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Measurement

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MEASUREMENT:
Measurement is the heart of scientific discipline. It is the process of assigning numbers to objects or observations, the level of measurement being a function of the rules under which the numbers are assigned.
According to Zikmund, “Measurement is the process of describing some property of a phenomenon of interest, usually by assigning numbers in a reliable and valid way”.
In our daily life we are said to measure when we use some yardsticks to determine weight, height or some other features of a physical object. We also measure when we judge how well we like a song, intelligence, achievement, attitude, perception regarding quality. We, thus, measure physical object as well as abstract concepts. Measurement is a relatively complex & demanding task, especially so when it concerns qualitative or abstract phenomena.
So, technically speaking, measurement is a process of mapping aspects of a domain onto other aspects of a range according to some rule of correspondence. It is a collection of quantitative data.
TYPES OF MEASUREMENT:
1) Nominal measurement: All qualitative measurements are nominal, regardless of whether the categories differ from one another only in names. Nominal measurements represent the most elementary level of measurement in which values are assigned to an object for identification or classification purposes only. In nominal level of measurement, the categories differ from one another only in names. In other words, one category of a characteristic is not necessary higher or lower, greater or smaller than other category. Sex (male & female), religious (Muslim, Hindu, christen etc.) are the example of the nominal measurement. In measure scale, nominal level is the lowest or weakest level of measurement & the resulting data are nominal data. This makes it impossible to conduct standard mathematical operations such as addition, subtraction, division & multiplication.
2) Ordinal measurement: The 2nd type of measurement scale is known as the ordinal measurement. An ordinal scale has all the properties of a nominal scale plus one of its own. Besides, categorizing individuals, objects, responses, or a property into sub-groups on the basis of common characteristics, it ranks the sub-groups in a certain order. They are arranged either in ascending or descending order according to the extent a sub-group category. A student rank in his graduation class involves the use of an ordinal scale. One has to be very careful in making statement about scores based on ordinary scales. For instance, if Karim’s position in his class is 10 & Rahim’s position is 40, it cannot be said that Karim’s position is four times as good as that of Rahim. Ordinal scales only permit the ranking of items from highest to lowest. In ordinary scale have only a ranking meaning, the appropriate measure of central tendency is the median. Correlations are restricted to various rank order method.
3) Interval measurement: The interval level of measurement includes all the properties of nominal and ordinal but an addition property that the difference (interval) between values is known and of constant size. The interval measurement describes variables that have more or less equal intervals, or meaningful distances between their ranks. For example, if you were to ask somebody if they were first, second, or third generation immigrant, the assumption is that the distance or number of years, between each generation is the same. All crime rates in criminal justice are interval level measures, as is any kind of rate.
4) Ratio measurement: The ratio level of measurement describes variables that have equal intervals and a fixed zero (or reference) point. It is possible to have zero income, zero education, and no involvement in crime, but rarely do we see ratio level variables in social science since it's almost impossible to have zero attitudes on things, although "not at all", "often", and "twice as often" might qualify as ratio level measurement.
Advanced statistics require at least interval level measurement, so the researcher always strives for this level, accepting ordinal level (which is the most common) only when they have to. Variables should be conceptually and operationally defined with levels of measurement in mind since it's going to affect how well you can analyze your data later on.
PURPOSES OF MEASUREMENT:
The purposes of measurement are described below:
1) Differentiation of things:
For the differentiation of things from one to another, measurement is necessary. In our daily life, we only distinguish the character and qualities of things, and on the basis of this, we reject or choose certain things. Qualitative differences are the first fruits of enquiry in sciences. But it is not enough to know only the qualitative differences in daily life or in sciences. It is more necessary to know the magnitude of such differences precisely. This is required for exactitude and accuracy of statement and for discovering comprehensive principles on the basis of which the subject matter can be known to be systematically related. If we can know the degrees of qualitative differences, we can not only rule out errors but can take up adequate measures to control the indicated changes as well if required. In sciences, the accurate measurement of phenomenon can give us great practical control over the studied subject, and can make possible the formulation of principles or laws which can make confirmation or refutation unambiguous and clear.
2) Substitution quantitative distinctions to qualitative distinctions with knowing meaning: Quantitative distinctions are substituted for qualitative ones, for theoretical and practical reasons. But many people, without knowing the meaning and justification, often use quantitative distinctions. For indicating the qualitative differences, the use of numbers requires a careful examination, if we are to avoid absurdity and errors. In order to deal with simple matters in our daily life and in sciences, we need sometimes a more intricate technique than a bare common sense method is required for formulating, collecting and estimating evidence. Investigations cannot be properly and fruitfully carried on without the introduction of quantitative methods.
FORMAL CONDITIONS OF MEASUREMENT:
For measuring the qualitative differences the minimum requirements for employing numbers may be stated in the following first two conditions:
1) In a set of n bodies given, A1, A2,…..An, one must, with reference to a certain quality, be able to arrange them in such a way that between only two bodies one and only one of the following relations holds: (i) A1 >A2 (ii) A1<A2 (iii) A1=A2. On the basis of the signs > or <, the qualitative differences in bodies can be studied. The relation > must be asymmetrical.
2) If A1>A2 and A2>A3, then A1>A3. This is known as transitivity condition.
The above two conditions are sufficient for the measurement of intensive qualities, e.g., density, temperature etc. For the measurement of extensive qualities, they are necessary but not sufficient. Measurement of extensive qualities requires some physical process of addition which should have the following formal properties:
3) If A1 + A2 = A3 then A2 + A1 = A3.
4) If X = Y, then X + Z > Y (where the value of z is not zero or negative).
5) If A=X and B=Y, then A+B = X+Y.
6) (A+B) +C = A+ (B+C).
If these conditions are satisfied, measurement becomes possible. With the fulfillment of the first two conditions, it cannot be said that all the six conditions hold. If the I.Q. of a man is twice that of another, we only mean that the first man is higher than the other on a specific scale of preference. It is absurd to say that the first has twice the intelligence or training, because operation for adding intelligence or training has been found out which is consistent with the last four essential conditions.
MEASUREMENT OF QUALITATIVE DATA:
In social sciences, we face problems which are subjective and qualitative, e.g., skills, values, attitudes, utility, etc. Qualitative data cannot be quantitatively or objectively measured. But qualitative data cease to be of much scientific value unless such data are quantified.
Prof. Menegazzi pleads for greater attention to the qualitative aspect of social life-to the synthetic or aggregative approach to the problems. It is to some extent possible to measure the intensive and extensive qualities. The qualitative data can be translated more or less satisfactorily to quantitative terms. The technique of such translation has several steps: description, categorization, and determination of quantitative incidence and inter-relations. These steps are generally known as “content analysis”.
Measurement of intensive qualities:
There are some things, e.g., hardness, density, intelligence, etc., which have non-additive qualities. These qualities are called intensive qualities. These qualities can be measured only in the sense that the different degrees of the quality may be arranged in a series. In this case, the question regarding “how much” or “how many times” are meaningless: the qualities cannot be added. The varying degrees of quality can be indicated by assigning different numbers. But in this way we can’t got the correct measurement. It should not be considered that measurement requires nothing more than the assigning of numbers. But by assigning numbers we can only indicate the degree if intensity, i.e., which one is higher and which one is lower.
Measurement of extensive qualities:
There are some things the qualities or properties of which are additive, e.g., areas, angles, electric current, lengths etc. The properties which are additive are called extensive properties. Numbers can be employed to measure the quantitative relations. In order to measure the weight of something, we are to construct a scale or ladder of weights. By the measurement of weight with the help of a scale, we can know experimentally whether one is heavier than other or not.
VALIDITY AND RELIABILITY OF MEASUREMENT:
Validity of measurement:
Validity is the most critical criteria and indicates the degree to which an instrument measures what it is supposed to measure. It implies that the scale actually should measure what it claims to measure validity, may be tested by the help of the opinions of the experts for instance- unemployment is measured in term of time, but it can also be measured in terms of income.
According to Zikmund, “Validity is the accuracy of a measure or the extent to which a score truthfully represents a concept”.
Validity can also be thought of as utility. In other words, validity is the extent to which differences among being tested. It may be tested by the help of the opinions of the experts.
One can consider three types of validity in this connection:
a) Content validity: Content validity seeks to answer whether the empirical indicators (tests, scales, questions etc.) fully represent the domain of the underlying concept being studied. In this sense, content validity concerns the degree to which the content of a set of items adequately represents the universe or domain of all relevant items under study. If the instrument contains a representative sample of the universe, the content validity is good. Its determination is primarily judgmental and intuitive.
According to Zikmund, “Content validity refers to the degree that a measure covers the breadth of the domain of interest”.
b) Criterion-related validity: It addresses the question, how well does my measure work in practice? Criterion validity, variously called pragmatic validity, concurrent validity or predictive validity, involves multiple measurement of the same concept. It refers to the ability of a measure to correlate with other standard measures of similar constructs or established criteria.
c) Construct validity: Construct validity is the most complex and abstract. A measure is said to possess construct validity to the degree that it confirms to predicted correlations with other theoretical propositions. Construct validity is the degree to which scores on a test can be accounted for by the explanatory constructs of a sound theory. For determining construct validity, we associate a set of other propositions with the results received from using our measurement instrument.
## If the above stated criteria and tests are met with, we may state that our measuring instrument is valid and will result in correct measurement; otherwise we shall have to look for more information and/or resort to exercise of judgment.
RELIABILITY OF MEASUREMENT:
Reliability is important test of sound measurement. A scale is reliable if it gives the same result consistently when applied to the same sample. Reliable measuring instrument does contribute to validity, but a reliable instrument need not be a valid instrument. A tailor measuring fabrics with a measuring tape obtains a value of the length of the fabric as 20 inches. If the tailor takes repeated measures of the fabric and each time comes up with the same length, it is said that the tape measure is reliable.
Two aspects of reliability:
The stability aspect is concerned with securing consistent results with repeated measurements of the same person and with the same instrument. We usually determine the degree of stability by comparing the results of repeated measurements.
The equivalence aspect considers how much error may get introduced by different investigators or different samples of the items being studied. A good way to test for the equivalence of measurements by two investigators is to compare their observations of the same events. Reliability can be improved in the following two ways: (i) By standardizing the conditions under which the measurement takes place (ii) By carefully designed directions for measurement with no variation from group to group, by using trained and motivated persons to conduct the research and also by broadening the sample of items used. This will improve equivalence aspect.
SCALING TECHNIQUE:
Scaling is the assignment of objects to numbers or semantics according to a rule. In scaling, the objects are text statements, usually statements of attitude, opinion, or feeling.
Scaling describes the procedures of assigning numbers to various degrees of opinion, attitude and other concept. This can be done in two ways
1) Making a judgment about characteristic of an individual and then placing him directly on a sale that has been defined in terms of that characteristics and
2) Constructing questionnaires in such a way that the score of individuals’ responses assigns him a place on scale.
A scale is a continuum, consisting of the highest point and the lowest point along with several intermediate points between these two extreme points. 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.
Finally, Scaling can be 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.”
RELIABILITY OF SCALE:
Reliability refers to the consistency of a measure. A measure is said to have a high reliability if it produces consistent results under consistent conditions. For example, measurements of people’s height and weight are often extremely reliable. A scale must be reliable. The following method can be used to test the reliability of a scale:
1) Re-test Method: According to this method, the same scale is applied twice to the same population for the same objectives and if the two results are similar, the scale is regarded as reliable. For this matter, the test can be done on two similar groups also.
2) Multiple Form: According to this technique, two types of scales are constructed, and they are applied to the same population. In case the two results are more or less similar, the scales may be regarded as reliable.
3) Split-half method: in this method the scale may be divided into two equal parts. Then each part is taken as a whole (as a complete scale) and measurement is made separately. The correlation between the two scores obtained in this way is estimated, and if the degree of correlation is high, the scale may be regarded as reliable.
DIFFICULTIES IN SCALING:
1) The difficulty of applying rigorous and objective tests in attitude measurement arises from the fact that such measurement is indirect, for attitude is inferred from verbal responses. An attitude is an abstraction, and as such, it is almost impossible to assess its validity directly.
2) Social phenomena are complex and quantitative in nature. The concepts themselves are not defined properly. Thus quantitative measurement is a baffling affair.
3) A scale is applicable to a particular group or class. It is not universally applicable. Human behavior is heterogeneous and unpredictable.
4) There is no universally valid or recognized measuring rod. The measuring unit itself may be variable. A valid scale in the ultimate analysis is also a subjective consideration. But the most baffling problem is the criterion of validity.
5) The intangibility of social phenomena is an obstacle to scale construction. The score of the scale cannot be correctly tested because of the intangibility of the social phenomena.
6) Human behavior is flexible and variable whatever attitude is expressed at a point of time may not be taken as reliable. Even a value scale may not remain valid during the period of analysis. There is often a dichotomy between the expressed attitudes and overt action.
7) The social phenomena cannot be experiment in a controlled way. The phenomena may be individual, private or esoteric. Therefore they cannot be properly watched and evaluated. Thus scale cannot measure all the causative variables involved.
These are the limitations of scaling. Despite these limitations, the scaling technique can be improved to measure the social phenomena more or less accurately.
TYPES OF SCALES:
1) Nominal scale: A nominal scale consists of two or more named categories into which individual objects or responses are classified. In a nominal, it is possible to distinguish two or more categories relating to the specified attributive the member of these categories differ with respect to the specified attribute which is measured. It is a simple method of classification rather than an arrangement along a continuum. The question of dimension is not important in this type of scale. If desired, the different groups may be numbered. Classification of individuals according to religion is an example of scale.
According to Zikmund, “Nominal scales represent the most elementary level of measurement in which values are assigned to an object for identification or classification purposes only”.
Nominal scale is the least powerful level of measurement. It indicates no order or distance relationship and has no arithmetic origin. A nominal scale simply describes differences between things by assigning them to categories.
2) Ordinal scale: The lowest level of the ordered scale that is commonly used is the ordinal scale. The ordinal scale places events in order, but there is no attempt to make the intervals of the scale equal in terms of some rule. Rank orders represent ordinal scales and are frequently used in research relating to qualitative phenomena. A student’s rank in his graduation class involves the use of an ordinal scale. In this type of scale, numbers, 1, 2, 3, etc. are assigned to indicate only the relative position. The scale purports to give ranks to the individual along the specified continuum. But such a scale, like the nominal scale, does not measure the distance between the positions. In this scale, it is very essential to determine the order of position in relation to the attribute which is being measured. Thus, the use of an ordinal scale implies a statement of ‘greater than’ or ‘less than’ (an equality statement is also acceptable) without our being able to state how much greater or less. 3) Interval scale: This scale has equal units of measurement. Thus, it is possible to interpret not only the order of scale scores but also the distance between them.
According to Zikmund, “Scales that have both nominal and ordinal properties, but that also capture information about differences in quantities of a concept from one observation to the next is called interval scale”.
Thus, two persons with scale positions 4 and 5 are as apart as two persons with scale positions 10 and 11. A person having the score of 10 cannot be regarded as two times higher or better than a person whose score is 5. When we talk of 10 degree Celsius rise in temperature, it does not mean that it is twice as hot as 5 degree Celsius.
In an interval scale, the interval remains equal. Interval scales provide more powerful measurement than ordinal scales for interval scale also incorporates the concept of equality of interval. As such more powerful statistical measures can be used with interval scales. The primary limitation of the interval scale is the lack of a true zero; it does not have the capacity to measure the complete absence of a trait or characteristic.
4) Ratio scale: Ratio scales have an absolute or true zero of measurement. The scale incorporates the properties of an interval scale together with a fixed origin or zero point.
According to Zikmund, “Ratio scales represents the highest form of measurement in that they have all the properties of interval scales with the additional attribute of representing absolute quantities, characterized by a meaningful absolute zero”.
Weight, length and time are the examples of ratio scales. On the basis of a ratio scale, one can compare both differences in scores and the relative magnitude of scores.
For instance, the difference between ten and fifteen minutes is the same as that between fifteen and twenty minutes is twice as long as five minutes. Generally, all statistical techniques are usable with ratio scales and all manipulations that one can carry out with real numbers can also be carried out with ratio scale values.
RANK ORDER SCALES:
A Rank Order scale gives the respondent a set of items and asks them to put the items in some form of order. The measure of 'order' can include such as preference, importance, liking, effectiveness and so on. The order is often a simple ordinal structure (A is higher than B). It can also be done by relative position (A scores 10 whilst B scores 6). In this method, the judge is required to rank individuals in relation to one another. In a rating scale, the individual rater himself may be the subject of rating. This is known as self-rating. Self-rating has its own advantage and limitations. However, self-rating has been attitudes like intensity, importance, liking and so on. It is two types:
1) Paired comparison: This is a simple method of ranking scale. In this type of scale, two stimuli are presented before the judges, out of which the better is to be selected. The continuum is properly defined. For example, if job 2 is preferred to job 3, and job 3 is preferred to job 4, then by the transitivity axiom, job 2 is preferred to job 4.
2) Horowitz method: Horowitz applied a ranking scale for testing social prejudices. He took 8 pictures of Negros and 4 pictures of white children. These 12 pictures are shown to the school children who were asked to indicate their preferences.
ATTITUDE SCALES:
The term scaling is applied to the attempts to measure the attitude objectively. Attitude is a resultant of number of external and internal factors. Depending upon the attitude to be measured, appropriate scales are designed. Scaling is a technique used for measuring qualitative responses of respondents such as those related to their feelings, perception, likes, dislikes, interests and preferences. In this type of scale, the attitude of an individual towards a matter, thing, object or system can be known from the score of his responses given on a questionnaire. The score will place on a scale. He simply expresses his like or dislike, agreement or disagreement with the issue involved, as given in the forms of questions. On the basis of his reply, he is assigned a score which indicates his position.
This type of technique is used in measuring the social attitudes. In the attitude scale, some relevant statements are to be considered by the respondents. The statements are formed in such a way as to be intimately related to the attitude which is sought to be measured. Indirect statements may sometimes be used to reveal the attitude. Secondly, the scale should be able to specify the various but crucial shades of opinions. For instance, extreme, moderate, and neutral attitudes must be expressed through the statements so that the respondents have several reasonable ways of expressing their attitudes. Thus the method of scale formulation remains very decisive, and so is the method of scoring.
Depending on the differences in these regards, there may be various types of attitude scale. 1) Point scale 2) Differential scale: Under such an approach the selection of items is made by a panel of judges who evaluate the items in terms of whether they are relevant to the topic area and unambiguous in implication. 3) Summated scale: Summated scales (or Likert-type scales) are developed by utilizing the item analysis approach wherein a particular item is evaluated on the basis of how well it discriminates between those persons whose total score is high and those whose score is low. 4) Cumulative scale: Cumulative scales or Louis Guttmann’s scalogram analysis, like other scales, consists of series of statements to which a respondent expresses his agreement or disagreement. The special feature of this type of scale is that statements in it form a cumulative series. The technique developed by Louis Guttmann is known as scalogram analysis, or at times simply ‘scale analysis. Scalogram analysis refers to the procedure for determining whether a set of items forms a unidimensional scale. A scale is said to be unidimensional if the responses fall into a pattern in which endorsement of the item reflecting the extreme position results also in endorsing all items which are less extreme.

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