Session 4 1
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 Numbers
Assigned Finish
to Runners 7 8 3
Ordinal Rank Order Finish
of Winners
Third Second First
place place place
Interval Performance
8.2 9.1 9.6
Rating on a
0 to 10 Scale
15.2 14.1 13.4
Ratio Time to Finish
in Seconds
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Nominal Ordinal Interval Ratio
Scale Scale Scale Scale
Preference Preference $ spent last
No. Store Rankings Ratings 3 months
1-7 11-17
1. Parisian 7 79 5 15 0
2. Macy’s 2 25 7 17 200
3. Kmart 8 82 4 14 0
4. Kohl’s 3 30 6 16 100
5. J.C. Penney 1 10 7 17 250
6. Neiman Marcus 5 53 5 15 35
7. Marshalls 9 95 4 14 0
8. Saks Fifth Avenue 6 61 5 15 100
9. Sears 4 45 6 16 0
10.Wal-Mart 10 115 2 12 10
▪ Aadhar Number
▪ Age
▪ ICC Cricket Rankings
▪ Time on table clock with two hands
▪ Sales data
▪ Income
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Scaling Techniques
Comparative Noncomparative
Scales Scales
Paired Rank Constant Q-Sort and Continuous Itemized
Comparison Order Sum Other Rating Scales Rating Scales
Procedures
Likert Semantic Stapel
Differential
▪ Comparative scales
▪ Direct comparison of objects
▪ Which class do you prefer? ‘Business Research methods’ or <any
other>
▪ 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.
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▪ 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 Finesse Vidal Head & Pert
Sassoon Shoulders
Jhirmack 0 0 1 0
Finesse 1a 0 1 0
Vidal Sassoon 1 1 1 1
Head & Shoulders 0 0 0 0
Pert 1 1 0 1
Number of Times 3 2 0 4 1
Preferredb
aA 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? 13
+5 +5
+4 +4
+3 +3
+2 +2X
+1 +1
QUALITY SERVICE
-1 -1
-2 -2
-3 -3
-4X -4
-5 -5
Our service is: Worst _ _ _ _ _ _ _ _ _ Best
Number of items, balanced vs. unbalanced, forced vs. non-forced, odd vs.
even….refer book
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Jovan Musk for Men is: Jovan Musk for Men is:
Extremely good Extremely good
Very good Very good
Good Good
Bad Somewhat good
Very bad Bad
Extremely bad Very bad
Scale Evaluation
Reliability Validity Generalizability
Test/ Alternative Internal
Content Criterion Construct
Retest Forms Consistency
Convergent Discriminant Nomological
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▪ 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??
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