Measurement & Scaling Measurement: assigning numbers to empirical events in compliance with a mapping rule. Measurement is a procedure in which a researcher assigns numerals-numbers or other symbols to empirical properties (Variables) according to rules.The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable.

Measurement Measurement is a three part process: (1) Selecting observable empirical events.(2) Developing a set of mapping rules: a scheme

for assigning numbers or symbols to represent aspects of the event being measured.

(3) Apply the mapping rule/s to each observation of that event.

Note: term empirical is used to describe, explain, and make predictions by relying on information gained through observation.

Measurement What is the male to female ratio among attendees

in an auto show?To solve this problem, you observe those who enter the show area. If a person is female, you record an F, if male, an M. instead, any other symbol 0, and 1, or #, and * may be used.

What is your opinion on the demand of an automatic windscreen wiper in a modern car?Very desirable 5 4 3 2 1 very undesirable

Measurement theorists say rating scale for such processes.

Measurement and scaling Measurement scales: the four levels from lowest

to greatest precision are: Nominal Scale (measurement). Ordinal Scale (measurement). Interval Scale (measurement). Ratio Scale (measurement).

(source: Neuman, W. Lawrence, page 134)

Nominal scale It also referred to as qualitative or categorical

measurement. Nominal scale is simply a system of assigning number

symbols to events in order to label them. Such numbers can not be considered to be associated

with an ordered scale. The numbers are just convenient labels for the

particular class of events (have no quantitative value). Nominal scale is least powerful level of measurement. It

indicates no order or distance relationship. Nominal scale simply describes differences between

things by assigning them to categories. It is useful to classify major subgroups of the population.

Nominal scaleExamples:(1) Gender: Male = 1, Female = 2.(2) Education level: SLC = 1, plus two = 2,

Bachelor = 3, Master = 4, PhD = 5.(3) Religious: Hindu = 1, Christian = 2,

Buddhist = 3, Muslim = 4.(4) Citizen: Nepalese=1, Chinese = 2, Indian = 3,

Pakistani = 4, Bhutanese = 5.Therefore, it is nothing but a system of giving name for different groups.

Ordinal scale Ordinal measurement provides a system for ranking

observations from least to most or most to least. For example, position of individuals finishing a race:

first, second, third, etc. Letter grades-A, B, C, D, F. Opinion measures that organizes observations in terms

of categories such as strongly agree = 1, agree =2, neither agree nor disagree =3, disagree = 4, strongly disagree = 5.

People may be asked to mark the number representing his/her degree of agreement or disagreement with the statement.

The numerals serve only as ranks for ordering observation from least to most in terms of characteristics measured. They do not provide information on the size of the difference between measurement categories.

Ordinal scale A students rank in his graduation class

involves the use of an ordinal scale. A statement of greater than or less than (or

equal to) is also acceptable. The numbers of this scale have only a rank

meaning.

Interval scale Interval measures everything the nominal and

ordinal scales do, plus it can specify the amount of distance between categories (e.g. Fahrenheit or Celsius temperature- 5 degree, 10 degree, 45 degree, 90 degree; IQ scores-95, 110, 125).

Arbitrary zero may be used in interval measures. They are just there to help keep score. For example, 0 degree Celsius is not the absence of all heat.

Ratio Scale Ratio measures do every thing all the other levels do,

plus there is a true zero. It makes possible to state relations in terms of

proportion or ratios. Example-money income, $10, $50, $100, $500, etc.;

years of formal schooling- 1 year, 10 years, 13 years, etc.; Age of a person-note that a 40-year-old has lived twice as long as a 20-year-old.

Because of arbitrary zeros of some interval measures, it can be confusing between interval and ratio scales. Example- a rise in temperature from 30 to 60 degrees is not really a doubling of the temperatures, although the numbers double, because zero degrees is not the absence of all heat.

Ratio scales Ratio scales represent actual amounts of variable.

Measure of physical dimensions such as weight, height, distance, length, volume, area, pressure, money amounts, etc are examples.

All statistical techniques are usable with ratio scale. Multiplication and division can be used with this scale

but not with other scales mentioned above. If the nature of the variables permit, the researcher

should use the most precise scale of measurement. The studies related to physical sciences demand the use

of ratio scales. The studies related to behavioral sciences limited to interval scale.

(source: Kothari, page-72)

Commonly used scalesLikert scale: Rensis Likert developed this scale in 1930s. Used to measure of a persons attitude in ordinal level. Likert scales usually ask people to indicate whether they

agree or disagree with a statement. Or people might be asked whether they approve or disapprove.

Likert scales need a minimum of two categories: agree and disagree.

Two choices gives only crude measure. Therefore it is better to use four or more (five in

general) categories. Number of categories can be increased by adding

strongly agree, some what agree, very strongly agree

Types of Likert scales Self-esteem scale: All in all, I am inclined to feel that I am a

failure: (1) almost always true (2) often true (3) sometimes true (4) seldom true (5) never true

A student evaluation of instruction scale: Overall I rate the quality of instruction in this

course as: Excellent Good Average Fair Poor.A market research mouthwash rating scale: Brand (X, Y) dislike completely, dislike

somewhat, dislike a little, like a little, like somewhat, like completely.

Likert scale Work group supervisor scale:

My supervisor: never seldom Some-times

often always

Lets members know what is expected of them

1 2 3 4 5

Is friendly and approachable 1 2 3 4 5

Treats all unit members as equals 1 2 3 4 5

Semantic differential scale Odgoods semantic differential scale

developed in the 1950s. Purpose was to provide an indirect measure of

how a person feels about a concept, object, or other person.

This technique measures subjective feelings toward something by using adjectives.

Most objectives have polar opposites. Example: light/dark, hard/soft, slow/fast, etc.

It uses polar opposite adjectives to create rating scale.

Semantic differential Semantic differential used for many purposes. Marketing research-it tells how consumers feel about a

product. Political advisors-use it to discover what voters think

about a candidate or issue. Therapist use it to determine how a client perceives

him or herself. To use semantic differential, a researcher presents

subjects with a list of paired opposite adjectives with a continuum of 7 to 11 points between them.

The subjects (raters) mark the spot on the continuum between the adjectives that express their feelings.

Example-how do u feel about the idea of divorce? Bad - - - - - - - - - Good

Constant sum scale This scale helps the researcher to discover proportions. The participant allocates points to more than one

attribute or property indicant, such that the total a constant sum usually 100 or 10.

Example- u have 100 points to distribute among the following characteristics of the X restaurant. Indicate the relative importance of each attribute:----Food quality---Atmosphere---Service---Price

----------------------------------100 Total

Graphic rating scale (GRS) GRS was originally created to enable

researcher to discern fine differences. Theoretically, an infinite number of ratings are

possible if participants are sophisticated enough to differentiate and record them.

They are instructed to mark their response at any point along a continuum.

Usually, the score is a measure of length from either end point.

The results may be ordinal, interval or ratio data.

Graphic rating scaleExample: how likely are u to recommend complete

care to others? (place an X at the position along the line that best reflects your judgment)

Very likely I--------------------------------I very unlikelyGive alternative with graphic. Use pictures, icons, or other visuals to

communicate with the rater and represent a variety of data types. Graphic scales are often used with children, whose more limited vocabulary prevents the use of scales anchored with words.

Ranking scales In such scale, participant directly compares two or

more objects and makes choices among them. Ranking scales can be grouped into two categories-

paired comparison & forced ranking. Paired comparison- participants can express attitudes

unambiguously by choosing between two objects. Ordinal data can be used.

Example-for each pair of two seat sports car listed, place a check (X) beside the one you would most prefer if you had to choose between the two.

-Mustang-BMW

The number of judgments required in a paired comparison is [(n) (n-1)/2], where n = number of objects to be judged.

Ranking scaleForced ranking scale: In such scale, a list of attributes to be ranked is provided. For example-rank the quality dimensions of a resident in

your order of preference. Place the number 1 next to the most preferred, 2 by the second choice, and so forth.-affordable-additional features-durable-external environment (location)-consideration of the principles of Bastu.

Measurement & Scaling Measurement MeasurementMeasurement and scaling Nominal scaleNominal scaleOrdinal scale Ordinal scaleInterval scaleRatio Scale Ratio scalesCommonly used scales Types of Likert scales Likert scale Semantic differential scale Semantic differential Constant sum scale Graphic rating scale (GRS) Graphic rating scaleRanking scales Ranking scale