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Measurement, Scales & Indexes Messung, Skalen, Indizes Quantitative Methoden der BW Dr. Regina Dittrich Measurement, Scales & Indexes Messung, Skalen, Indizes Quantitative Methoden der BW Dr. Regina Dittrich November 20, 2006 Karin Beck & Michał Lemański

Content Overview • Attitudes • Measurement - Accuracy of Measurement - Criteria for Reliability 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 2 • Exam Questions

Attitudes directly affect purchase decisions and these, in turn, directly affect attitudes. Attitude 3 Attitudes directly affect purchase decisions and these, in turn, directly affect attitudes. Attitude 3 Action/ Behavior

Three Components of Attitude Cognitive Component 4 Affective Component Action Component Three Components of Attitude Cognitive Component 4 Affective Component Action Component

Components of Attitude • Cognitive or knowledge • Represents the information that a person 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 5

Measurement/Messung I Measurement is the process of assigning numbers or other symbols to certain Measurement/Messung I 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 Example: Water consumption in cubic metres to find out the portion of people 6 watching a certain series on TV

Measurement/Messung II • Standardized process of assigning numbers to certain characteristics of objects • 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? 7

Empirisches und numerisches Relativ für eine Nominalskala Measurement/Messung III Empirisches Relativ Numerisches Relativ Skallenniveau Empirisches und numerisches Relativ für eine Nominalskala Measurement/Messung III Empirisches Relativ Numerisches Relativ Skallenniveau Source: R. Dittrich & R. Hatzinger „Grundlagen und Probleme des Messens in der psychiatrischen Forschung“ PU Wien 8

Accuracy of Measurement I Gütekriterien • Objectivity/Objektivität - Repetition of the procedure by another Accuracy of Measurement I Gütekriterien • 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 Valid but not Reliable 9 Reliable & Valid

Accuracy of Measurement II Gütekriterien • Sensitivity/Sensibilität - Extent to which ratings provided by 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 10

Criteria for reliability Scale reliability – … extent to which a scale can produce Criteria for reliability Scale reliability – … extent to which a scale can produce the same results in repeated trials • Equivalent form/Paralelltest-Methode technique 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 – 11 results are being tested by correlation

Scaling is the process of creating a continuum on which the objects are located Scaling is the process of creating a continuum on which the objects are located according to the amount of the measured characteristic they posses. 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. 12

Scales - Differentiation Nominal scale Non-metric scales Information content increases Ordinal scale Interval scale Scales - Differentiation Nominal scale Non-metric scales Information content increases Ordinal scale Interval scale Metric scales Ratio scale 13

Scales used in questionnaire design I Nominal scale/Nominalskala • The only property is identity 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. 14

Nominal Scales: Examples Scales Example 1: Please indicate your current marital status. _____ Married Nominal Scales: Examples Scales Example 1: Please indicate your current marital status. _____ Married ____ Single, never married ____Widowed Example 2: Do you like or dislike chocolate ice cream? ____ Like ____ Dislike Example 3: Please check those information and HCP service areas in which you have had a faceto-face or telephone conversation with a representative of your main HCP in the past six month. (Check as many as apply. ) ____ Appointments ____ Treatment at home ____ Referral to other HCP ____ Prescriptions ____ Medical test results ____ Hospital stay Some other service area(s); Please specify 15 __________________

Ordinal Scales: Examples Scales Which category best describes your knowledge about the assortment of Ordinal Scales: Examples Scales Which category best describes your knowledge about the assortment of services offered by your main HCP? (Please check just one category. ) ____ Complete knowledge of services ____ Good knowledge of services ____ Basic knowledge of services ____ Little knowledge of services ____ No knowledge of services 16

Scales used in questionnaire design II Interval scale • the numbers used to rank Scales used in questionnaire design II 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 17

Interval Scales: Examples Scales Example 1: Approximately how many charges for overdrawn checks (NSF Interval Scales: Examples Scales Example 1: Approximately how many charges for overdrawn checks (NSF checks) has “your” bank imposed on you in the past year? ____ 0 -3 ____ 4 -7 ____ 8 -11 ____ 12 -15 ____ 16 -19 Example 2: 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 24 Example 3: In which of the following categories does your current age fall? ____1 to 10 ____ 21 to 30 ____ 41 to 50 ____11 to 20 ____ 31 to 40 ____ 51 to 60 18 ____ 61 -70

Ratio Scales: Examples Scales Example 1: Please circle the number of children under 18 Ratio Scales: Examples Scales Example 1: Please circle the number of children under 18 years of age currently living in your household. 0 1 2 3 4 5 6 7 (If more than 7, please specify: ____. ) Example 2: In the past seven days, how many times did you go shopping at a retail shopping mall? ____ # of times Example 3: In whole years, what is your current age? ____ # of years old 19

Types of Scales and their properties 20 Types of Scales and their properties 20

Single - Item Scales • Itemized-category Scales … most widely used single-item scale. It 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. 21

Itemized Category Scales • Scales in which the respondent selects from a limited number Itemized Category Scales • Scales in which the respondent selects from a limited number of categories • What is your overall satisfaction with Mc. Donalds Hamburgers? Very satisfied 22 Quite Satisfied Somewhat satisfied Not at all satisfied

Pictorial Scales/Illustrierte Skalen • Various categories of the scale are depicted pictorially • Format Pictorial Scales/Illustrierte Skalen • Various categories of the scale are depicted pictorially • Format must be comprehensible to respond allow accurate response Example: • 23 The taste of Honey Munch Cereal is:

Issues in visualizing scales • Due to cultural differences scales have to be adapted 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……… 24

Cross-cultural Issues in Scale Development I • Number of Scale Categories • • 2 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 • 25 balanced vs. unbalanced Smiling Faces: US vs. Africa

Cross-Cultural Issues in Scale Development II Different Appearances of pictorial scales 26 Cross-Cultural Issues in Scale Development II Different Appearances of pictorial scales 26

Guttman Scale/Guttman Skala • … measures only a single trait - (property called unidimensionality, 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 27

Multiple-Item Scales – e. g. Likert scale Likert Scales: Require respondents to indicate the Multiple-Item Scales – e. g. Likert scale 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. 28

Likert Scale/Likert Skala For each of the listed statements, please check the one response Likert Scale/Likert Skala For each of the listed statements, please check the one response that best expresses the extent to which you agree or disagree with that statement. Definitely Statements Generally Slightly Generally Definitely Agree Disagree ___ ___ ___ ___ ___ ___ I buy many things with a credit card. ___ This is a single item I wish we had a lot more money. My friends often come to me for advice. I am never influenced by advertisements. 29 Together, the 4 items constitute the scale

Indexes/Indices • An index (for example a price index or stock market index) is 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*X 1 + 1*X 2 + 1*X 3 0 0 1 30 0 1 1 0

Big-Mac Index • Big Mac index - informal way of measuring the purchasing power 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. 31

Big-Mac Scale of standard of living ABM … Working Time (Minutes) for 1 Hamburger Big-Mac Scale of standard of living ABM … Working Time (Minutes) for 1 Hamburger BSP … Gross National Product HDI … Human Development Index 32

Exam Questions 1. Diskutieren Sie die Maße für Reliabilität und führen Sie hierfür ein 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. 33