S4_scale_measurements.pdf

Session 4

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 Measurement: Assigning numbers or some other symbols to the

characteristics of certain objects  Scaling: Involves creating a continuum on which measurements on

objects are located.

 Types of scales/data: Nominal, Ordinal, Interval, Ratio

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Numbers/name/labels are assigned. ▪ 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. ▪ Only a limited number of statistics, all of which are based on frequency counts, are permissible, e.g., percentages, and mode. ▪ Examples: Marital status, gender

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▪ Numbers are assigned to objects to indicate the relative extent

▪ 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 ▪ In addition to the counting operation, ordinal scales permit the use of

statistics based on centiles, e.g., percentile, quartile, median. ▪ Examples: Rank the movies

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▪ Numerically equal distances on the scale, comparison is meaningful

▪ Location of the zero point is not fixed ▪ Can be represented as y = a + bx ▪ Ratios are not meaningful (no absolute zero) ▪ Statistical techniques allowed: arithmetic mean, standard deviation,

correlation, regression etc. ▪ Examples: temperature, IQ

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▪ Possesses all the properties of the nominal, ordinal, and interval scales.

▪ Absolute zero point. ▪ Ratios are meaningful ▪ Only proportionate transformations of the form y = bx, where b is a

positive constant, are allowed. ▪ All statistical techniques can be applied to ratio data. ▪ Examples: Length, Weight

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Scale Nominal

Ordinal

Numbers Assigned to Runners

Finish 7

8

3

Rank Order of Winners

Interval

Performance Rating on a 0 to 10 Scale

Ratio

Time to Finish in Seconds

Finish Third place

Second place

First place

8.2

9.1

9.6

15.2

14.1

13.4

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Nominal Scale

Ordinal Scale

Interval Scale

No. Store

Preference Rankings

Preference Ratings 1-7 11-17

1. Parisian 2. Macy’s 3. Kmart 4. Kohl’s 5. J.C. Penney 6. Neiman Marcus 7. Marshalls 8. Saks Fifth Avenue 9. Sears 10.Wal-Mart

7 2 8 3 1 5 9 6 4 10

79 25 82 30 10 53 95 61 45 115

5 7 4 6 7 5 4 5 6 2

15 17 14 16 17 15 14 15 16 12

Ratio Scale $ spent last 3 months

0 200 0 100 250 35 0 100 0 10

▪ Aadhar Number

▪ Age ▪ ICC Cricket Rankings ▪ Time on table clock with two hands ▪ Sales data ▪ Income

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Scaling Techniques

Noncomparative Scales

Comparative Scales

Paired Comparison

Rank Order

Constant Q-Sort and Sum Other Procedures

Likert

Continuous Itemized Rating Scales Rating Scales

Semantic Differential

Stapel

▪ Comparative scales ▪ Direct comparison of objects ▪ Which class do you prefer? ‘Business Research methods’ or ▪ Can have ordinal/rank order data (or non-metric data) ▪ Paired comparison, rank order, constant sum ▪ Non-comparative scales ▪ Each object is scaled independently ▪ Rate the food at IIMR Canteen on scale of 1 to 5 – taste, quality, price etc. 11

▪ Non-comparative scale ▪ Continuous ▪ Itemized rating: likert scale, semantic differential, stapel scale.

How would you rate XYZ as a department store? Probably the worst - - - - - - -I - - - - - - - - - - - - - - - - - - - - - - Probably the best

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Instructions: We are going to present you with ten pairs of shampoo brands. For each pair, please indicate which one of the two brands of shampoo you would prefer for personal use.

Recording Form:

Jhirmack

Jhirmack

aA

Finesse 0

Vidal Sassoon 0

Head & Shoulders 1

Pert

0

1

0

1

1

Finesse

1a

Vidal Sassoon

1

1

Head & Shoulders

0

0

0

Pert

1

1

0

1

Number of Times Preferredb

3

2

0

4

0

0 1

1 in a particular box means that the brand in that column was preferred over the brand in the corresponding row. A 0 means that the row brand was preferred over the column brand. bThe number of times a brand was preferred is obtained by summing the 1s in each column.

New Coke?

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+5 +4 +3 +2 +1

+5 +4 +3 +2X +1

QUALITY

SERVICE

-1 -2 -3 -4X -5

Our service is:

-1 -2 -3 -4 -5

Worst _ _ _ _ _ _ _ _ _ Best

Number of items, balanced vs. unbalanced, forced vs. non-forced, odd vs. even….refer book 14

Jovan Musk for Men is: Extremely good Very good Good Bad Very bad Extremely bad

Jovan Musk for Men is: Extremely good Very good Good Somewhat good Bad Very bad

Scale Evaluation

Reliability

Test/ Retest

Alternative Forms

Validity

Internal Consistency

Content

Convergent

Criterion

Generalizability

Construct

Discriminant

Nomological 16

▪ Measurement error= random error + systematic error ▪ Causes of errors- mood, fatigue, health, different environment, not

understandable, error in coding, entering etc.

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▪ Reliability- extent to which a scale produces consistent results ▪ Test-retest reliability ▪ Repeated measurement of same person/group under same

circumstances ▪ Issues to be handled- time difference (ideal 2-4 weeks), interactive bias, boredom, anger or attempt to remember ▪ Internal consistency reliability- assess through summated scale ▪ Split-half reliability method ▪ Correlation coefficient between two splits (of items) is obtained ▪ Coefficient/Cronbach alpha- average of all possible split half coefficients

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▪ Validity : Measuring what one wants to measure ▪ Content/face validity

▪ Subjective judgement by an expert (SAT/CAT?) ▪ Criterion validity ▪ Concurrent

▪ Data and criterion variables are collected simultaneously (midterm exam

and teacher’s ranking of students should correlate) ▪ Predictive validity ▪ Collect data on scale at one point and on criterion variable in future time e.g. master chef

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▪ Construct validity – Why a scale works ▪ Convergent -> Extent of correlation of scale with other item of the same

construct ▪ Discriminant -> Extent to which a item does not correlate with other construct ▪ Nomological -> theoretical ground Reliability is a necessary, but not sufficient, condition for validity.

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Any more examples?? 22