Measurement and scaling

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5.1 Chapter summary

This chapter will introduce the concept of measurement and scaling. It will also provide discussion on the primary scales of measurement and go on to classify and describe both comparative and noncomparative scaling techniques. It will also discuss how an appropriate scaling technique be chosen in developing a right question. It will also focus on the concepts of validity and reliability in details.

5.2 Importance of measurement and scaling in marketing research

Like sampling we use measurement regularly in our daily lives. For example, if someone asks you of your favourite newspaper, your mind may create a list and you shall decide your favourite most newspaper from that. While deciding on that favourite newspaper your mind would have used several criteria such as your reading pattern, content of the newspaper, various other features such as writers involved, format, colour and pictures used, and columnists you prefer. Furthermore, your mind would have also told you the most preferred the second most preferred and even least preferred newspaper. The criteria your mind is using in deciding the favourite newspaper is called measurement. In research terms, measurement is nothing but the assignment of numbers or other symbols to characteristics of objects according to certain pre-specified rules. One of the important things to note here is that researchers do not measure objects but some characteristics of it. So in reality, researchers do not measure consumers but their perceptions, beliefs, attitudes, preferences and so on. The idea of assigning numbers can be helpful in two ways in accurate understanding of a phenomenon; (1) it allows statistical testing and (2) it helps facilitate easier communication as people have a clear idea with regard to what 10% or 20% means worldwide. Furthermore, numbers also provide objectivity in understanding a phenomenon. This added accuracy due to numbers is essential to effective decision making.

Scaling can be defined as an extension to the process of measurement. To successfully measure a phenomenon the researcher must gather appropriate raw data. The appropriateness of the raw data being collected depends directly on the scaling technique used by the researcher. Scaling can be defined as the process of assigning a set of descriptors or rules to represent the range of possible responses to a question about a particular phenomenon.52 To illustrate, consider that a retail store manager wishes to know consumers' preference regarding the store's brand image. The researcher develops a scale where in 1 = extremely favourable and 10 = least favourable. The consumers now can respond using these boundaries. So scaling in a way is placing respondents n a continuum with respect to their preference of the store's brand image. Using the scale researchers can measure consumer responses easily. Moreover, can carry out some statistical analysis and also provide results which can easily be understood and acted upon by the manager. As one can observe, measurement and scaling is highly important in marketing research due to the overall objectivity they provide.

5.3 Scales of measurement: fundamental properties

There are four primary scales of measurement: nominal, ordinal, interval and ratio. However, before we get into defining them and understanding their use in marketing research we need to focus on the basic properties which help us identify the scales. Drawing from mathematical theory, there are four scaling properties that a researcher can use in developing scales: assignment, order, distance and origin.

5.3.1 Assignment property

The assignment property is also referred as description or category property. It refers to the researcher's employment of unique descriptors, or labels to identify each object within a set. For example, a researcher asking a question 'are you going to buy a new music system in the next six months?' can assign two descriptors to record the response from consumers; namely yes or no. Similarly another question relating to more preferred brand by consumers with regard to music system can have various brand names mentioned as descriptors.

5.3.2 Order property

The second measurement scale property, order property, refers to the relative magnitude between the descriptors.53 The relative magnitude refers to three basic properties of any object mathematically. For example, if they are two objects A and B, there are three basic mathematical possibilities: (1) A is greater than B; (2) A is lesser than B; and (3) A is equal to B. Order property helps in identifying these properties.

5.3.3 Distance property

The distance property refers to a measurement scheme where exact difference between each of the descriptors is expressed in absolute.54 For example, if you bought 4 cans of a drink and your friend bought 2 cans of the same drink you bought two more cans than your friend. Normally, the distance property is restricted to those situations where the raw responses represent some type of natural numerical answer.

5.3.4 Origin property

The origin property is a measurement scheme wherein exists a unique starting point in a set of scale points. For the most part, the origin property refers to a numbering system where zero is the displayed or referenced starting point in the set of possible responses. Other such origin property responses could be 'dissatisfied', 'neither dissatisfied nor satisfied', and 'highly satisfied'.

When developing scale measurements, it is important to understand and remember that the more scaling properties that can be simultaneously activated in a scale design, the more sophisticated raw data. As a scale design includes more scaling properties, it increases the amount of raw data that can be collected by the researcher. Furthermore, it is interesting to note here that each scaling property builds on the previous one. For example, a scale which includes order property will have assignment property built in. Similarly, a scale which possesses distance property will have assignment and order property both. An origin property based scale will have all assignment, origin and distance properties included in itself. This will become further clear as we discuss the basic levels of scale.

5.4 Primary scales of measurement

As stated in the last section there are four primary scales of measurement: nominal, ordinal, interval and ratio. Each of these scales of measurement provides specific scaling properties (assignment, order, distance and origin).

Scales Measurement

5.4.1 Nominal scale

A nominal scale is the most basic of four scales of measurement. It refers to figuratively labelling scheme in which the numbers serve only as labels or tags for identifying and classifying objects. In a way, it caters to researcher's need for assignment property. For example, identifying each respondent by assigning them a number is nominal scaling. Nominal scale is also used in most sports with each player assigned a specific unique number. In marketing research nominal scale is used in identifying respondents, products, attributes and so on. Nominal scale is also used for classification purposes in marketing research where scaled numbers serve as labels for classes or categories. For example, nominal scale is used in gender classification. The numbers in nominal scale do not reflect the amount of the characteristics possessed by the objects. For example, a marathon runner with a number 4500 does not mean he is superior to another marathon runner with a number 7200. The only permissible operation on the numbers in a nominal scale is counting. Only a limited number of statistical processes, such as percentages, mode, chi-square and binominal tests can be carried out using nominal scale based data.

5.4.2 Ordinal scale

The structure of ordinal scale activates both the assignment and order scaling properties. This scale allows respondents to express relative magnitude between the answers to a question. In simple words, the ordinal scale allows respondents to order their response in a hierarchical fashion. At the start of this chapter we discussed the example of favourite newspaper. That example is an ordinal scale where a respondent can determine whether an object has more or less of a characteristic than some other object. Thus, ordinal scale provides relative magnitude however cannot provide relative distance. Common examples of ordinal scale include ranking of sportsman, ranking of brands, quality rankings and organization rankings in business magazines, several socioeconomic characteristics such as occupational status. In marketing research, ordinal scale is used to create various lists such as fortune 500 list of top global companies, best 100 companies to work with and so on. Various statistical analysis techniques can be used to describe and infer information from ordinal scale including percentile, mean, and rank-order correlation.

5.4.3 Interval scale

An interval scale possesses assignment, order and distance properties. So, an interval scale provides a researcher all the information of an ordinal scale, and at the same time, allows comparison between different objects. For example, in ordinal scale when newspapers are ranked from 1 - 5 it is impossible to define the preference distance between the newspapers. In simple words, we cannot possibly say that the difference of preference between newspaper 1 and newspaper 2 as well as newspaper 2 and newspaper 3 is the same. However, using interval scale we can actually provide the preferential difference between the two objects (newspapers). This kind of scale is most appropriate when the researcher wants to collect state-of-behaviour, state-of-intention or certain kind of state-of-being data.55 For example, if we ask two respondents about how much time do they spend reading a newspaper everyday, we can not only identify who spends more or less time in comparison to other but also we can know the exact difference in minutes (or other time interval) between the two respondents. Adding to our earlier example of best 100 companies to work with, if the researchers had asked the respondents to rate the companies on a rating scale it would have provided the distance between the companies and more meaningful information can be obtained. In an interval scale zero point (origin) is not fixed. Both origin and the units of measurement in interval scale are arbitrary. In marketing research, ratio scale is used to measure attitudes, opinions, index numbers and so on. All technique which can be applied to nominal and ordinal data can be used in interval scale measurement. Furthermore, many other statistical techniques, can be employed to analyse interval scale related data including range, mean, standard deviation, product-moment correlation, t-tests, ANOVA, regression and factor analysis.

5.4.4 Ratio scale

A ratio scale contains all the four scaling properties (assignment, order, distance and origin) in one. In other words, it possesses all the properties of nominal, ordinal, and interval scales and in addition an origin. Thus, in ratio scale, we can identify or classify objects, rank the objects, and can compare intervals or differences. Ratio scale is the most sophisticated of all scales and it enables the researcher not only to identify the absolute differences between each scale point but also to make absolute comparisons between the responses. It is also meaningful to compute ratios of scale value. For example, the difference between 10 and 15 and is the same as 30 and 35. Furthermore, 30 is 3 times as large as 10 in an absolute sense. Regular examples concerning ratio scale include weight, height and age. In marketing research, ratio scale is used when measuring variables such as sales, cost, customer numbers and so on. All statistical techniques can be applied to ratio scale based data. This includes specialised statistics such as geometric mean, harmonic mean and coefficient of variation.

5.5 Comparative and non-comparative scaling

Researchers have identified several important characteristics for developing high quality scales. The high quality scales require (a) understanding the defined problem; (b) establishing detailed data requirements; (c) identifying and developing the constructs and (d) understanding the complete measurement scale. The above stated key features can assist marketing researchers in developing a reliable and valid scale.

As you would have observed from all of the earlier chapters that one of the major aims for managers in today's world is to understand their consumers' and market's reaction to various stimuli. This stimuli results in a specific set of reaction and researchers are mostly given task to measure and interpret the reaction prior to it occurs. Managers are interested in knowing consumers' attitudes, beliefs, preferences, as well as competitive reactions among other important market phenomena. In this section we shall discuss how researchers can take on the task of measurement using various scaling techniques.

The scaling techniques regularly employed in marketing research can be classified into two basic strands: (a) comparative scaling and (b) non-comparative scaling. As the name suggests comparative scaling involves direct comparison of stimulus objects with one another. For example, managers are generally interested in knowing consumer preference regarding their brand in comparison to a competitor's brand. A researcher can then ask question such as what of the two brands consumer prefers and this would provide the manager a clear idea of what consumer preferences are. There are several techniques which are used in building comparative scale such as paired comparison, rank order, constant sum scale, and q-sort.

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