob satisfaction and have extrovert personalities should exhibit high
performance. f they do not then we can &uestion the construct validity of the
measure
Convergent validity: xtent to which scale correlates positively with other
measures of the same construct.For e.g to show the convergent validity of a
test of arithmetic skills, we might correlate the scores on our test with scores
on other tests that purport to measure basic maths ability, where high
correlations would be evidence of convergent validity. )oncurrent validity
differs from convergent validity in that it focuses on the power of the focal test
to predict outcomes on another test or some outcome variable.
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Discriminant validity: xtent to which a measure does not correlate with
other constructs from which it is supposed to differ. 'or example, an
operationalisation of anxiety should be able to distinguish between people
who are anxious and those who are depressed or suicidal
Nomological validity: xtent to which scale correlates in theoretically
predicted ways with measures of different but related constructs. type of
validity in which a measure correlates positively in the theoretically predicted
way with measures of different but related constructs.
'or example, the tendency to purchase prestige brands should show a
high correlation with a person!s need for status and materialism and anegative correlation with price sensitivity
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Re&ia$i&it%
test = retests!&it ha&f
Sensiti,it%: a$i&it% to
dis"riminate amon# meanin#fu&di7eren"es in attitudes
Genera&isa$i&it%
Re&e,an"%Re&e,an"e H re&ia$i&it%
,a&idit%
Internationa& MR