Measurement and Scaling Techniques

Measurement and scaling techniques

Measurement and ScalingMeasurement 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.

Measurement and ScalingScaling involves creating a continuum upon which measured objects are located.

Consider an attitude scale from 1 to 100. Each respondent is assigned a number from 1 to 100, with 1 = Extremely Unfavorable, and 100 = Extremely Favorable. Measurement is the actual assignment of a number from 1 to 100 to each respondent. Scaling is the process of placing the respondents on a continuum with respect to their attitude toward department stores.

Measurement

Measurement stands for the assignment of numbers to the characteristics of persons, objects or events on the basis of certain principles. Methods of measurement of attitude (qualitative or abstract data type) consists of:

Nominal scale Ordinal scale Interval scale Ratio scale

Nominal scaleThe procedure consists in classifying persons,

events or objects into a no. of mutually exclusive groups on the basis of the presence or absence of a particular characteristic.

E.g. categorizing people acc. to their religion, age Basic empirical operation-determination of

equality-counting of numbers, only frequencies can be calculated.

Measure of central tendency-mode Test of significance-chi-square, binomial

Nominal scale-example

workersskilled

unskilledEmployed 324 516

Unemployed 110 120

Classification of male, female, smoker, non-smoker

Ordinal scaleThese are ranking scales acc. to which objects can be

categorized on the basis of “more than” or “less than”.E.g. consumer oriented marketing research, consumer

can rank the order of preferences for a number of brands or different qualities of goods.

Basic empirical operation-determination of greater or less Measure of central tendency-median Rank correlation method Tests of significance-non parametric methods

Ordinal scale-example

Whether the respondent likes soft drinks or not. I strongly like it +2 I like it +1 I am indifferent 0 I dislike it -1 I strongly dislike it -2

Interval scaleIt shows equality of differences. Intervals indicate equal

quantities of the variable that is measured. It measures not only as to which category is greater or better but also by “how much”. There is no unique origin or zero for the scale.

e.g. centigrade and Fahrenheit temp scales start with different points of origin.

Basic empirical operation-determination of equality of intervals.

Measure of central tendency-mean, median or mode Measure of dispersion-range, std. dev. Test of significance-t-test, ANOVA, factor analysis

Interval scale-example

Temperature 100°c 80°c 120°cInterval scales are more preferred as they are

quicker to complete.

Ratio scale

It possesses not only the characteristic properties of the interval scale of measurement but also a natural true 0 or absolute zero scale position or point

E.g. height, weight and distance Basic empirical operation-determination of

equality of ratios-multiplication and division. Measure of central tendency-geometric mean Measure of dispersion –coefficient of

variation

Ratio scale-examples

Sales, units produced, no. of customers, costs, age ,etc.

Primary Scales of MeasurementTable 8.1

Scale Basic Characteristics

Common Examples

Marketing Examples

Nominal Numbers identify & classify objects

Social Security nos., numbering of football players

Brand nos., store types

Percentages, mode

Chi-square, binomial test

Ordinal Nos. indicate the relative positions of objects but not the magnitude of differences between them

Quality rankings, rankings of teams in a tournament

Preference rankings, market position, social class

Percentile, median

Rank-order correlation, Friedman ANOVA

Ratio Zero point is fixed, ratios of scale values can be compared

Length, weight Age, sales, income, costs

Geometric mean, harmonic mean

Coefficient of variation

Permissible Statistics Descriptive Inferential

Interval Differences between objects

Temperature (Fahrenheit)

Attitudes, opinions, index

Range, mean, standard

Product-moment

7 38

Primary Scales of MeasurementScaleNominal Numbers

Assigned to Runners

Ordinal Rank Orderof Winners

Interval PerformanceRating on a

0 to 10 Scale

Ratio Time to Finish, in

Seconds

Figure 8.1

Thirdplace

Secondplace

Firstplace

Finish

Finish

8.2 9.1 9.6

15.2 14.1 13.4

Illustration of Primary Scales of Measurement

Nominal Ordinal RatioScale Scale Scale

Preference $ spent last No. Store Rankings 3 months

1. Lord & Taylor2. Macy’s3. Kmart4. Rich’s5. J.C. Penney 6. Neiman Marcus 7. Target 8. Saks Fifth Avenue 9. Sears 10.Wal-Mart

IntervalScale Preference Ratings1-7 11-17

7 79 5 15 02 25 7 17 2008 82 4 14 03 30 6 16 1001 10 7 17 2505 53 5 15 359 95 4 14 06 61 5 15 1004 45 6 16 010 115 2 12 10

Scaling techniques

Attitude cannot be observed directly…

The instrument that is used for measurement is called scale.

The techniques that are used for the construction of the scales are scale construction techniques.

Classification of scales:Single item vs. multiple item scaleComparative vs. non-comparative scales

A Classification of Scaling Techniques

Likert Semantic Differential

Stapel

Scaling Techniques

Non-comparativeScales

Comparative Scales

Paired Comparison

Rank Order

Constant Sum

Q-Sort and Other Procedures

Continuous Rating Scales

Itemized Rating Scales

A Comparison of Scaling Techniques Comparative scales involve the direct comparison of stimulus

objects. Comparative scale data must be interpreted in relative terms and have only ordinal or rank order properties.

How do you rate Barista in comparison to CCD on quality of beverages?

Comparison of various attributes of Domino’s Pizza and Pizza Hut…

  In non-comparative scales, each object is scaled

independently of the others in the stimulus set. The resulting data are generally assumed to be interval or ratio scaled.

Evaluate the quality of food in a restaurant on a five pt scale.

Comparative Scaling TechniquesPaired Comparison Scaling A respondent is presented with two objects and asked to select

one according to some criterion. The data obtained are ordinal in nature. Paired comparison scaling is the most widely used comparative

scaling technique. With n brands, [n(n - 1) /2] paired comparisons are required Under the assumption of transitivity, it is possible to convert

paired comparison data to a rank order. Limitations Useful when the number of items is limited. The order in which the objects are presented may introduce

bias in results.

Obtaining Shampoo Preferences Using Paired ComparisonsInstructions: 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 Sassoon

Head & Shoulders

Pert

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 Preferredb

3 2 0 4 1

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.

Paired Comparison Selling

The most common method of taste testing is paired comparison. The consumer is asked to sample two different products and select the one with the most appealing taste. The test is done in private and a minimum of 1,000 responses is considered an adequate sample. A blind taste test for a soft drink, where imagery, self-perception and brand reputation are very important factors in the consumer’s purchasing decision, may not be a good indicator of performance in the marketplace.

A paired comparison taste test

Comparative Scaling TechniquesRank Order Scaling Respondents are presented with several objects simultaneously

and asked to order or rank them according to some criterion. It is possible that the respondent may dislike the brand ranked 1

in an absolute sense. Furthermore, rank order scaling also results in ordinal data. Only (n - 1) scaling decisions need be made in rank order

scaling.

Preference for Toothpaste Brands Using Rank Order Scaling

Instructions: Rank the various brands of toothpaste in order of preference. Begin by picking out the one brand that you like most and assign it a number 1. Then find the second most preferred brand and assign it a number 2. Continue this procedure until you have ranked all the brands of toothpaste in order of preference. The least preferred brand should be assigned a rank of 10. No two brands should receive the same rank number. The criterion of preference is entirely up to you. There is no right or wrong answer. Just try to be consistent.

Brand Rank Order1. Crest _________ 2. Colgate _________

3. Aim _________ 4. Gleem _________ 5. Macleans _________ 6. Ultra Brite _________

7. Close Up _________ 8. Pepsodent _________ 9. Plus White _________ 10. Stripe _________

Preference for Toothpaste Brands Using Rank Order Scaling

Form

Comparative Scaling TechniquesConstant Sum Scaling Respondents allocate a constant sum of units, such as 100

points to attributes of a product to reflect their importance. If an attribute is unimportant, the respondent assigns it zero

points. If an attribute is twice as important as some other attribute, it

receives twice as many points. The sum of all the points is 100. Hence, the name of the scale. It is widely used in allocating weights which the consumer may

assign to the various attributes of a product.

Importance of Bathing Soap AttributesUsing a Constant Sum Scale

InstructionsOn the next slide, there are eight attributes of bathing soaps. Please allocate 100 points among the attributes so that your allocation reflects the relative importance you attach to each attribute. The more points an attribute receives, the more important the attribute is. If an attribute is not at all important, assign it zero points. If an attribute is twice as important as some other attribute, it should receive twice as many points.

Form Average Responses of Three Segments Attribute Segment I Segment II Segment III1. Mildness2. Lather 3. Shrinkage 4. Price 5. Fragrance 6. Packaging 7. Moisturizing 8. Cleaning Power

Sum

8 2 4 2 4 17 3 9 7

53 17 9 9 0 19 7 5 9 5 3 20

13 60 15 100 100 100

Importance of Bathing Soap AttributesUsing a Constant Sum Scale

Q-Sort and Scaling It discriminate among a relatively large number of

objects quickly. Uses a rank order procedure in which objects are

sorted into piles based on similarity with respect to some criterion.

E.g. respondents are given 100 attitude statements on individual cards and asked to place them into 11 piles, ranging from “most highly agreed with” to “least agreed with”. The number of objects to be placed in each pile is pre-specified, often to result in a roughly normal distribution of objects over the whole set.

The data generated is ordinal in nature.

Graphic rating scale The various points are usually put along the line to

form a continuum and the respondent indicates his rating by simply making the appropriate point on a line that runs from one extreme to the other.

Indicate your preference for fast food.l---------------------------------l-----------------------------------l

Least preferred Most referredAssumption-respondents can distinguish the fine shade

in differences between the preferences.The coding, editing and tabulation of data generated

through such a procedure is difficult.

Itemized rating scale

The respondents are provided with a scale that has a no. brief descriptions associated with each of the response categories.

Balanced vs. unbalance scales

Balanced scalesEqual number of favourable and unfavourable categoriesHow important is price to you in buying a car?Very importantRelatively importantNeither imp. nor unimp.Relatively unimportantVery unimportant

Unbalanced scalesIf the distribution is dominantly favourable or unfavourableHow important is rice to you in buying a new car?More imp. than any other factorExtremely imp.ImportantSomewhat importantUnimportant

Likert’s summated scale

This scale is based on item analysis. The responses may be based on 5-point or 7-point scale.

A researcher gathers a large no. of statements pertaining to the attitude under investigation.

On the basis of a 5-pt scale a group of individuals are asked to indicate their responses.

The most favorable response is given a score 5 and the most unfavorable is given lowest score 1.

Likert’s summated scale The total score of each respondent is obtained. The investigator may select a significant part

(say 25%) of the highest scores and also (say 25%) of the lowest scores. These two parts represent the most favorable and most unfavorable attitudes.

The statements that consistently correlate with these two extreme attitudes are finally selected and retained for the research purpose.

Merits

Necessity of panel of judges does not arise. Greater precision and accuracy is ensured, in

regard to the responses, mainly because the response to each statement is obtained.

Not time consuming.

Demerits The five positions on the scale are not equally

spaced. The total score of a respondent can remain

the same for different combinations of responses, hence the total score may not be realistically meaningful.

The exact degree of responsiveness cannot be precisely expressed. If a response deals with more agreeable or less agreeable, then the exact extent of agreeability or disagreeability cannot be stated.

Thurstone’s differential scale Based on technique of equal appearing intervals Brief statements relating to the views about a particular

issue covering different ranges of attitude are gathered. A panel of judges are approached to sort them into

several piles. Each judge is required to place them in 11 groups so

that the most unfavorable gets placed in the first group and the most favorable in the 11th group.

Statements with which judges do not agree are omitted.

Thurstone’s differential scale

After sorting, a complete tabulation is made to determine the number of times each statement is included in the number of piles.

The scale values for each statement are determined graphically in the form of an ogive or cumulative freq. curve.

The final scale is then made, selecting 15-20 statements preferably those on which judges have least disagreement.

Merits

Scale is useful as a simple and reliable measure in regard to a specific attitude.

Demerits

Construction of these scales is costly, time-consuming and cumbersome

The process of dividing the scale into eleven units is quite arbitrary.

Scale values assigned to statements are influenced by the attitudes, background, and intelligence of judges who may see things differently from the actual respondents.

This scale does not allow subjects to express the intensity of their responses.

example

|--------------|----------|---------|-------------|Strongly agree agree undecided disagree strongly disagreeScore value

5 4 3 2 1

Guttman’s cumulative scale Scaling procedure is called scalogram analysis. It is based on a series of statements that posses a

cumulative effect in the sense that the statements which are related amongst themselves form a cumulative series.

An affirmative reply to a statement at one end, implies affirmative replies to the statements prior to that statement.

A respondent who agrees positively to statement no.5 also agrees positively to statements 4,3,2,1.

It is a uni-dimensional scale measures only one variable only

Scalogram analysisRespondent item no. score category 5 4 3 2 1------------------------------------------------------------------------------------------

A x x x x x 5B x x x x 4C x x x 3D x x 2E x 1F 0

--------------------------------------------------------------------------------------X denotes agreement with the itemScore 3 implies that the respondent is not in agreement with the

items 4 and 5 but agrees to items 3, 2, 1.

Semantic differential scale

This scale refers to a 7pt rating procedure in respect of a number of attributes and according to the bipolar adjectives denoting the extreme points.

The central position denotes neutrality. The extreme characteristics are given names

and the in between characteristics are represented by blank spaces.

Example Customer relationship services of three different hotels, in a certain city

score valuePrompt service N L M slow serviceHelpful staff N M L unhelpfulPolite N M L impoliteEfficient M N L inefficientroom service room serviceClean N M L dirty

environment environment high quality M L N very poorFood service quality food serviceCorrect billing N L M incorrectService billing serviceThe scores in respect of the hotels L, M, N are -4, 0 and 12 resp.

Rating scales

Graphic scales show a continuous scale evaluation.

The measurer can mark his rate at any point on the continuous straight line graph.|-------------|-------------|-------------|-------------|

Outstanding very good satisfactory poor very poor

Rating scalesDiscrete scale rates or describes an object or person into a

certain categories usually five on a discrete (discontinuous) pattern.

The performance of a student in a test may be rated in the following manner.

OutstandingVery goodSatisfactoryPoor Very poorThis is a descriptive scale. Scale can be in terms of grades:Using alphabets such as A+, A, B+, B, C or numerical 5,4,3,2,1

Attitude scales

Attitude scale measure one or more aspects of an individual’s or group’s attitude towards some object. Commonly used attitude scales are:

Thurstone’s differential scale Likert’s summated scale Guttman’s cumulative scale Semantic differential scale