Measurement & Scaling

Chapter 8

Measurement (nominal, ordinal, interval, ratio)

Comparative vs Non-comparative Scaling

Measurement: definisi, apa yang di ukur ?

� Penentuan indeks, verifikasi terhadap tinggi, berat, ciri fisik lainnya adalah pengukuran.

� Seberapa bagus sebuah lagu, lukisan, � Seberapa bagus sebuah lagu, lukisan, kepribadian seseorang, merupakan pengukuran.

� Mengukur: menemukan batas-batas, dimensi-dimensi, kuantitas, atau kapasitas sesuatu, dgn membandingkan dgn sebuah standar .

Measurement : definisi, apa yang di ukur ?

� Pengukuran: pemberian angka atas kejadian, obyek, atau aktivitas empiris yg memenuhi kaidah-kaidah yg berlaku.

� Ada 3 proses pengukuran : � Ada 3 proses pengukuran : 1) Menseleksi kejadian-kejadian empiris yg dapat

diamati (observable)2) Mengembangkan serangkaian mapping rules:

pemberian angka atau simbol untuk mewakili aspek-aspek dari kejadian yg sedang diukur.

3) Menerapkan mapping rules pada setiap pengamatan kejadian itu

Pengukuran (measurement)

� Pengukuran: pemakaian satuan kuantitatif/ kualitatif pada objek (subjek) penelitian; ygmendeskripsikan jumlah atau tingkatproperti yang dimiliki objek tersebut.

� Satuan yang dipakai harus generally accepted.� Misal: berat badan� satuan yang diterima

umum adalah kg , bukan gram, walaupun sama-sama menyatakan berat.

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Jenis Data Berdasarkan

Skala Ukurnya

1. NOMINAL: membedakan obyek, misal jenis kelamin (1=pria, 2=wanita).

2. ORDINAL: membedakan obyek dan menyatakan urutan menurut besar kecil, misal pendidikan (1=SD, 2=SLTP, 3=SMU, 4=PT).pendidikan (1=SD, 2=SLTP, 3=SMU, 4=PT).

3. INTERVAL: membedakan obyek, menyatakan urutan menurut besar kecil, dan adanya interval yang sama, misal nilai ujian.

4. RATIO: membedakan obyek, menyatakan urutan menurut besar kecil, adanya interval yang sama, dan adanya NOL mutlak, misal berat suatu produk.

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Jenis Data

Sifat

Membedakan

Ada Urutan/

Tingkatan

Ada Interval

Adatitik nolmutlak

Jenis Data Berdasarkan Skala Ukur

Nominal √√√√

Ordinal √√√√ √√√√

Interval √√√√ √√√√ √√√√

Rasio √√√√ √√√√ √√√√ √√√√

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Data Nominal

� Contoh: gender, ID number, marital status, pekerjaan

� Hanya melakukan kategorisasi variabel yang diukur.� Satu objek penelitian hanya masuk pada satu

kategori.kategori.� Angka hanya label. Pemberian skor hanya sekedar

untuk membedakan (jadi dapat dibolak-balik)� Tidak memiliki jarak.� Tidak mengandung nilai yang menunjukkan

rangking/urutan.� Aplikasi statistik yang diperbolehkan hanya modus

dan distribusi frekuensi.7

Data Nominal

Jenis Pekerjaan

Pengukuran

(pemberian skor) yang

mungkin

Contoh: Pengukuran “Pekerjaan Responden”

mungkin

Pegawai

Wirausaha

Pelajar/Mahasiswa

1

2

3

3

2

1

2

1

3

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Data Ordinal

� Melakukan kategorisasi variabel� Kategori yang ada dapat diurutkan (order)� Berlaku formula: bila a > b, b > c, maka a > c.� Hanya ada urutan, tapi jarak (interval) antar

kategori tidak sama. kategori tidak sama. � Misal: “sangat puas” lebih baik dibandingkan

“puas”, dan “tidak puas” juga lebih baik dibandingkan “sangat tidak puas”; namun jarak “sangat puas” dengan “puas” ≠ jarak antara “tidak puas” dengan “sangat tidak puas”.

� Aplikasi statistik yang diperbolehkan (berlaku) modus, distribusi frekwensi, dan median.

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Data Ordinal -- contoh

Below are the attributes used by many customers to select a restaurant. Give ranking for each attribute from 1 for the attribute you consider as the most important, to 7 for the attributes you consider as the least important, when you select a restaurant.�

least important, when you select a restaurant.� Price ………..� Service speed ………..� Location ………..� Consistency of food quality ………..� Food variation ………..� Staff friendliness ………..� Portion size ………..

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Data Ordinal -- contoh

Tingkat PendidikanPengukuran (skor) yang

mungkin

Pengukuran “Tingkat Pendidikan Responden”

Tingkat Pendidikan mungkin

SD dan sederajatSMP dan sederajatSMA dan sederajat

S1

4321

1234

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Data Interval

� Memiliki sifat seperti data skala nominal & ordinal. Jarak satu kategori dengan kategori lainnya jelas.

� Misal IPK mhsw A=4 dan mhsw B=2, maka jarak � Misal IPK mhsw A=4 dan mhsw B=2, maka jarak IPK kedua mhs = 2.

� Namun data interval belum bisa dibandingkan secara mutlak (bukan berarti kepintaran A 2x B)

� Aplikasi statistik yang diperbolehkan modus, frekwensi, median, serta mean dan standar deviasi.

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Data Interval -- contoh

From the range 1 to 6 below, give rating on the latest fast-food restaurant you visited, where 1 for extremely unsatisfying to 6 for extremely satisfying :

Extremely Extremelyunsatisfying satisfyingunsatisfying satisfying

• Price 1 2 3 4 5 6• Staff friendliness 1 2 3 4 5 6• Variation 1 2 3 4 5 6• Service speed 1 2 3 4 5 6• Food quality 1 2 3 4 5 6• Portion size 1 2 3 4 5 6

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Data Rasio

� Example: height, weight, length, age, money, etc.

� Memiliki sifat seperti yg terdapat dalam data nominal, ordinal dan intervalnominal, ordinal dan interval

� Plus…data dapat dibandingkan secara absolut;Misal: uang A $25, B $75, maka dapat langsung dibandingkan bahwa uang A adalah sepertiga dari uang B.

• Plus…data rasio, angka NOL-nya mutlak (punya arti)

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PerbandinganPerbandingan skalaskala pengukuranpengukuran utamautama

Scale BasicCharacteristics

CommonExamples

MarketingExamples

Permissible StatisticsDescriptive Inferential

Nominal Numbers identify &classify objects

Social Securitynos., numberingof footballplayers

Brand nos.,store types

Percentages,mode

Chi-square,binomial test

Ordinal Nos. indicate therelative positions ofobjects but not the

Qualityrankings,rankings of

Preferencerankings,market

Percentile,median

Rank-ordercorrelation,Friedmanobjects but not the

magnitude ofdifferences betweenthem

rankings ofteams in atournament

marketposition,social class

FriedmanANOVA

Interval Differencesbetween objects canbe compared, zeropoint is arbitrary

Temperature(Fahrenheit,Celsius)

Attitudes,opinions,index .

Range, mean,standarddeviation

Product-momentcorrelation, ttests, regression

Ratio Zero point is fixed,ratios of scalevalues can becompared

Length, weight Age, sales,income, costs

Geometricmean,harmonicmean

Coefficient ofvariation

Scaling

� Prosedur pemberian bilangan (atau simbol-simbol lain) pada suatu objek agar memberi-kan pengetahuan tentang ciri obyek yang diukur/ditanyakan. diukur/ditanyakan.

� Secara berurut angka/bilangan diberikan untuk menunjukkan sesuatu pada objek.

Scaling

� Contoh1: Sikap terhadap suatu universitas dapat diukur pada berbagai skala untuk menangkap indikator dari suatu variabel atau dimensi mengenai awareness, feeling, minat.

� Contoh2: untuk mengukur temperatur udara, ditunjukkan oleh variasi dari ekspansi/ kontraksi merkuri yang ada pada tabung merkuri.

Memilih skala pengukuran

� Memilih dan mengembangkan skala pengukuran perlu mempertimbangkan berbagai faktor yang akan berpengaruh pada reliabilitas, validitas, dan kepraktisan sebuah skala.

� Faktor-faktor itu adalah :• Research Objective• Research Objective• Response types• Data Properties• Number of dimensions• Balanced or unbalanced• Forced or unforced choices• Number of scale points• Rater errors

Skala Pengukuran

Secara garis besar, skala pengukuran dibedakan jadi 2: 1. Comparative scaling . Pengukuran terhadap satu objek dilakukan dengan cara membanding-satu objek dilakukan dengan cara membanding-kan langsung objek ybs dengan objek lainnya. 2. Non-comparative scaling . Satu objek diukur secara independen/bebas, tidak dibandingkan dengan objek yang lainnya.

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A Classification of Scaling Techniques

Scaling Techniques

Non-comparative

ScalesComparative

Scales

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Paired

Comparison

LikertSemantic

DifferentialStapel

Paired

Comparison

Rank

Order

Constant

Sum

Q-shortContinuous

Rating ScalesItemized

Rating Scales

COMPARATIVE SCALING

1. Paired Comparison2. Rank Order Comparison3. Constant Sum3. Constant Sum4. Q-Sort

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1 Paired Comparison Scaling

� A respondent is presented with two objects

and asked to select one according to some

criterion. criterion.

� The data obtained are ordinal in nature.

� Paired comparison scaling is the most widely

used comparative scaling technique.

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1 Paired Comparison – Contoh…

The most common method of taste testing is paired comparison. The consumer is asked to sample two different products and select the one with the most appealing taste.

The test is done in private and a minimum of 1,000 responses is considered an adequate sample. A blind taste test for a soft drink, where imagery, self-perception and brand reputation are very important factors in the consumer’s purchasing decision,

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very important factors in the consumer’s purchasing decision, may not be a good indicator of performance in the marketplace. The introduction of New Coke illustrates this point. New Coke was heavily favored in blind paired comparison taste tests, but its introduction was less than successful, because image plays a major role in the purchase of Coke.

A paired comparison taste test

2. Rank Order Scaling

� Respondents are presented with several objects simultaneously and asked to order or rank them according to some criterion.

� It is possible that the respondent may dislike the brand ranked 1 in an absolute sense.

� It is possible that the respondent may dislike the brand ranked 1 in an absolute sense.

� Furthermore, rank order scaling also results in ordinal data.

� Faster & easier than paired comparison scaling.

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Brand Rank Order

1. Maxam _________

2. Colgate _________

3. Pepsodent _________

Preference for Toothpaste Brands

Using Rank Order Scaling

Form

3. Pepsodent _________

4. Close-Up _________

5. Ciptadent _________

6. Sensodyne _________

7. Ritadent _________

8. Formula _________

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3. Constant Sum Scaling

� Responden diminta mengalokasikan sejumlah angka (misal 100) ke dalam beberapa atribut untuk merefleksikan tingkat kepentingan atribut tersebut.

� Total tingkat kepentingan dari semua atribut harus = sejumlah angka yang ditetapkan (sesuai contoh = 100).

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3. Constant Sum Scaling

Example: Mohon bagi angka 100 ke dalam beberapa hal di bawah ini yang menggambar-kan tingkat kepentingannya, ketika Anda memutuskan memilih sebuah bank:memutuskan memilih sebuah bank:

Fasilitas/gedung --------Kehandalan --------Responsiveness dari staf --------Kemampuan staf --------Keramahtamahan staf --------+TOTAL 100

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4. Q-Sort

� Responden diminta untuk memilah berbagai hal (objek) ke dalam beberapa kelompok, setelah itu beberapa kelompok teratas diminta untuk diurutkan.

� Example: Dengan menggunakan “drop card”, mohon ambil 3 yang terpenting, kemudian dari 3 tersebut, tolong diurutkan.

� Exercise: List consideration attributes in purchasing a cellular phone

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NON-COMPARATIVE SCALING

1. Continuous Scaling 2. Itemize Scaling:

2.1. Likert Scale 2.1. Likert Scale 2.2. Semantic Differential Scale (skala perbedaan semantik/bunyi)2.3. Stapel Scale

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1. Continuous Rating Scale

Responden menilai sebuah objek dengan cara menempat-kan penilaian mereka pada range jawaban yang telah disediakan

Contoh: How would you rate Matahari as a department store?Contoh: How would you rate Matahari as a department store?Version 1Probably the worst - - - - - - -I - - -.- - - - - - - - - - - - - - - - - - - Probably the best

Version 2Probably the worst - - - - - - -I - -.- - - - - - - - - - - - - - - - - -- - Probably the best0 10 20 30 40 50 60 70 80 90 100

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2. 2. Itemized Rating ScalesItemized Rating Scales

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 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 1. The Likert scales2. Semantic differential scales3. Stapel scales

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The Likert Scale

� An extremely popular means for measuring attitudes. Respondents indicate their own attitudes by checking how strongly they agree or disagree with statements. agree or disagree with statements.

� Response alternatives: “strongly agree”, “agree”, “uncertain”, “disagree”, and “strongly disagree”.

� Can be 1 to 5, 1 to 7, or 1 to 9 scale.

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Examples of Likert Scale

The Likert scale requires the respondents to indicate a degree of Agreement or disagreement with each of a series of statements about the stimulus objects.

Strongly Disagree Neutral Agree Strongly disagree agree

1. Hero sells high quality goods 1 2 3 4 5

2. Hero has poor in-store service 1 2 3 4 5

3. I like to shop at Hero. 1 2 3 4 5

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Semantic Differential

� Item jawaban yang tersedia adalah berbentuk bipolar, yaitu 2 kutub dari negatif sampai positif.Item jawaban merupakan kata sifat � Item jawaban merupakan kata sifat (adjectives).

� Item jawaban dapat diberi skor 7, 6, 5, 4, 3, 2, 1, atau +3, +2, +1, 0, -1, -2, -3.

� Item jawaban disesuaikan dengan bunyi pertanyaan (semantik)-nya.

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Examples of Semantic

Differential

HERO Supermarket:Convenient --:--:--:--:-X-:--:-- : InconvenientCheap --:--:--:--:--:-X-:-- : ExpensiveModern --:--:--:--:--:--:-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.

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A Semantic Differential for Measuring

Self- Concepts, Person Concepts, and

Product Concepts1) Rugged :---:---:---:---:---:---:---: Delicate

2) Excitable :---:---:---:---:---:---:---: Calm

3) Uncomfortable :---:---:---:---:---:---:---: Comfortable

4) Dominating :---:---:---:---:---:---:---: Submissive

5) Thrifty :---:---:---:---:---:---:---: Indulgent

6) Pleasant :---:---:---:---:---:---:---: Unpleasant

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6) Pleasant :---:---:---:---:---:---:---: Unpleasant

7) Contemporary :---:---:---:---:---:---:---: Obsolete

8) Organized :---:---:---:---:---:---:---: Unorganized

9) Rational :---:---:---:---:---:---:---: Emotional

10) Youthful :---:---:---:---:---:---:---: Mature

11) Formal :---:---:---:---:---:---:---: Informal

12) Orthodox :---:---:---:---:---:---:---: Liberal

13) Complex :---:---:---:---:---:---:---: Simple

14) Colorless :---:---:---:---:---:---:---: Colorful

15) Modest :---:---:---:---:---:---:---: Vain

Stapel

� Modern versions of the Stapel scale place a single adjective as a substitute for the semantic substitute for the semantic differential when it is difficult to create pairs of bipolar adjectives.

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Stapel Scale

A unipolar rating scale with ten categories numbered from -5 to +5, without neutral point (zero). This scale

is usually presented vertically. HERO SUPERMARKET+5 +5+4 +4

Responden diminta memberikan skor persetujuan mereka+4 +4

+3 +3+2 +2+1 +1

HIGH QUALITY POOR SERVICE-1 -1-2 -2-3 -3-4 -4-5 -5

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skor persetujuan merekaatas hal yang ditanyakan.

Bila setuju, pilih kutub (+) dan tentukan level “setuju”-nya,

demikian sebaliknya.

Jenis-jenis rating scale

� Simple category rating scale : data nominal� Multiple-choice, Single-Response Scale : data nominal� Multiple-choice, Multiple-Response Scale : data nominal� Likert Scale, Summated Rating : data interval

Semantic differential scale : data interval� Semantic differential scale : data interval� Numerical scale : data ordinal atau data interval� Multiple Rating List Scale : data interval� Constant-sum scale : data ratio� Staple scale : data ordinal atau data interval� Graphic Rating Scale : data ordinal, interval atau ratio

Skala Rating dari sampelSkala Rating dari sampelSkala Rating dari sampelSkala Rating dari sampel

� Simple Category Scale (dichotomous) : data nominal

� Multiple-Choice, Single-Response Scale : data nominal

� Multiple -choice, Multiple -Response Scale� Multiple -choice, Multiple -Response Scale(checklist) ; data nominal

� Likert Scale, Summated Rating Scale : data interval

� Semantic Differential Scale : data interval� Numerical Scale : data ordinal or interval

Simple Category Scale (dichotomous) : data nominal� “I plan to purchace a MindWriter laptop in the next 12 months.”

□ Yes□ No

Multiple-Choice, Single-Response Scale : data nominal� “ What newspaper do you read most often for financial news ? “

□ East City Gazette□ West City Tribune□ Regional Newspaper□ National Newspaper□ National Newspaper□ Other ( specify : ................)

Multiple-choice, Multiple-Response Scale (checklist) ; data nominal:� “Check any of the source you consulted when designing your new home : “

□ Online planning services□ Magazines□ Independent contractor/builder□ Developer’s models/plans□ Designer□ Architect□ Other ( specify: ..........)

� Likert Scale, Summated Rating Scale : data interval� “The internet is superior to traditional libraries for comprehensive

searches”Strongly Agree Neither agree Disagree StronglyAgree Nor disagree disagree(5) (4) (3) (2) (1)

� Semantic Differential Scale : data interval� “Lands’ End Catalog”

Fast ----:----:----:----:----:---- SlowHigh Quality ----:----:----:----:----:---- Low QualityHigh Quality ----:----:----:----:----:---- Low Quality

� Numerical Scale : data ordinal or intervalExtremely ExtremelyFavorable 5 4 3 2 1 UnvaforableEmployee’s cooperation in teams ----Employee’s knowledge of task ----Employee’s planning effectiveness ----

� Multiple Rating List Scale : data interval“Please indicate how important or unimportant each service characteristic is ”

Important Unimportant- Fast reliable repair 7 6 5 4 3 2 1- Service at my location 7 6 5 4 3 2 1- Maintenance by manufacturer 7 6 5 4 3 2 1- Knowledgeable Technicians 7 6 5 4 3 2 1- Notification of upgrades 7 6 5 4 3 2 1- Service contract after warranty 7 6 5 4 3 2 1- Service contract after warranty 7 6 5 4 3 2 1

� Constant-sum scale : data ratio“Taking all the supplier characteristics we’ve just discussed and now considering cost, what is their relative important to you (dividing 100 units between)”Being one of the lowest cost suppliers --------All other aspects of supplier performance --------

Sum 100

� Staple scale : data ordinal atau data interval(Company Name)

+5 +5 +5+4 +4 +4+3 +3 +3+2 +2 +2+1 +1 +1+1 +1 +1Technology Exciting World ClassLeader Products Reputation-1 -1 -1-2 -2 -2-3 -3 -3-4 -4 -4-5 -5 -5

� Graphic Rating Scale : data ordinal, interval atau ratio : data ordinal or interval

“How likely are you to recommend CompleteCare to others ? (place an x at the position along the line that best reflects your judgment):line that best reflects your judgment):

Very Likely I----------------------------I Very Unlikely☺ I--------------------------- I �

(alternative with graphic)

Skala Rating dari sampel

� Multiple Rating List Scale : data interval� Constant-Sum Scale : data ratio� Stapel Scale : data ordinal or interval� Graphic Rating Scale : data ordinal or

interval or ratiox

Never I--------------------------------I Always

Lihat : Donald R Cooper hal 345 - 346

Skala Rating dari sampel

� Multiple Rating List Scale : data interval

2 4 1 2 Participant score

Lihat : Donald R Cooper hal 345 - 346

x x x x 4

- x x x 3

- - x x 2

- - - x 1

- - - - 0

Skala Rating dari sampel

� Constant-Sum Scale : data ratioYou have 100 points to distribute among the following characteristics of the Dallas Steakhouse. Indicate the relative importance of each attribute :

------- Food Quality------- Atmosphere------- Service------- Price100 TOTAL

Lihat : Donald R Cooper hal 345 - 346

Skala Ranking dari sampel

� Paired – Comparison Scale : data ordinal

� Forced Ranking Scale : data ordinal� Forced Ranking Scale : data ordinal

� Comparative Scale : data ordinal

Lihat : Donald R Cooper hal 347 - 348