Measurement & Scaling (Unit2)

 

Measurement

 ·         Measurement may be defined as the assignment of numbers to characteristics of objects, persons, states, or events according to rules.

·         Measurement is the mapping of the values on a set of numbers.

 

 

·         We do not measure a person or object but only its characteristics - age, height, weight etc.

·         The number does not necessarily mean numbers that are added or subtracted, multiplied or divided but numbers are used as symbols to represent certain characteristics.

·         The critical aspect is to decide how numbers are to be assigned to the characteristics to be measured.

 

Measurement & Concepts

A concept is simply an invented name for a property of an object, person, state or event. Many concepts or constructs signify a group of things like market share, attitude, brand loyalty etc.

Many concepts do not have such easily observed physical referents e.g. attitude, product image, social class etc. Attention must be given to define precisely what is meant by a concept.

 

Two' approaches are necessary to define a concept. 

1. conceptual definition       2. Operational Definition  

 Conceptual definitions - defines the central idea or absence of the concept. Or defines in terms of other concepts. It must be able to distinguish it from similar other concepts. Eg Brand Loyalty from repeat purchase behaviour.

 

Operational Definition- describes the activities the researcher must complete in order to assign a value to the concept.

 

 Reasons of Measurement Error 

1. Respondent Characteristics - social class, intelligence will differ among genders, subculture, or nationality.

2. Short term characteristics - hunger, thirst, fatigue, anger.

3. Situational Characteristics - home/ mall, alone / with spouse, temperature, heat, light, noise, interruption, whether.

4. Researcher factors - gender, age, style , looks

5. Instrumental Factors - unclear instructions, ambiguous questions, confusing terms, 

6. Characteristics of the response process.-  Checking the wrong responses or vice versa.

7. Mistakes in interpreting, coding, tabulating.

 

 

Types of Measurement Scales used in Research

There are four different scales of measurement used in research; nominal, ordinal, interval and ratio. The rules used to assign numerals objects define the kind of scale and level of measurement. A brief account of each scaling type is given below;

1.      Nominal Scales: Nominal scale is the simplest form of measurement.

·         Used to categorize objects or events

·         It serves only as a label for a class or category.

·         A variable measured on a nominal is one which is divided into two or more categories,

For example, gender is categorized as male or female,

A question as to whether a family owns an iPhone can be answered ‘Yes’ or ‘No’.

It is simply a sorting operation in which all individuals or units or answers can be placed in one category or another (i.e. the categories are exhaustive).

The essential characteristic of a nominal scale is that in terms of a given variable, one individual is different from another and the categories are discriminate (i.e. the categories are mutually exclusive). This characteristic of classification if fundamental to all scales of measurement.

·         Nominal scales that consist only two categories such as female-male, agree-disagree, aware-unaware, yes-no, are unique and are called dichotomous scales. Such dichotomous nominal scales are important to researchers because the numerical labels for the two scale categories can be treated as though they are of interval scale value.

·         Other examples are Social Security nos., number assigned to players, In BR for identifying respondents, brands, stores.

2.      Ordinal Scales: Ordinal scales have all the properties of a nominal scale, but, in addition, categories can be ordered along a continuum, in terms of a given criterion.

It is a ranking scale in which numbers are assigned to objects to indicate the relative extent to which some characteristic is possessed.

Given three categories A, B and C, on an ordinal scale, one might be able to say, for e.g., that A is greater than B and B is greater than C.

If numerals are assigned to ordinal scale categories, the numerals serve only as ranks for ordering observations from least to most in terms of the characteristic measured and they do not indicate the distance between scale that organizes observations in terms of categories such as high, medium and low or strongly agree, agree, not sure, disagree, and strong disagree.

Other examples are – ranking of teams in tournaments, socioeconomic class, and occupational status.

3.      Interval Scales: Interval scales incorporate all the properties of nominal and ordinal scales and in addition, indicate the distance or interval between the categories. In formal terms one can say not only that A is greater than B and B is greater than C but also that (A-B)=(B-C) or (A-C)=(A-B)+(B-C).

In an interval scale is one where there is no absolute zero point.

Examples of interval scale include temperature scale. Or in marketing when the response is Agree strongly, agree fairly, agree, disagree, disagree strongly.

Because in an interval scale there is no absolute zero point it can be placed anywhere along a continuum.

4.      Ratio Scales: It allows the researcher to identify or classify objects, rank order the objects and

It has a true zero point or a point at which the characteristic that is measured is presumed to be absent. Examples of ratio scales include, weight, length, income, expenditure and others. In each there is a concept of zero income, zero weight, sales, costs, market potential, market share etc.

It possesses all the properties of nominal, ordinal and interval scales.

 

Each of the above four types of scales have a unique method of measurement. Both nominal and ordinal scales consist of discrete number of categories to which numbers are assigned. Thus, a variable such as number of families owning a BMW or iPhone can only take values of 0, 1, 2 3 4 etc. It cannot have values such as 1.5 or 2.5 as the units are integers and indivisible. But interval and ratio scales take any value between two integers, as the variables are continuous. For example, given any ages however close, it is possible to find a third which lies in between. Interval and ratio scales are superior to normal and ordinal scales and a wealth of statistical tools can be employed in their analysis. The different statistical tools are related to these different measurement  scales in research, in that there is usually a correspondence between mathematical assumptions of the statistical tool and the assumptions of the scale of measurement. Care must be always taken to match the tools used with the scale of measurement of variables and to use a method which implies a higher scale measurement than   the variable allows.