Measurement and Scaling

1. Measurement and Scaling

2. Measurement and Scaling Measurement means assigning numbers or other symbols to characteristics of objects according to certain prespecified rules. • One-to-one correspondence between the numbers and the characteristics being measured. • The rules for assigning numbers should be standardized and applied uniformly. • Rules must not change over objects or time.

3. Measurement and Scaling Scales: Used to measure characteristics of objects under consideration

4. Nominal Scales Four Basic Scales of Measurement Ordinal Scales Interval Scales Ratio Scales

5. Primary Scales of MeasurementNominal Scale • The numbers serve only as labels or tags for identifying and classifying objects. • When used for identification, there is a strict one-to-one correspondence between the numbers and the objects. • The numbers do not reflect the amount of the characteristic possessed by the objects. • The only permissible operation on the numbers in a nominal scale is counting.

6. Primary Scales of MeasurementOrdinal Scale • A ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic. • Can determine whether an object has more or less of a characteristic than some other object, but not how much more or less. • Any series of numbers can be assigned that preserves the ordered relationships between the objects. • In addition to the counting operation allowable for nominal scale data, ordinal scales permit the use of statistics based on centiles, e.g., percentile, quartile, median.

7. Primary Scales of MeasurementInterval Scale • Numerically equal distances on the scale represent equal values in the characteristic being measured. • It permits comparison of the differences between objects. • It might be meaningful to take ratios of scale values. • Statistical techniques that may be used include all of those that can be applied to nominal and ordinal data, and in addition the arithmetic mean, standard deviation, and other statistics commonly used in research.

8. Primary Scales of MeasurementRatio Scale • Possesses all the properties of the nominal, ordinal, and interval scales. • It has an absolute zero point. • It is meaningful to compute ratios of scale values. • All statistical techniques can be applied to ratio data.

9. Scales of Measurement

10. Third place Second place First place Scales of Measurement Scale NominalNumbers Assigned to Runners OrdinalRank Order of Winners IntervalPerformance Rating on a 0 to 10 Scale Ratio Time to Finish, in Seconds Finish 7 8 3 Finish 8.2 9.1 9.6 15.2 14.1 13.4

11. Sources of Error in Measurement • Respondent • Situation • Measurer • Instrument

12. Criteria for Good Measurement • VALIDITY( Indicates the degree to which an instrument measures what it is actually supposed to measure) • RELIABILITY( The tendency of a respondent to respond in the same or similar manner to an identical or near identical question) • SENSTIVITY(The ability of a measuring instrument to measure the meaningful difference in the responses obtained from subjects under study) • PRACTICALITY( in terms of economy, convenience and interpretability)

13. NOMINAL SCALE NOMINAL SCALES ARE DEFINED AS THOSE THAT USE ONLY LABEL; THAT IS, THEY POSSESS ONLY THE CHARACTERISTIC OF DESCRIPTION THE RESPONSE DOES NOT INCLUDE ANY LEVEL OF INTENSITY

14. EXAMPLES • DESIGNATIONS AS TO RACE, RELIGION, • TYPE OF DWELLING • GENDER • BRAND LAST PURCHASED • ANSWERS THAT INVOLVE YES-NO, AGREE-DISAGREE • OR ANY OTHER INSTANCE IN WHICH DESCRIPTORS CAN NOT BE DIFFERENTIATED EXCEPT QUALITATIVELY

15. IF ONE DESCRIBES RESPONDENTS IN A SURVEY ACCORDING TO THEIR OCCUPATION— BANKER, DOCTOR, COMPUTER PROGRAMMER— ONE HAS USED A NOMINAL SCALE

16. NOMINAL- SCALED QUESTIONS CHECK ALL THE BRANDS YOU WOULD CONSIDER PURCHASING • SONY • VIDEOCON • SAMSUNG • LG

17. DO YOU AGREE OR DISAGREE THAT “DELTA IS READY WHEN YOU ARE”? AGREE DISAGREE

18. WHICH OF THE FOLLOWING SUPERMARKETS HAVE YOU SHOPPED IN THE LAST 30 DAYS? • EBONY • STAR MALL • SAB MALL • MIGROS • SAHARA MALL

19. DO YOU LIKE OR DISLIKE CHOCOLATE ICE CREAM? • LIKE • DISLIKE

20. ORDINAL SCALE AN ORDINAL SCALE IS OBTAINED BY RANKING OBJECTS OR ARRANGING THEM IN ORDER WITH REGARD TO SOME COMMON VARIABLE

21. THE QUESTION IS SIMPLY WHETHER EACH OBJECT HAS MORE OR LESS THAN SOME OTHER OBJECT

22. IT PERMITS THE RESEARCHER TO RANK ORDER THE RESPONDENTS OR THEIR RESPONSES THE RESEARCHER CAN RANK ORDER THE RESPONSES INTO HIERARCHICAL PATTERN

23. THIS SCALE DOES NOT ALLOW A RESEARCHER TO DETERMINE THE ABSOLUTE DIFFERENCE IN ANY OF THE ORDINAL RELATIONSHIPS

24. ORDINAL- SCALED QUESTIONS PLEASE RANK EACH BRAND IN TERMS OF YOUR PREFERENCE PLEASE PLACE “1” BY YOUR FIRST CHOICE, A “2” BY YOUR SECOND CHOICE, AND SO ON • SONY • VIDEOCON • SAMSUNG • LG • BPL • PHILLIPS

25. INTERVAL SCALE INTERVAL SCALES ARE THOSE IN WHICH THE DISTANCE BETWEEN EACH DESCRIPTOR IS KNOWN IT DEMONSTRATES ABSOLUTE DIFFERENCESBETWEEN EACH SCALE POINT

26. THE DISTANCE IS NORMALLY DEFINED AS ONE SCALE UNIT FOR EXAMPLE, A COFFEE BRAND RATED “3” IN TASTE IS ONE UNIT AWAY FROM ONE RATED “4”

27. IN AN INTERVAL SCALE THE NUMBERS USED TO RANK THE OBJECTS ALSO REPRESENT EQUAL INCREMENTS OF THE ATTRIBUTE BEING MEASURED

28. THIS MEANS THAT DIFFERENCES CAN BE COMPARED THE DIFFERENCE BETWEEN 1 AND 2 IS SAME AS BETWEEN 2 AND 3 BUT ONLY HALF THE DIFFERENCE BETWEEN 2 AND 4

29. THE LOCATION OF ZERO POINT IS NOT FIXED, SINCE ZERO DOES NOT DENOTE THE ABSENCE OF THE ATTRIBUTE BOTH ZERO POINT AND UNITS OF MEASUREMENT ARE ARBITRARY

30. SOME TIME A RESEARCHER MUST IMPOSE A BELIEF THAT EQUAL INTERVALS EXIST BETWEEN THE DESCRIPTORS

31. THAT IS: IF YOU WERE ASKED TO EVALUATE A STORE’S SALES PEOPLE BY SELECTING A SINGLE DESIGNATION FROM THE LIST OF • EXTREMELY FRIENDLY • VERY FRIENDLY • SOME WHAT FRIENDLY • SOME WHAT UNFRIENDLY • VERY UNFRIENDLY • EXTREMELY UNFRIENDLY

32. THE RESEARCHER WOULD PROBABLY ASSUME THAT EACH DESIGNATION WAS ONE UNIT AWAY FROM THE PRECEDING ONE IN THESE CASES WE SAY THAT THE SCALE IS “ASSUMED INTERVAL”

33. INTERVAL – SCALED QUESTIONS PLEASE RATE EACH BRAND IN TERMS OF ITS OVERALL PERFORMANCE • BRAND RATING (CIRCLE ONE) • VERY POORVERY GOOD MONT BLANC 1 2 3 4 5 6 7 8 9 10 PARKER CROSS

34. INDICATE YOUR DEGREE OFAGREEMENT WITH FOLLOWING STATEMENTS BY CIRCLING THE APPROPRIATE NUMBER • STATEMENT STRONGLY STRONGLY • AGREE DISAGREE • I ALWAYS LOOK FOR BARGAINS 1 2 3 4 5 • I ENJOY BEING OUT DOORS 1 2 3 4 5 • I LOVE TO COOK 1 2 3 4 5

35. RATIO SCALE RATIO SCALES ARE THE ONES IN WHICH TRUE ZERO ORIGIN EXISTS— SUCH AS -ACTUAL NUMBER OF PURCHASES IN A CERTAIN TIME PERIOD, -RUPEES SPENT, MILES TRAVELED ETC.

36. THIS CHARACTERISTIC ALLOW US TO CONSTRUCT RATIOS WHEN COMPARING THE RESULTS OF MEASUREMENT

37. A RATIO SCALE TENDS TO BE MOST SOPHISTICATED SCALE IN THE SENSE THAT IT ALLOWS THE RESEARCHER NOT ONLY TO IDENTIFY THE ABSOLUTE DIFFERENCES BETWEEN EACH SCALE POINT BUT ALSO TO MAKE ABSOLUTE COMPARISONS BETWEEN THE RESPONSES

38. EXAMPLE IN COLLECTING DATA ABOUT HOW MANY CARS ARE DRIVEN BY HOUSEHOLDS IN DELHI, A RESEARCHER KNOWS THAT DIFFERENCE BETWEEN DRIVING ONE CAR AND DRIVING THREE CARS IS ALWAYS GOING TO TWO

39. FURTHER MORE, WHEN COMPARING A ONE – CAR FAMILY TO THREE – CAR FAMILY WILL HAVE SIGNIFICANTLY HIGHER TOTAL CAR INSURANCE AND MAINTENANCE COSTS THAN A ONE – CAR FAMILY

40. SUCH RATIOS ARE INAPPROPRIATE FOR INTERVAL SCALES, SO WE ARE NOT ALLOWED TO SAY THAT ONE STORE WAS ONE HALF AS FRIENDLY AS ANOTHER

41. RATIO-SCALED QUESTIONS PLEASE INDICATE YOUR AGE --- YEARS

42. APPROXIMATELY HOW MANY TIMES IN THE LAST MONTH HAVE YOU PURCHASED ANY THING OVER Rs.1000 IN VALUE AT NANZ STORE? 0 1 2 3 4 5 MORE ( SPECIFY_ )

43. HOW MUCH DO YOU THINK A TYPICAL PURCHASER OF A Rs. 5 LAKH TERM LIFE INSURANCE POLICY PAYS PER MONTH THAT POLICY? Rs.__________

44. WHAT IS THE PROBABILITY THAT YOU WILL USE A LAWYER’S SERVICES WHEN YOU ARE READY TO MAKE A WILL? ______PERCENT

45. TYPICALLY THE ISSUES LIKE QUANTITY SOLD NUMBER OF CONSUMERS PROBABILITY OF PURCHASE ETC. FORM RATIO SCALE MEASUREMENT

46. ASSESSING A RESPONDENT’S LIKING OF SOFTDRINKS WITH NOMINAL ORDINAL, INTERVAL AND RATIO SCALES NOMINAL SCALE WHICH OF THE FOLLOWING SOFT DRINKS ON THE FOLLOWING LIST DO YOU LIKE? CHECK ALL THAT APPLY • COKE • THUMS UP • MOUNTAIN DEW • PEPSI • SEVEN UP • SPRTIE

47. ORDINAL SCALE PLEASE RANK THE SOFT DRINKS ON THE FOLLOWING LIST ACCORDING TO YOUR DEGREE OF LIKING FOR EACH, ASSIGNINIG MOST PREFERRED DRINK RANK=1 AND YOUR LEAST PREFERRED DRINK RANK=6 • COKE • THUMS UP • MOUNTAIN DEW • PEPSI • SEVEN UP • SPRTIE

48. INTERVAL SCALE PLEASE INDICATE YOUR DEGREE OF LIKING OF EACH OF THE SOFTDRINKS ON THE FOLLOWING LIST BY CHECKING THE APPROPRIATE POSITION ON THE SCALE DISLIKE DISLIKE LIKE LIKE A LOT ALOT COKE THUMS UP MOUNTAIN DEW PEPSI SEVEN UP SPRTIE

49. RATIO SCALE PLEASE DIVIDE 100 POINTS AMONG EACH OF THE FOLLOWING SOFT DRINKS ACCORDING TO YOUR DEGREE OF LIKING FOR EACH • COKE • THUMS UP • MOUNTAIN DEW • PEPSI • SEVEN UP • SPRITE

50. Scaling Techniques Noncomparative Scales Comparative Scales Continuous Rating Scales Itemized Rating Scales Paired Comparison Rank Order Constant Sum Q-Sort and Other Procedures Semantic Differential Stapel Likert A Classification of Scaling Techniques