Measurement & Scaling

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; yg mendeskripsikan jumlah atau tingkat

properti 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.

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.

Jenis Data Sifat Membeda kan Ada Urutan/ Tingkatan Ada Interval Ada titik nol mutlak

Jenis Data Berdasarkan Skala Ukur

Nominal _√√√√

Ordinal _{√√√√ √√√√}

Interval _{√√√√ √√√√ √√√√}

Rasio _{√√√√ √√√√ √√√√ √√√√}

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.

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 8

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.

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 ………..}

Data Ordinal -- contoh

Tingkat Pendidikan

Pengukuran (skor) yang mungkin

Pengukuran “Tingkat Pendidikan Responden”

Tingkat Pendidikan mungkin

SD dan sederajat SMP dan sederajat SMA dan sederajat

S1 4 3 2 1 1 2 3 4 11

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.

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 Extremely unsatisfying satisfying unsatisfying 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 13

Data Rasio

Example: height, weight, length, age, money,

etc.

Memiliki sifat seperti yg terdapat dalam data

nominal, ordinal dan interval nominal, 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)

Perbandingan

Perbandingan skala

skala pengukuran

pengukuran utama

utama

Scale Basic Characteristics Common Examples Marketing Examples Permissible Statistics Descriptive Inferential

Nominal Numbers identify & classify objects Social Security nos., numbering of football players Brand nos., store types Percentages, mode Chi-square, binomial test

Ordinal Nos. indicate the relative positions of objects but not the

Quality rankings, rankings of Preference rankings, market Percentile, median Rank-order correlation, Friedman objects but not the

magnitude of differences between them rankings of teams in a tournament market position, social class Friedman ANOVA Interval Differences

between objects can be compared, zero point is arbitrary Temperature (Fahrenheit, Celsius) Attitudes, opinions, index . Range, mean, standard deviation Product-moment correlation, t tests, regression

Ratio Zero point is fixed, ratios of scale values can be compared

Length, weight Age, sales, income, costs Geometric mean, harmonic mean Coefficient of variation

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

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

Skala Pengukuran

Secara garis besar, skala pengukuran dibedakan jadi 2:

1. Comparative scaling. Pengukuran terhadap satu objek dilakukan dengan cara 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.

A Classification of Scaling Techniques

Scaling Techniques Non-comparative Scales Comparative Scales 20 Paired Comparison Likert Semantic Differential Stapel Paired Comparison Rank Order Constant Sum Q-short Continuous Rating Scales Itemized Rating Scales

COMPARATIVE SCALING

1. Paired Comparison

2. Rank Order Comparison

3. Constant Sum

3. Constant Sum

4. Q-Sort

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.

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,

23

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.

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.

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 _________ 25

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).

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

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

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

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 1

Probably the worst - - - -I - - -.- - - Probably the best

Version 2

Probably the worst - - - -I - -.- - - -- - Probably the best 0 10 20 30 40 50 60 70 80 90 100

2.

2. Itemized Rating Scales

Itemized 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 scales

2. Semantic differential scales 3. Stapel scales

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.

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

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.

Examples of Semantic

Differential

HERO Supermarket: Convenient --:--:--:--:-X-:--:-- : Inconvenient Cheap --:--:--:--:--:-X-:-- : Expensive 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.

A Semantic Differential for Measuring Self- Concepts, Person Concepts, and

Product Concepts 1) Rugged :---:---:---:---:---:---:---: Delicate 2) Excitable :---:---:---:---:---:---:---: Calm 3) Uncomfortable :---:---:---:---:---:---:---: Comfortable 4) Dominating :---:---:---:---:---:---:---: Submissive 5) Thrifty :---:---:---:---:---:---:---: Indulgent 6) Pleasant :---:---:---:---:---:---:---: Unpleasant 36 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.

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 38

skor persetujuan mereka atas 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

Skala Rating dari sampel

Skala Rating dari sampel

Skala Rating dari sampel

Skala 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 Strongly Agree Nor disagree disagree

(5) (4) (3) (2) (1)

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

Fast ----:----:----:----:----:---- Slow

High Quality ----:----:----:----:----:---- Low Quality High Quality ----:----:----:----:----:---- Low Quality

Numerical Scale : data ordinal or interval

Extremely Extremely

Favorable 5 4 3 2 1 Unvaforable

Employee’s cooperation in teams Employee’s knowledge of task

----
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

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 +1

Technology Exciting World Class Leader Products Reputation

-1 -1 -1

-2 -2 -2

-3 -3 -3

-4 -4 -4

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} 

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 ratio

x

Never I---I Always

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

Skala Rating dari sampel

Constant-Sum Scale: data ratio

You have 100 points to distribute among the following characteristics of the Dallas Steakhouse. Indicate the relative importance of each attribute :

--- Food Quality --- Atmosphere --- Service

--- Price 100 TOTAL

Skala Ranking dari sampel

Paired – Comparison Scale : data ordinal

Forced Ranking Scale : data ordinal

Forced Ranking Scale : data ordinal

Comparative Scale : data ordinal