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# Measurement and scaling

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### Measurement and scaling

1. 1. Scaling involves creating a continuum upon which measuredobjects are located. Attitude Scale 1 = Extremely Unfavorable 2 3 . . .100 = Extremely FavorableMeasurement ! Actual assignment of a NumbersScaling ! The process of placing the respondents on continuum
2. 2. PrimaryScalesofMeasurement Nominal! !Numbers!! Finish ! ! !Assigned !! 7 8 3Ordinal !Rank!Order! ! ! !of!Winners! Finish!! Third Second First place place placeInterval !Performance! ! ! !Rating!on!a!!!!!! 8.2 9.1 9.6 ! ! !0!to!10!Scale!!Ratio ! !Time!to!Finish ! ! 15.2 14.1 13.4 ! ! !in!Seconds!!!!!!!!!!!!!!
3. 3. PrimaryScalesofMeasurementNominalScale!"  Nominalmeasuresoﬀernamesorlabelsforcertain characteristics."  serve!as!Tags!for!identifying!objects.!!!"  Do!not!reﬂect!the!amount!of!the!characteristic!"  Counting!is!the!only!permissible!operation!"  Limited!number!of!statistics!based!on!frequency! counts o  Ex:!diﬀerent!types!of!blood:!A,!AB,!O,!B! o  1=A,!2=O,!3=B,!4=AB! o  !Male!=!0!and!Female!=!1,!‘sex’!is!measured!on!a! nominal!scale!
4. 4. PrimaryScalesofMeasurement OrdinalScale!"  Recordinformationabouttherankorderofscores."  Ordinal!measurements!describe!order!"  !but!not!relative!size!or!degree!of!diﬀerence!between!the!items! measured.!!"  In!this!scale!type,!the!numbers!assigned!to!objects!or!events! represent!the!rank!order!(1st,2nd!,3rd!,etc)!of!the!entities!assessed.!"  ordinal!variables!do!not!tell!us!anything!about!the!absolute! magnitude!of!the!diﬀerence!between!1st!and!2nd!or!between!2nd! and!3rd.!That!is,!we!know!1st!was!before!2nd,!and!2nd!was!before! 3rd,!but!we!do!not!know!how!close!3rd!was!to!2nd!or!how!close! 2nd!was!to!1st.!The!limits!of!ordinal!data!are!most!apparent!when! one!looks!at!the!distance!between!the!third!and!the!fourth!place! ﬁnishers.!!o  Ex:!A!horse!race,!which!says!only!which!horses!arrived!ﬁrst,! second,!or!third!but!include!no!information!about!race!times.!!
5. 5. PrimaryScalesofMeasurementIntervalScale!"  Interval scales tell us about the order of data points, and the size of the intervals in between data points."  Quantitative!attributes!are!all!measurable!on!interval! scales"  The location of the zero point is not fixed.!And!negative! values!can!be!used.o  An!example!of!an!Interval!scale!is!the!Farenheit!scale!of! temperature.!In!the!Farenheit!temperature!scale,!the! distance!between!20!degrees!and!40!degrees!is!the! same!as!the!distance!between!75!degrees!and!95! degrees.
6. 6. PrimaryScalesofMeasurementRatioScale!"  A ratio scale is an interval scale with a true zero point."  Possesses all the properties of the nominal, ordinal, and interval scales"  Meaningful to compute ratios of scale values"  All statistical techniques can be applied"  Most measurement in the physical sciences and engineering is done on ratio scales such as Mass, length, time, angle, energy."  The Klvine temperature!scale!has!a!non`arbitrary!zero!point! of!absolute!Zero,!which!is!denoted!0K!and!is!equal!to!`273.15! degrees!Celsius.!
7. 7. Eachtypeofquestioncorrespondstoalevelofmeasurement.Theselevelsofmeasurementwill determinewhattypeofdataanalysisweuse:"  All!qualitative!research!is!nominal.!"  All!categorical!data!in!which!there!is!no!diﬀerence!in! value!among!the!categories!is!nominal.!"  All!categorical!data!in!which!there!is!an!implied! ranking!(for!example,!high`medium`low)!is!ordinal.!!"  Any!question!that!asks!respondents!to!rank!order! responses!is!also!ordinal.!"  Any!question!in!which!the!response!is!a!number!or! can!be!interpreted!as!a!number!with!equal!values! among!the!data!points!is!ratio.!
8. 8. Classiﬁcation Noncomparative Rating Scales Continuous ItemizedRating Scales Rating Scales Semantic Stapel Likert Differential
9. 9. ContinuousRatingScale Respondents rate the objects by placing a mark at the appropriate position on a line that runs from one extreme of the criterion variable to the other. The form of the continuous scale may vary considerably. How would you rate Sears as a department store?
10. 10. ItemizedRatingScales "  The!respondents!are!provided!with!a!scale!that!has!a! number!or!brief!description!associated!with!each! category.!!! "  The!categories!are!ordered!in!terms!of!scale!position,! and!the!respondents!are!required!to!select!the!speciﬁed! category!that!best!describes!the!object!being!rated.!!! "  The!commonly!used!itemized!rating!scales!are!the!Likert,! semantic!diﬀerential,!and!Stapel!scales.! Usingthe5Tpointscaleprovided,pleaseAreyousatisﬁedwithour indicatehowsatisfyyouarewithourservice? service
11. 11. ItemizedRatingScales:(1)LikertScale/SummatedTRatingsScale
12. 12. ItemizedRatingScales: (2)SemanticDiﬀerentialScaleThe!semanticdiﬀerential!is!a!seven`point!rating!scale!with!end!points! associated!with!bipolar!labels!that!have!semantic!meaning.!!! ! Marks!&!Spencer!is:! Powerful! !``:``:``:``:`X`:``:``:!Weak! Unreliable!``:``:``:``:``:`X`:``:!Reliable! Modern! !``:``:``:``:``:``:`X`:!Old`fashioned!!"  The!negative!adjective!or!phrase!sometimes!appears!at!the!left!side!of! the!scale!and!sometimes!at!the!right.!!!"  This!controls!the!tendency!of!some!respondents,!particularly!those! with!very!positive!or!very!negative!attitudes,!to!mark!the!right`!or!left` hand!sides!without!reading!the!labels.!!!"  Individual!items!on!a!semantic!diﬀerential!scale!may!be!scored!on!either! a!`3!to!+3!or!a!1!to!7!scale.!!
13. 13. ItemizedRatingScales:(3)StapelScaleThe Stapel scale is a unipolar rating scale with ten categoriesnumbered from -5 to +5, without a neutral point (zero). Thisscale is usually presented vertically. +5 +5 +5 +4 +4 +4 +3 +3 +3 +2 +2X +2 +1 +1 +1HIGH QUALIT POOR SERVICE WIDE VARIETY -1 -1 -1 -2 -2 -2 -3 -3 -3 -4X -4 -4 -5 -5 -5
14. 14. Basic Noncomparative Scales BasicScale Examples Advantages Disadvantages CharacteristicsContinuou Place a mark on a co Reaction to TV Easy to Scoring can bes Rating ntinuous line commercials construct cumbersomeScale unless computerizedItemizedRating ScalesLikert Degree of agreement Measurement Easy to More timeScale on a 1 (strongly disa of attitudes construct, consuming gree) to 5 (strongly administer, agree) scale and understa ndSemantic Seven-point scale Brand, product Versatile Difficult toDifferenti with bipolar labels , and company construct bipolaral images adjectivesStapel Unipolar ten-point Measurement Easy to const Confusing andScale scale, -5 to +5, of attitudes ruct and admi difficult to apply without a neutral and images nister over point (zero) telephone
15. 15. Balanced and Unbalanced Scales Balanced Scale Unbalanced ScaleSurfing the Internet is Surfing the Internet is____ Extremely Good ____ Extremely Good____ Very Good ____ Very Good____ Good ____ Good____ Bad ____ Somewhat Good____ Very Bad ____ Bad____ Extremely Bad ____ Very Bad
16. 16. Rating Scale ConfigurationsA variety of scale configurations may be employed to measureSome examples include: the comfort of Nike shoesNike shoes are:1) Place an “X” on one of the blank spaces… Very VeryUncomfortable Comfortable2) Circle the number… Very 1 2 3 4 5 6 7 VeryUncomfortable Comfortable3) Place an “X” on one of the blank spaces… Very Uncomfortable Uncomfortable Neither Uncomfortable nor Comfortable Comfortable Very Comfortable
17. 17. SomeUniqueRatingScaleConﬁgurationsThermometer ScaleInstructions: Please indicate how much you like McDonald’s hamburgersby coloring in the thermometer. Start at the bottom and color up to thetemperature level that best indicates how strong your preference is. Like veryForm: much T 100 The image cannot be displayed. Your 75 computer may not have enough memory T to open the image, or the image may have been corrupted. Restart your computer, and then open the ﬁle again. If the red x 50 still appears, you may have to delete the image and then insert it again. T 25 Dislike very 0 muchSmiling Face ScaleInstructions: Please point to the face that shows how much you like theBarbie Doll. If you do not like the Barbie Doll at all, you would point to Face1. If you liked it very much, you would point to Face 5.Form: 1 2 3 4 5
18. 18. CriteriaforGoodMeasurement (1)# Reliability!–!Reliability!is!the!degree!to!which! measurements!are!devoid!of!error!and!therefore!in!the! position!to!yield!consistent!results,!also!over!repeated! attempts!over!time!(ordinal!measures!always!yield!the! same!order,!interval!measurements!always!yield!the!same! order!and!same!distance!between!the!measured!items)!# Validity!–!Validity!is!the!ability!of!a!scale!or!measuring! instrument!to!measure!what!it!is!intended!to!measure! (e.g.!is!absenteeism!from!work!a!valid!measure!of!job! satisfaction!or!are!there!other!inﬂuences!like!a!ﬂu! epidemic!which!is!keeping!employees!from!work)!
19. 19. CriteriaforGoodMeasurement (2)# Sensitivity!–!Sensitivity!is!the!ability!of!a!measurement! instrument!to!accurately!measure!variability!in!stimuli!or! responses!(e.g.!on!a!scale,!the!choices!very!strongly! agree,!strongly!agree,!agree,!don t!agree!oﬀer!more! choices!than!a!scale!with!just!two!choices!`!agree!and! don t!agree!–!and!is!thus!more!sensitive)!!!
20. 20. Scale Evaluation Scale Evaluation Validity Reliability ContentTest-Retest Internal Criterion Consistency Alternative Forms Construct Convergent Validity Discriminant Validity Nomological Validity