Meaning of Scaling Scaling describe the procedures of

assigning of numbers 0r symbols (i.e., quantitative measures) to subjective abstract concepts (or properties of objects) This can be done in two ways viz.,

1. Making a judgement about some characteristic of an individual and then placing him directly on a scale that has been defined in terms of that characteristic.

2. Constructing questionnaires in such a way that the score of individual’s responses assigns him a place on a scale.

Scaling involves creating a continuum upon which measured objects are located.

These scale –point positions are so related to each other that when the first point happens to be the highest point, the second point indicates a higher degree in terms of a given characteristic as compared to the third point and the third point indicates a higher degree as compared to the fourth and so on.

Numbers for measuring the distinctions of degree in the attitudes/opinions are, thus, assigned to individuals corresponding to their scale-positions.

Scaling has been defined as a “procedure for the assignment of numbers (or other symbols ) to a property of objects in order to impart some of the characteristics of numbers to the properties in question. ”

Nominal ScalesNominal Scales

Ordinal ScalesOrdinal Scales

Interval ScalesInterval Scales

Ratio ScalesRatio Scales

Scale Properties:In nominal scale the numbers serve only as labels

or tags for identifying and classifying objects. The ordinal scale is a ranking scale in which

numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic.

In interval scale numerically equal distances on the scale represent equal values in the characteristic being measured.

The ratio scale possesses all the properties of the nominal, ordinal, and interval scales. It has an absolute zero point.

Nominal ScaleA nominal scale is the simplest of the four scale types

and in which the numbers or letters assigned to objects serve as labels for identification or classification.

Example:

Males = 1, Females = 2 Sales Zone A = Islamabad, Sales Zone B = Rawalpindi Drink A = Pepsi Cola, Drink B = 7-Up, Drink C = Miranda

Ordinal Scale:Ordinal measurements describe order, but not

relative size or degree of difference between the items measured.

In this scale type,the numbers assigned to objects or events represent the rank order (1st,2nd,3rd,etc) of the entities assessed.

A likert scale is a type of ordinal scale and may also use names with an order such as:

❖ “Bad”, “medium” and “good” ❖ “very satisfied”, “satisfied”, “neutral”, “unsatisfied”,

“very unsatisfied”

Example of an ordinal scale:

The result of a horse race, which says only which horses arrived first, second, or third but include no information about race times.

Another example is military rank; they have an order, but no well defined numerical difference between ranks.

Examples of Ordinal:

Career Opportunities = Moderate, Good, Excellent Investment Climate = Bad, inadequate, fair, good, very

good Merit = A grade, B grade, C grade, D grade

A problem with ordinal scales is that the difference between categories on the scale is hard to quantify, ie., excellent is better than good but how much is excellent better?

Interval ScaleAn interval scale is a scale that not only arranges

objects or alternatives according to their respective magnitudes, but also distinguishes this ordered arrangement in units of equal intervals (i.e. interval scales indicate order (as in ordinal scales) and also the distance in the order).

Examples: Temperature Scale in Fahrenheit

Interval scales allow comparisons of the differences of magnitude (e.g. of attitudes) but do not allow determinations of the actual strength of the magnitude.

Ratio ScaleA ratio scale is a scale that possesses absolute

rather than relative qualities and has an absolute zero.

Examples: Money Weight Distance Temperature on the Kelvin Scale

Interval scales allow comparisons of the differences of magnitude (e.g. of attitudes) as well as determinations of the actual strength of the magnitude.

Scale Classification BasesThe number of assigning procedures or the scaling

procedures may be broadly classified on the following

bases: Subject orientation Response form Degree of subjectivity Scale properties Number of dimensions Scale construction techniques

Subject Orientation:Under it a scale may be designed to measure

characteristics of the respondent who completes it or to judge the stimulus object which is presented to the respondent.

In respect of the former, we presume that the stimuli presented are sufficiently homogeneous so that the between stimuli variation is small as compared to the variation among respondents.

In the latter approach, we ask the respondent to judge some specific object in terms of one or more dimensions and we presume that the between-respondent variation will be small as compared to the variation among the different stimuli presented to respondents for judging.

Response form:Under this we may classify the scales as

categorical and comparative.

Categorical scales are also known as rating scales. These scales are used when a respondent scores some object without direct reference to other objects.

Under comparative scales, which are also known as ranking scales, the respondent is asked to compare two or more objects.

Degree of subjectivity:With this basis the scale date may be based on

whether we measure subjective personal preferences or simply make non-preference judgements.

In the former case , the respondent is asked to choose which person he favours or which solution he would like to see employed, whereas in the latter case he is simply asked to judge which person is more effective in some aspect or which solution will take fewer resources without reflecting any personal preference.

Number of dimensions:In respect of this basis, scales can be

classified as ‘ unidimensional’ and ‘multidimensional’ scales.

Under the former we measure only one attribute of the respondent or object, whereas multidimensional scaling recognizes that an object might be described better by using the concept of an attribute space of ‘n’ dimensions, rather than a single-dimension continuum.

Scale construction techniques:Following are the five main techniques by

which scales can be developed.

Arbitrary approach Consensus approach Item analysis approach

Cumulative scales Factor scales

Arbitrary approach:It is an approach where scale is developed on

ad hoc basis. This is the most widely used approach. It is presumed that such scales measure the concepts for which they have been designed, although there is little evidence to support such an assumption.

Consensus approach:Here a panel of judges evaluate the items

chosen for inclusion in the instrument in terms of whether they are relevant to the topic area and unambiguous in implication.

Item analysis approach:Under it a number of individual items are

developed into a test which is given to a group of respondents.

After administering the test ,the total scores are calculated for everyone.

Individual items are then analyzed to determine which items discriminate between persons or objects with high total scores and those with low scores.

Cumulative Scales:Cumulative scales or Louis Guttman’s

scalogram analysis, like other scales, consist of series of statements to which a respondent expresses his agreement or disagreement.

Factor ScalesFactor scales are developed through factor

analysis or on the basis of intercorrelations of items which indicate that a common factor accounts for the relationships between items.

An important factor scale based on factor analysis is

✸ Semantic Differential(S.D), and ✸ Multidimensional Scaling.

Scale construction Techniques

Arbitrary approach - scales on ad hoc basisConsensus approach- panel of judges evaluateItem analysis approach- individual items into

testCumulative scales - ranking of itemsFactor scales – inter correlation of items

Important Scaling TechniquesThe important scaling techniques often used

in the context of research specially in context of social or business research are as follows:

Rating Scales

Ranking Scales

Rating Scales: The rating scale involves qualitative description of

a limited number of aspects of a thing or of traits of a person.

These ratings may be in such forms as “like-dislike”, “ above average, average, below average” etc.

There is no specific rule whether to use a two-points scale, three-point scale or scale with still more points.

In practice, three to seven points scales are generally used for the simple reason that more points on a scale provide an opportunity for greater sensitivity of measurement.

Graphic rating scaleThe graphic rating scale is quite simple and is

commonly used in practice. Under it the various points are usually put along the line to form a continuum and the rater indicates his rating by simply making a mark (such as ✔ ) at the appropriate point on a line that runs from one extreme to the other.

The following is an example of five-points graphic rating scale when we wish to ascertain people’s liking or disliking any product:

Graphic Rating Scale

Graphic Rating Scales

12-30

Itemized rating scale:The itemized rating scale(also known as

numerical scale) presents a series of statements from which a respondent selects one as best reflecting his evaluation.

Suppose we wish to inquire as to how well does a worker get along with his fellow workers?

In such a situation we may ask the respondent to select one, to express his opinion, from the following:

He is almost always involved in some friction with a fellow worker.

He is often at odds with one or more of his fellow workers.

He sometimes gets involved in friction.He infrequently becomes involved in friction

with others.He almost never gets involved in friction with

fellow workers.

Selected Itemized Rating Scales

PURCHASE INTENT

Definitely Probably Probably will Definitely will will buy will buy not buy not buy

LEVEL OF AGREEMENTStrongly Somewhat Neither Somewhat Stronglyagree agree agree disagree

disagree nor disagree

QUALITYVery Good Neither good Fair

PoorGood nor bad DEPENDABILITYCompletely Somewhat Not very Not

dependableDependable dependable dependable at all STYLEVery Somewhat Not very

Completely stylish stylish stylish unstylish

SATISFACTIONCompletely Somewhat Neither satisfied Somewhat

Completely Satisfied satisfied nor dissatisfied dissatisfied

dissatisfied

COSTExtremely Expensive Neither expensive Slightly VeryExpensive nor inexpensive inexpensive

inexpensive

EASE OF USE

Very easy Somewhat Not very easy Difficult to use

to use easy to use to use

COLOR BRIGHTNESSExtremely Very Somewhat Slightly

Not bright Bright bright bright bright

at all

MODERNITYVery Somewhat Neither Somewhat

Very Modern modern modern old-fashioned old-

fashioned nor old-fashioned

Ranking Scales:There are two generally used approaches of

ranking scales viz., Method of paired comparisons Method of rank order

Method of paired comparisons: Under it the respondent can express his

attitude by making a choice between two objects, say between a new flavour of soft drinks and an established brand of drink.

But when there are more than two stimuli to judge, the number of judgements required in a paired comparison is given by the formula:

N= n(n-1) 2Where N=number of judgements

n=number of stimuli or objects to be judged.

Obtaining Shampoo Preferences Using Paired Comparisons

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 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 SellingThe 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. The introduction of New Coke illustrates this point. New Coke was heavily favored in blind paired comparison taste tests, but its introduction was less than successful, because image plays a major role in the purchase of Coke.

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 Order

1. 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