Measurement and Scales

Transcription

1 Topic 5 Measurement and Scales LEARNING OUTCOMES By the end of this topic, you should be able to: 1. Define conceptualisation and operationalisation ; 2. Explain the four types of scales used in research; 3. Prescribe the measures of quality used; and 4. Assess the sources of measurement errors. INTRODUCTION This topic begins with an explanation of conceptualisation and operationalisation. The definition of concepts and the methods of measuring the concepts will help the researcher to determine the methods of collecting and analysing data. The process of defining concepts is important in a research to ensure that readers have the same understanding as the researcher; this will prevent any confusion or misunderstanding by readers in interpreting the meaning of the concept. Once the concept is defined, it is necessary to identify the methods to measure the concept. Measurement of the variables is an integral part of the research process and is an important aspect of a research design. Unless the variables are measured in some way, the researcher will not be able to test the hypothesis and find answers to complex research issues.

2 TOPIC 5 MEASUREMENT AND SCALES CONCEPTUALISATION In a research, we use concepts that vary in levels of abstraction; from simple concepts such as shoes, table and height, to the most abstract such as satisfaction, marketability, love and stress. It is necessary to clarify the meaning of the concepts used in order to draw meaningful conclusions about them. In daily life, we communicate through a system of vague agreements on the use of terms. In many cases, other people do not exactly understand what we wish to communicate and the meaning of the terms we use. This will cause conflict but we somehow get the word through. In the scientific research, however, this scenario is not acceptable; scientific research cannot operate in an imprecise context. Conceptualisation is the mental process of making imprecise notions (mental images-conceptions) into more specific meanings to enable communication and eventual agreement on the specific meanings of the terms. We specify what we mean when we use a particular term. The process of conceptualisation will produce specification of the indicators of what we have in mind on the concept we are studying. For example, the concept of compassion may comprise different kinds of compassion. There is compassion towards humans or animals. In addition, compassion may be an act or a feeling. It could also be seen in terms of forgiveness or pity. The grouping of the concept is known as dimension. Thus, conceptualisation involves both specifying dimensions and identifying the various indicators for each. The process of refining abstract concepts is called definition. By defining a concept, we derive its meaning to draw conclusions. The concepts are specified using the following: (a) (b) Nominal Definition A working definition for the purpose of an inquiry in assigning a meaning to a term. It helps to focus on how to strategise observation but not to make the actual observation. Operational Definition How the concept is measured by specifying what to observe, how to observe and how to interpret the observation. Operational definition is undertaken to measure a concept.

3 58 TOPIC 5 MEASUREMENT AND SCALES Conceptualisation may differ among researchers but definitions are specific and unambiguous. Therefore, even if one disagrees with the definitions, he has a good idea of how to interpret the results because the definitions are clear and specific. ACTIVITY 5.1 How do you define the concept of socio-economic status in terms of nominal definition and operational definition? 5.2 OPERATIONALISATION Once the concepts have been identified, the next step is the process of developing the specific research procedures/operations that will result in empirical observations representing those concepts in the real world. The process of linking a conceptual definition to a specific set of measurement techniques or procedures is called operationalisation. These are procedures to measure a concept either through a collection of data from a survey research or by conducting observation research. The following example explains this. Example 5.1 Operationalising the concept of an individual/person: Variable Individual Attributes Gender characteristics (male/female) Nominal Definition An individual is either a male or female Operational Definition If B defines/represents an individual Mapping out attributes: 1 represents an individual who is a male 0 represents an individual who is a female Thus, for B1, B2, B3, B4, B5, B6: B1 is measured as 1 if B1 is a male B2 = 0 if B2 is a female B3 is measured as 1 if B3 is a male B4 = 0 if B4 is a female B5 = 1, B6 = 0

4 TOPIC 5 MEASUREMENT AND SCALES 59 To be meaningful, the measurement must follow rules that specify procedures of assigning numbers to objects of reality. 5.3 VARIABLES At the theoretical level, concepts and constructs are used; whereas at the empirical level, the constructs are transformed into variables. Thus, variables are the construct or property to be studied. A variable consists of logical groupings or sets of attributes/values. An attribute is the intensity or strength of attachment to attitudes, beliefs and behaviours associated with a concept. It is a characteristic or quality of a concept/symbol to which numerals or values are assigned. Two important characteristics of a variable are: (a) Attributes composing the variable must be exhaustive. (b) Attributes composing a variable must be mutually exclusive. Below are five types of variable: (a) (b) (c) (d) (e) Dependent DV (criterion variable) is the variable of primary interest to the researcher. The goal is to understand and describe the dependent variable. Independent IV (predictor variable) influences the dependent variable either in a positive or a negative way. The variance in the dependent variable is accounted for by the independent variable. Moderating MV is a second independent variable and has a strong contingent contributory effect on the original stated IV-DV relationship. Extraneous EV is a random variable that has little impact on the relationship. Intervening IVV shows the link between IV and DV; it acts as a DV with respect to an IV and as an IV with respect to a DV. ACTIVITY 5.2 What are the relationships between IV, DV and IVV? How does the inclusion of MV change or affect the relationship?

5 60 TOPIC 5 MEASUREMENT AND SCALES 5.4 MEASUREMENT The concepts used in a research are divided into objects or properties. Objects are things such as shirts, hands, computers, shoes, books and papers. Things that are not so concrete such as genes, nitrogen, attitudes, stocks and peer-group pressure are also included as objects. Properties or attributes, on the other hand, are the characteristics of the objects. An individualês physical characteristics are indicated in terms of weight, height and posture. An individualês psychological attributes are shown in terms of attitudes and intelligence. The social characteristics of the person include leadership ability, social status or class affiliation. The object and the characteristics can be measured in a research study. Measuring the properties indicators of the objects makes the measurement of the objects or characteristics more sensible. It is easy to see that A is older than B, and C participates more than D in a group discussion. Indicators such as age, working experience and number of reports done can be easily measured. Hence, they are so commonly accepted that one considers the properties to be observed directly. However, properties such as an individualês ability to solve problems, motivation for success, political affiliation and sympathetic feelings are more difficult to measure. Since they cannot be measured directly, they have to be gauged by making inferences to the presence or absence of certain behaviour or attitude by observing some indicators or pointer measurement. Essentially, the measuring process consists of giving numbers or symbols to empirical events based on a set of rules. The process of making the measurement involves three steps: selecting observable objects or properties; using numbers or symbols to represent aspects of the events or objects; and applying a mapping rule to connect the observation to the symbol. Thus, some mapping rules are devised to transfer the observation of the property indicators using these rules. The accepted rules in using numbers to map the observation of the indicators include: (a) Order of numbers One number is greater than, less than or equal to another number; (b) Difference between numbers The difference between any pair of numbers is greater than, less than or equal to the difference between any other pair of numbers; and (c) The number series has a unique origin indicated by the number zero.

6 TOPIC 5 MEASUREMENT AND SCALES 61 SELF-CHECK 5.1 Why is it necessary to define the concepts of research clearly? Level of Measurement Once the operationalisation of the concepts has been established, the concepts need to be measured in some manner. A scale is a tool or mechanism by which individuals are distinguished based on the variables of interest in the study. The scale or tool could be gross or fine-tuned. A gross scale broadly categorises individuals on certain variables. A fine-tuned scale differentiates individuals on the variables with varying degrees of sophistication. Using these rules of order, distance and origin of the data are classified into the following types of scales: (a) Nominal Measure (Scale) Nominal data is widely used in social science research. It is characterised by a set of categories that are exclusive and exhaustive. When nominal data is used, the only arithmetic operation that can be done is the numeration of members in each group. If numbers are used to identify categories, then they are recognised as labels only and have no quantitative value. Nominal measures are the least useful form of measurement because they suggest no order or distance relationship and have no arithmetic origin. Moreover, the measurements have no information on the varying degree of the property measured. Although nominal data is weak, it is still useful. In an exploratory study of which the objective is to uncover relationship rather than secure precise measurements, nominal data is valuable. Studies to provide insights into important data patterns can be easily accomplished using nominal data. SELF-CHECK 5.2 Give three examples of nominal scale.

7 62 TOPIC 5 MEASUREMENT AND SCALES (b) Ordinal Measure (Scale) An ordinal scale not only categorises the variables in a way that denotes differences among the various categories, it also rank-orders the categories in a meaningful way. The ordinal scale would be used for an ordered series of relationship. The preference would be ranked and numbered 1, 2 or 3. The ordinal scale helps the researcher to determine the percentage of each preference level first preference, second preference and so on. The ordinal scale gives more information than the nominal scale. It goes beyond giving difference in categories and on how respondents can distinguish them by rank ordering. Do take note that the ordinal scale does not give any indication of the magnitude of the differences among the ranks. The following example explains this. Example 5.2 Please indicate your preference among the types of examination designs below by using the following scales: 1. Least Preferred 2. Preferred 3. Most Preferred Types of Questions Ranking of Preference (a) Objective questions 3 (b) Subjective questions 1 (c) Combination of both 2 (c) Interval Measure (Scale) The interval scale allows the researcher to perform arithmetical operations on the data and to measure the distance between any two points on the scale. It allows the calculation of means and standard deviations of the responses on the variables. The interval scale not only grouped individuals according to certain categories and indicates the order of the groups, but also measures the magnitude of the differences among the individuals. The following example explains this.

8 TOPIC 5 MEASUREMENT AND SCALES 63 Example 5.3 Using the scale below, please indicate your choice for each of the items that follow, by circling the number that best describes your feeling. 1. Strongly disagree 2. Disagree 3. Neutral 4. Agree 5. Strongly Agree (a) The facilities here are adequate (b) The services provided are sufficient (c) The people here are friendly (d) The prices here are cheap The interval scale has equal magnitude of differences in the scale point. The magnitude of difference represented by the space between 1 and 2 on the scale is the same as the magnitude of difference represented by the space between 4 and 5, or between any other two points. Any number can be added to or subtracted from the numbers on the scale. Assuming the magnitude of the difference is still retained, if a 6 is added to all five points on the scale, the interval scale will become 6 to 11; the magnitude of the difference between 7 and 8 is still the same as the magnitude of the difference between 10 and 11. Thus, the origin or the starting point could be any arbitrary number. The interval scale taps the differences, the order and the equality of the magnitude of the differences in the variable. It is a more powerful scale than the ordinal and nominal scales. It allows the measuring of the central tendency, mean, dispersion, range, standard deviation and variance. (d) Ratio Measure (Scale) The disadvantage of using the interval scale is related to its arbitrary origin. This can be overcome by using the ratio scale as it has an absolute origin or zero point, which is a meaningful measurement point. So, the ratio scale not only measures the magnitude of the differences between points on the scale but also taps the proportions of the differences. The ratio scale is the most powerful of the four scales because it has a unique zero origin and subsumes all the properties of the other four scales (see Table 5.1).

9 64 TOPIC 5 MEASUREMENT AND SCALES Scales Table 5.1: Properties of the Four Measures (Scales) Highlights Difference Order Distance Unique Origin Measure of Central Tendency Measure of Dispersion Nominal Yes No No No Mode Ordinal Yes Yes No No Median Interval Yes Yes Yes No Ratio Yes Yes Yes Yes Arithmetic mean Arithmetic/ geometric mean Semi interquartile range. Standard deviation, variance, coefficient of variation. Standard deviation, variance, coefficient of variation. Example 5.4 (c) How many books have you read in the last two weeks? (d) How many times have you visited a shopping complex in the last month? The measures of central tendency of the ratio scale could be either the arithmetic or the geometric mean; and the measure of dispersion could be the standard deviation, variance or the coefficient of variation. ACTIVITY What is the meaning of measurement in a research study? Give three steps of the measurement process. 2. What is the level of measurement concept based on?

10 TOPIC 5 MEASUREMENT AND SCALES 65 SELF-CHECK 5.3 What are the essential differences among the nominal, ordinal, interval and ratio scales? 5.5 SCALING TECHNIQUES Four different types of scales are used to measure the operationally defined dimensions and elements of a variable. It is necessary to know the methods of scaling; the process of assigning numbers or symbols to elicit the attitudinal responses of subjects towards objects, events or persons. There are two main categories of attitudinal scales rating scale and ranking scale Rating Scales Rating scales have several categories and are used to elicit responses with regard to the object, event or person studied. The following are some examples of rating scales often used in social science research. (a) Dichotomous Scale (Simple Category Scale) This dichotomous scale is used to elicit a Yes or No response; a nominal scale is used to measure the response. Do you purchase product A? Yes No

11 66 TOPIC 5 MEASUREMENT AND SCALES (b) Category Scale (Multiple Choice - Single Response Scale) The category scale uses multiple items to elicit a single response; the nominal scale is also used to measure the response. Where did you purchase your tickets? (i) Train station (ii) Grocery outlet (iii) Fast-food restaurant (iv) Petrol station (v) Others (c) Category Scale (Multiple Choice - Multiple Response Scale) Among the easy reading magazines listed below, which ones do you like to read? (i) Time (ii) ReaderÊs Digest (iii) National Geographic (iv) Far Eastern Economic Review (v) Vogue (vi) Family (vii) Others (specify) (d) Summated Rating Scale One of the most popular application of summated rating scale is the Likert Scale. The Likert scale is designed to examine how strongly subjects agree or disagree with statements on a five-point scale. The responses over a number of items tapping a particular concept or variable are then summated for every respondent. This is an interval scale and the differences in the responses between any two points on the scale remain the same.

12 TOPIC 5 MEASUREMENT AND SCALES 67 Usage of computer systems has helped to improve the performance of students. (i) Strongly Agree 1 (ii) Agree 2 (iii) Neither agree nor disagree 3 (iv) Disagree 4 (v) Strongly disagree 5 (e) Semantic Differential Scale Several bipolar attributes are identified at the extremes of the scale and respondents are asked to indicate their attitudes towards a particular individual, object or event on each of the attributes. The semantic differential scale is used to assess respondentsê attitudes towards a particular brand, advertisement, object or individual. The responses are plotted to obtain a good idea of their perceptions and are measured as an interval scale. How do you feel about the idea of war? Bad Good Fair Unfair Clean Dirty Modern Traditional (f) Numerical Scale The numerical scale is similar to the semantic scale, with the difference that numbers on a five-point or seven-point scale are provided, with the bipolar adjectives at both ends. The scale used is an interval scale. How do you feel about the idea of war? Bad Good Fair Unfair Clean Dirty Modern Traditional

13 68 TOPIC 5 MEASUREMENT AND SCALES (g) Fixed or Constant Sum Scale In this type of scale, the respondents are asked to distribute a given number of points across various items. This scale uses the ordinal measure. In choosing the accommodation facility, indicate the importance to attach the following five aspects by allotting points for each to a total of 100. Room space Room décor Cleanliness Price Housekeeping service Total points 100 (h) Staple Scale The staple scale provides simultaneous measures of the direction and intensity of the attitude towards the items under study. The characteristics of interest to the study are placed at the centre and a numerical scale ranging from +3 to 3 are put on either side of the item. The scale gives an idea on the gap of the individual response to the stimulus. It does not have an absolute zero, thus it is an interval scale. Please indicate how you would rate the restaurant with respect to each of the characteristics mentioned below, by circling the appropriate number. Services Cleanliness Prices Ranking Scale The respondents make comparisons between two or more objects/items and make choices among them (ordinal in nature). Often, the respondents are asked to select one as the best or the most preferred. This ranking may be conclusive if there are only two choices to be compared. If there are more than two choices, it may result in ties, which may not be helpful. Suppose that 35% of the respondents choose product A, 25% choose product B and 20% choose each of

14 TOPIC 5 MEASUREMENT AND SCALES 69 the product C and D as of importance to them. Which product is the most preferred? It is not acceptable to conclude that product A is the most preferred since 65% of the respondents did not choose that product. This ambiguity can be avoided by using alternative methods of ranking. (a) Paired Comparison In using this scale, the respondents are asked to choose among a small number of objects; two objects at a time. This helps to assess preferences because the respondents can express attitudes unambiguously by choosing between two objects. The number of paired comparisons that will be judged by the respondents for n objects is {(n)(n 1)/2}. If n = 4, then the number of paired comparisons will be {(4)(4 1)/2 = 6}. The greater the number of objects, the greater the number of paired comparisons that will be presented to the respondents. This will tire the respondents mentally. This technique is good if the number of objects is small. Example 5.5 For each pair of national parks, place a check beside the one you most prefer if you had to choose between the two. (i) (ii) Taman Negara Malaysia Endau Rompin National Park Mulu National Park Sabah National Park (iii) Taman Negara Malaysia Sabah National Park (iv) Mulu National Park Endau Rompin National Park (v) Taman Negara Malaysia Mulu National Park (b) Forced Choice This choice enables the respondents to rank objects relative to one another, among alternatives provided. This is easier for the respondents, especially if the number of choices to be ranked is limited in number.

15 70 TOPIC 5 MEASUREMENT AND SCALES Example 5.6 Please rank the following daily newspaper you would like to subscribe in order of preference, assigning 1 for the most preferred choice and 5 for the least preferred. (i) New Strait Times (ii) Utusan Malaysia (iii) The Star (iv) Malay Mail (v) Harian Metro (c) Comparative Scale This scale gives a point of reference to assess attitudes towards the current object, event or situation under study. The technique is ideal if the respondents are familiar with the standard. Example 5.7 Compared to your previous visit to this holiday destination, your present visit is: More enjoyable About the same Less enjoyable MEASUREMENT QUALITY A good measurement gives an accurate counter or indicator of the concept that we want to measure. It must also be easy and efficient. A precise measure indicates fineness or distinction between the attributes of the variable. Although a precise measure is superior to an imprecise measure, but precision is neither always necessary nor desirable. It is important to note that precision does not mean accuracy. An accurate measure indicates how close the measure is to the real thing/value. Measurements are subject to random and systematic biases or errors; hence in research one cannot get 100% accuracy. The test of reliability and validity of the measurement becomes important.

16 TOPIC 5 MEASUREMENT AND SCALES Reliability, Validity and Practicality Three major criteria are often used to determine the quality of a measurement tool: reliability, validity and practicality. Reliability and validity are associated with how concretely connected the measures are to the constructs because perfect reliability and validity are impossible to achieve. It is important to establish the truthfulness, the credibility or the believability of findings, with no random or systematic errors. Thus, reliability and validity are considered as the scientific criteria of the measurement. Reliability is related to the consistency of the measurement, which means the recurrences are measured with an identical method or under very similar conditions. If a particular technique is applied repeatedly to the same object and yields the same result each time, then this indicates consistency. The criteria take into account the degree to which the measurement is free of random error. Reliability can be assessed by posing the following questions (Easterby-Smith et al., 2002): (a) (b) (c) Will the measures give the same results on other occasions? Will similar observations be reached by other observers? Is there transparency in how sense was made from the raw data? Validity is concerned with truthfulness a match between a construct, or the way the idea is packaged in a conceptual definition and measures. It reflects how well an idea about reality fits with actual reality the extent to which the empirical measurement adequately reflects the real meaning of the concept. In other words, it measures what it is supposed to reflect. Major threats to validity include: (a) (b) History If certain events or factors that have impact on the relationships occur unexpectedly while the study is being conducted, and this history of events confounds the cause-effect relationship between the variables, then the validity of the results may be affected. Maturation Effects The time passage of the relationship can influence the cause and effect among variables and cannot be controlled. The maturation effects are a function of processes operating within the respondents as a result of the time passage. Examples of maturation processes include growing older, getting tired, getting bored and feeling hungry.

17 72 TOPIC 5 MEASUREMENT AND SCALES (c) (d) Testing Effects A pre-test given to the subjects in order to improve the instruments used may actually have effects on the actual test or post-test; the very fact that the respondents were exposed to the pre-test might influence their responses. Instrumentation Effects The effects on validity may occur because of changes in the measuring instrument between pre-test and post-test. Example 5.8 Relationship between reliability and validity are shown using this example: You use a bathroom scale to measure your weight. If the scale measures your weight correctly, then the scale as a measuring tool is both reliable and valid. If the scale is tampered and consistently gives an overweight of 6 kg every time it is used, it is reliable but not valid. If the scale gives an erratic weight reading from time to time, it is neither reliable nor valid. Practicality is correlated with the operational requirement of the measurement process. The criterion of practicality involves the aspects of economy, convenience and interpretability. To achieve a high degree of reliability and validity, one may require high expenditure that may be beyond the budget for research; thus there has to be some form of trade off between the ideal measures and the budget. Data collection techniques are always dictated by budget constraints and other economic factors. The measuring device should also be easy to administer; the design of the instruments used should allow easy comprehension and have complete and clear instructions. If the instrument is to be administered by people other than the designer, then it must also be easy to interpret. 5.7 SOURCES OF MEASUREMENT ERRORS In an ideal situation, a study design should be able to control the precision and ambiguity of the measurement. However, an ideal situation is impossible. Therefore, the next best thing to do is to go for the reduction of errors. The researcher should be aware of the sources of potential errors such as systematic and random errors. (a) Respondent as an Error Source These are errors resulting from the differences in the responses due to the nature of the individual respondents. Some responses related to the

18 TOPIC 5 MEASUREMENT AND SCALES 73 characteristics of the respondents may be anticipated and may be quite stable but other effects of the characteristics may be less obvious. An individual who has had a traumatic experience may have a different outlook of a certain situation. The respondent may be reluctant to state his views or feelings, or may not have much knowledge of the situation and he may be giving guesses as his response. Other factors that may affect the respondents like fatigue, boredom, anxiety, impatience and variations in moods may also affect the responses. (b) (c) (d) Situational Factors Any condition that may place strains on the interview can have serious effects on the interview-respondent rapport. If the interview is carried out in the company of other people, friends, relatives and children, the responses can be distorted by others joining in, distractions or by others just merely being there. Some may feel they are being intruded upon and thus may not willingly give their responses. Measurer as an Error Source If the interviewer or enumerator changes the wordings, paraphrases or reorders the sequences of the questions, these could lead to errors. The first impression of the interviewer to the respondent can introduce bias. The voice tone of the interviewer can encourage or discourage certain replies. The failure of the recorder to record the full responses may affect the findings. When data is not entered correctly for analysis or a faulty statistical analysis is used by the researcher, it may introduce further bias. Instrument as an Error Source If the instrument used is defective, two major sources of distortions can occur. The first, which uses complex wordings, syntax and jargon beyond the comprehension of the respondents, can lead to confusion and ambiguity. Questions that violate the criteria of a good survey design will cause respondents to give biased answers. Leading questions, ambiguous meanings and multiple questions are some examples of sources of errors in the instruments. The second source of errors related to the instrument is the incomplete inclusion of the content items. It is impossible to include all potentially important issues related to a problem. Although the instruments may take into account the majority of the issues, there could be some that are left out on purpose.

19 74 TOPIC 5 MEASUREMENT AND SCALES SELF-CHECK 5.4 What are the four major sources of measurement errors? Give an example of how each source can affect the measurement results in a face-to-face interview. SELF-CHECK 5.5 Tick True or False for each statement below. No. Question True False 1. Time dimension is a basis for classifying research design. 2. In the most literal sense, what are measured are the indicators. 3. An interval scale is defined as one that has both order and distance but no unique origin. 4. If a measure is reliable, it must be valid. 5. A nominal measure can only have two categories. 6. Classifying someone as employed or unemployed treats employment as a nominal variable. Choose the correct answer 1. Which of the following is an incorrect classification of scale? (a) Attitude measured on an interval scale (b) Weight measured in ratio scale (c) Gender measured using ordinal scale (d) Position in an examination using ordinal scale

20 TOPIC 5 MEASUREMENT AND SCALES Measurement should meet the criteria of practicality, which is typically defined as: (a) Economy, accuracy and interpretability (b) Convenience, economy and interpretability (c) Economy, consistency and interpretability (d) Convenience, economy and consistency 3. A researcher must decide in the process of operationalisation: (a) What to measure (b) What level of measurement to use (c) How to measure (d) All of the above In scientific research, the measurements used must be precise and controlled. In the process of measurement, what is actually done is measuring the properties of the objects rather than the objects themselves. To be exact, what are measured are the indicants of the properties. Measurements usually use some type of scale to classify or quantify the data collected. Four types of scales are used in increasing order of power: nominal, ordinal, interval and ratio. The nominal scale highlights the differences by classifying objects or persons into groups, and provides the least amount of information on the variable. The ordinal scale provides some additional information by rank-ordering the categories of the nominal scale. The interval scale also provides users with information on the magnitude of the differences in the variable. The ratio scale indicates the magnitude and proportion of the differences.

21 76 TOPIC 5 MEASUREMENT AND SCALES The data becomes more precise when we move from the nominal to the ratio scale and allow the use of more powerful statistical tests. Sound measurement must meet the criteria of validity, reliability and practicality. Validity reveals the degree to which an instrument measures what it is supposed to measure. A measure is reliable if it provides consistent results each time it is used. Reliability is a partial contributor to validity but a measurement tool may be reliable without being valid. A measure meets the criteria of practicality if it is economical, convenient and interpretable. Conceptualisation Dichotomous scale Internal measure Measurement Nominal definition Nominal measure Ordinal measure Operational definition Operationalisation Ranking scale Ratio measure Staple scale Variables