Measurement, Scales & IndexesMessung, Skalen, Indizes

Quantitative Methoden der BWDr. Regina Dittrich

November 20, 2006

Karin Beck & Michał Lemański

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Content Overview

• Attitudes

• Measurement

- Accuracy of Measurement

- Criteria for Reliability

• Scaling

- Types of scales

- Issues in visualizing scales

- Guttman Scale

- Multiple-Item Scales - Likert Scale

• Indexes

- Big-Mac index

• Exam Questions

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Attitudes

AttitudeAction/

Behavior

Attitudes directly affect purchase decisions and these, in turn, directly affect attitudes.

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Three Components of Attitude

Affective Component

Cognitive Component

ActionComponent

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Components of Attitude

• Cognitive or knowledge

• Represents the information that a person has about an object

• Affective or liking

• The overall feeling of liking or disliking that a person has towards the object

• Intention

• Person’s expectations of future behavior towards the object

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Measurement/Messung I

Example: Water consumption in cubic metres to find out the portion of people

watching a certain series on TV

Measurement is the process of assigning numbers

or other symbols to certain characteristics

of the object of interest.

The number or symbol assigned

• should have one to one correspondence

• should be consistent over time

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Measurement/Messung II

• Standardized process of assigning numbers

to certain characteristics of objects

• Type of measurement depends on type of data!

How can you measure love or creativity?

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Empirisches und numerisches Relativ für eine Nominalskala Measurement/Messung III

A

B

C

D

E

F

0

1

=

- 0

- 1

Empirisches Relativ Numerisches Relativ Skallenniveau

Source: R. Dittrich & R. Hatzinger „Grundlagen und Probleme des Messens in der psychiatrischen Forschung“ PU Wien

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• Objectivity/Objektivität- Repetition of the procedure by another researcher should

produce the same results; weakest criteria; e.g. 2 teachers correcting one paper different grades

• Reliability/Reliabilität - Reliability is the consistency of a set of measurements or

measuring instrument. It does not imply validity. A reliable measure is measuring something consistently, but not necessarily what it is supposed to be measuring.

• Validity/Validität- A measure has validity if it measures what it is supposed to

measure; main objective: construction of many valid measuring instruments

Accuracy of Measurement I Gütekriterien

Valid but not

Reliable

Reliable &

Valid

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Accuracy of Measurement II Gütekriterien

• Sensitivity/Sensibilität- Extent to which ratings provided by a scale are able to

discriminate between the respondents who differ with respect to the construct being measured

• Relevancy/Relevanz- Relevance = reliability * validity

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• Equivalent form/Paralelltest-Methodetechnique to establish scale reliability by measuring and correlating the ensures of 2 equivalent scaling instruments; e.g. measurement of temperature with a digital or mercury thermometer

• Test-Retest/Test-Retest-Methode

technique of measuring a scale reliability by administering the same scale to the same respondents at 2 different types or to 2 different samples of respondents under similar conditions; e.g. Repeated Telephone Survey (panel longitudinal study) Problems: No learning process!

• Split-half test/Methode der Testhalbierung

technique used to evaluate the internal consistency of scales measurement that have multiple dimensions; e.g. Exam with 20 questions with the same degree of difficulty – split into 2 groups – results are being tested by correlation

Criteria for reliability

Scale reliability – … extent to which a scale can produce the same results in repeated trials

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Scaling is the process of creating a continuum on which

the objects are located according to the amount

of the measured characteristic they posses.

Scaling

Als Skalierung bezeichnen wir eine Messung auf der Basis eines Skalierungsmodels. Die Skalierung ist damit ein Spezialfall der Messung. Ein Skalierungsmodell unterstellt gewisse, teilweise empirisch prüfbare Annahmen über die Struktur der Beobachtungen.

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Scales - Differentiation

Nominal scale

Ordinal scale

Interval scale

Ratio scale

Metric scales

Non-metric scales

Information content

increases

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Scales used in questionnaire design I

Nominal scale/Nominalskala

• The only property is identity of a scale item and any comparisons of numbers is meaningless.

• E.g. Marital status of respondents

Ordinal scale/Ordinalskala

• Categories are ranked and arranged in order with regard to some common variable.

• E.g. Finishing order of a horse race.

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Nominal ScalesNominal Scales: Examples

Example 1:Example 1:

Please indicate your current marital status.Please indicate your current marital status.

_____ Married ____ Single ____ Single, never married ____Widowed_____ Married ____ Single ____ Single, never married ____Widowed

Example 2:Example 2:

Do you like or dislike chocolate ice cream?Do you like or dislike chocolate ice cream?

____ Like____ Like ____ Dislike____ Dislike

Example 3:Example 3:

Please check those information and HCP service areas in which you have had a face-Please check those information and HCP service areas in which you have had a face-to-face or telephone conversation with a representative of your main HCP in the past to-face or telephone conversation with a representative of your main HCP in the past six month. (Check as many as apply.)six month. (Check as many as apply.)

____ Appointments____ Appointments ____ Treatment at home____ Treatment at home ____ Referral to other HCP____ Referral to other HCP

____ Prescriptions____ Prescriptions ____ Medical test results____ Medical test results ____ Hospital stay____ Hospital stay

Some other service area(s); Please specify Some other service area(s); Please specify ________________________________________________________________________

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Ordinal ScalesOrdinal Scales: Examples

Which category best describes your knowledgeWhich category best describes your knowledge

about the assortment of services offered by your main HCP?about the assortment of services offered by your main HCP?

(Please check just one category.)(Please check just one category.)

____ Complete knowledge of services____ Complete knowledge of services

____ Good knowledge of services____ Good knowledge of services

____ Basic knowledge of services____ Basic knowledge of services

____ Little knowledge of services____ Little knowledge of services

____ No knowledge of services____ No knowledge of services

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Scales used in questionnaire design

Interval scale

• the numbers used to rank the objects also

represent equal increments of the attribute being measured.

• E.g. Time when to go to bed, finishing times in horse-race

Ratio scale

• It is an interval scale with a meaningful zero point. It is the only scale that permits comparisons of absolute magnitude.

• Eg: Weight, market share and dollars in saving account

Scales used in questionnaire design II

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Interval ScalesInterval Scales: Examples

Example 1:Example 1:

Approximately how many charges for overdrawn checks (NSF checks)Approximately how many charges for overdrawn checks (NSF checks)

has “your” bank imposed on you in the past year?has “your” bank imposed on you in the past year?

____ 0-3____ 0-3____ 4-7____ 4-7____ 8-11____ 8-11 ____ 12-15____ 12-15 ____ 16-19____ 16-19

Example 2:Example 2:

When do you usually go the bed? When do you usually go the bed?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 241 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Example 3:Example 3:

In which of the following categories does your current age fall?In which of the following categories does your current age fall?

____1 to 10____1 to 10 ____ 21 to 30____ 21 to 30 ____ 41 to 50____ 41 to 50 ____ 61-70____ 61-70

____11 to 20____11 to 20 ____ 31 to 40____ 31 to 40 ____ 51 to 60____ 51 to 60

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Ratio ScalesRatio Scales: Examples

Example 1:Example 1:

Please circle the number of children under 18 years of agePlease circle the number of children under 18 years of age

currently living in your household.currently living in your household.

00 11 22 33 44 55 66 77 (If more than 7, please specify: ____.)(If more than 7, please specify: ____.)

Example 2:Example 2:

In the past seven days, how many times did you go shopping at a retail In the past seven days, how many times did you go shopping at a retail shopping mall?shopping mall?

____ # of times____ # of times

Example 3:Example 3:

In whole years, what is your current age?In whole years, what is your current age?

____ # of years old____ # of years old

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Geometric and harmonic mean, coefficient of variation

Sales, incomes, units produced, costs, age

There is a meaningful zero

Certain scales with special instructions

Ratio

Mean, standard deviation, product moment correlations / t-tests, ANOVA, regression, factor analysis

Index numbers, temperature scales, attitude measures

Intervals between adjacent ranks are equal

Likert, Thurstone, Stapel

Interval

Percentile, median, rank-order correlation / Friedman ANOVA

Rankings (preference, class standing)

Objects are greater or smaller

Comparative, Rank order, Itemized Category, Paired Comparison

Ordinal or Rank Order

Percentages, mode / chi -square

Classification (by sex, geographic are, social class)

Objects are either identical or different

Dichotomous “yes” or “no” scales.

Nominal

Statistics / Statistical Tests

Typical Application

Rules for Assigning Number

Types of Attitude Scale

Type of Measurement Scale

Types of Scales and their properties

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Single - Item Scales

• Itemized-category Scales

… most widely used single-item scale. It gives respondents options to indicate his/her opinions about the object being measured.

• Rank-order Scales

… requires respondents to arrange objects in ascending or descending order with regard to some criterion. Used widely in international surveys.

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Itemized Category Scales

• Scales in which the respondent selects from

a limited number of categories

• What is your overall satisfaction with McDonalds Hamburgers?

Very satisfied Quite Satisfied Somewhat satisfied Not at all satisfied

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Pictorial Scales/Illustrierte Skalen

• Various categories of the scale are depicted pictorially

• Format must be comprehensible to respond and allow accurate response

Example:

• The taste of Honey Munch Cereal is:

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Issues in visualizing scales

• Due to cultural differences scales have to be adapted to different cultural environments

• Issues to be considered:

• Educational system

• Illiteracy rate

• Social habits

• Natural environment

• Etc………

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Cross-cultural Issues in Scale Development I

• Number of Scale Categories

• 2 to 15

• Strength of the Anchors

• colorful vs. very colorful vs.

extremely colorful

• Labeling of the Categories

• no labels vs. some labels vs. all

labels

• Balance of a Scale

• balanced vs. unbalancedSmiling Faces: US vs. Africa

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Cross-Cultural Issues in Scale Development II

Different Appearances of pictorial scales

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Guttman Scale/Guttman Skala

• … measures only a single trait

- (property called unidimensionality, a single dimension underlies responses to

the scale)

• Hypothetical, perfect Guttman scale consists of a unidimensional set of items that are ranked in order of difficulty from least extreme to most extreme position

- Example: person scoring "7" on a 10 item Guttman scale, will agree with items

1-7 and disagree with items 8,9,10

• Important property of Guttman's model is that a person's entire set of responses to all items can be predicted from their cumulative score because the model is deterministic

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Likert Scales: Require respondents to indicate

the degree of agreement or disagreement with

a number of statement related to the characteristics

of the object.

Semantic Differential Scales: They are used very widely in Market Research to reflect the set of beliefs or attitudes the respondent has about an object.

Multiple-Item Scales – e.g. Likert scale

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Likert Scale/Likert Skala

Statements

Definitely

Agree

Generally

Agree

Slightly

Agree

Slightly

Disagree

Generally

Disagree

Definitely

Disagree

I buy many things

with a credit card. ___ ___ ___ ___ ___ ___

I wish we had a lot

more money. ___ ___ ___ ___ ___ ___

My friends often

come to me for

advice. ___ ___ ___ ___ ___ ___

I am never

influenced by

advertisements. ___ ___ ___ ___ ___ ___

For each of the listed statements, please check the one response that bestexpresses the extent to which you agree or disagree with that statement.

Together, the 4 items constitute the scale

This is a single item

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Indexes/Indices

• An index (for example a price index or stock market index) is a benchmark of activity, performance or any evolution in general.

• An index is a number that represents a price or value of an aggregate of goods, services, wages, or other measurable quantity in comparison with a reference number for a previous period of time.

• Examples: Consumer price indexes (an inflation measurement) or a country GDP index (an economic growth measurement) can be used, among other things to adjust salaries, bonds interest rates, tax thresholds

• Simplest Index: IND = 1*X1 + 1*X2 + 1*X3

0 0 0

1 1 1

0 1 0

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Big-Mac Index

• Big Mac index - informal way of measuring the purchasing power parity (PPP) between two currencies.

- It is obtained by dividing the price of a Big Mac in one country (in its currency) by the price of a Big Mac in another country (in its currency). This value is then compared with the actual exchange rate; if it is lower, then the first currency is under-valued (according to PPP theory) compared with the second, and conversely, if it is higher, then the first currency is over-valued

-Price of a Big Mac is $2.50 in the United States and £2.00 in the United

Kingdom; thus, the PPP rate is 2.50/2.00 = 1.25. If, in fact, the US dollar

buys £0.55 (or £1 = $1.81), then the pound is over-valued (1.81 > 1.25)

with the respect to the dollar by 44.8% in comparison with the price of the

Big Mac in both countries.

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Big-Mac Scale of standard of living

ABM BSP HDIChicago 14 (1) 22.240 (3) 0,961 (5,5)Zurich 21 (2) 33.610 (1) 0,986 (1)Frankfurt 23 (3) 23.650 (2) 0,967 (3)Vienna 27 (4) 20.140 (4) 0,961 (5,5)Amsterdam 28 (5) 18.780 (5) 0,984 (2)Madrid 31 (6) 12.450 (6) 0,965 (4)Buenos Aires 66 (7) 2.790 (8) 0,910 (7)Mexico 90 (8) 3.030 (7) 0,876 (8)Bombay 92 (9) 330 (10) 0,439 (10)Nairobi 177 (10) 340 (9) 0,481 (9)

ABM … Working Time (Minutes) for 1 Hamburger

BSP … Gross National Product

HDI … Human Development Index

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Exam Questions

1. Diskutieren Sie die Maße für Reliabilität und führen Sie hierfür ein Beispiel an.

2. Welche Skalenniveaus kennen Sie und wie lassen sich diese definieren?

3. Bitte erklären Sie was man unter einem Index versteht und beschreiben Sie diesen anhand eines selbst gewählten Beispiels.