INTRODUCTION
THE CONCEPT OF MEASUREMENT SCALES
TYPES OF SCALES
1 Name scale
2 Order scale
3 Interval scale
4 Relationship scale
5 Other scales
6 The relationship between different schools
CONCLUSION
INTRODUCTION
The relevance of the study lies in the fact that in his work, a psychologist quite often faces the problem of measuring individual psychological characteristics, such as creativity, neuroticism, impulsivity, properties of the nervous system, etc. For this purpose, special measuring procedures, including tests, are being developed in psychodiagnostics.
In addition, experimental methods and models for studying mental phenomena in the cognitive and personal spheres are widely used in psychology. These can be models of cognitive processes (perception, memory, thinking) or features of motivation, value orientations, personality, etc. The main thing is that during the experiment the characteristics being studied can receive quantitative expression. Quantitative data obtained from a carefully designed experiment using specific measurement procedures is then used for statistical processing.
Any measurement is made using a measurement tool. What is measured is called a variable, and what is measured is called a measurement instrument. The results of a measurement are called data or results (they say “measurement data were obtained”). The data obtained can be of different quality - refer to one of four measurement scales. Each scale limits the use of certain mathematical operations, and accordingly limits the use of certain methods of mathematical statistics.
The purpose of the essay is to study the concept and classification of a measurement scale.
.Consider the concept of a measuring scale.
.Analyze the classification and main types of measuring scales.
.Make a comparative analysis of comparative scales.
In the process of completing the abstract, the following methods were used: induction and deduction, comparison, etc.
The sources of information for writing the work were textbooks, periodicals on the topic of research, scientific works of Gusev A.N., Stevenson S., Peregudov F.I., Tarasevich F.P., Kornilov T.V.
1. CONCEPT OF MEASUREMENT SCALES
Measurement can be an independent research method, but it can also act as a component of an integral experimental procedure. As an independent method, measurement serves to identify individual differences in the behavior of subjects and their reflection of the world around them, as well as to study the adequacy of the reflection and structure of individual experience.
Measurement in the experimental procedure is considered as a method of recording the state of the object of study and, accordingly, changes in this state in response to experimental influence.
The concept of a measuring scale was introduced into psychology by the American scientist S. Stevens. His interpretation of the scale is still used in scientific literature today.
So, assigning numbers to objects creates a scale. The creation of a scale is possible because there is an isomorphism between formal systems and systems of actions performed on real objects.
A numerical system is a set of elements with relationships implemented on it and serves as a model for a set of measured objects.
There are several types of such systems and, accordingly, several types of scales. Operations, namely ways of measuring objects, determine the type of scale. The scale, in turn, is characterized by the type of transformations that can be attributed to the measurement results. If this rule is not followed, the structure of the scale will be disrupted and the measurement data will not be meaningfully interpretable.
The type of scale uniquely determines the set of statistical methods that can be used to process measurement data.
Scale (Latin scala - ladder) - a tool for measuring the continuous properties of an object; is a numerical system where the relationships between various properties of objects are expressed by the properties of a number series.
P. Suppes and J. Zines gave the classic definition of a scale: “Let A be an empirical system with relations (ESR), R be a complete numerical system with relations (FSR), F be a function that homomorphically maps - A into a subsystem - R (if in the domain there are no two different objects with the same measure, which is a mapping of isomorphism). Let us call an ordered triple a scale<А; R; f>».
Typically, the real number system or its subsystem is chosen as the numerical system R. Set A is a collection of measurable objects with a system of relations defined on this set. Mapping f is a rule for assigning a certain number to each object.
Currently, the definition of Suppes and Zines has been clarified. Firstly, G is introduced into the definition of the scale - a group of admissible transformations. Secondly, the set A is understood not only as a number system, but also as any formal sign system that can be placed in a homomorphism relationship with an empirical system. So the scale is four<А; R; f; G>. According to modern ideas, it is the group G that acts as an internal characteristic of the scale, and f is only a link between the scale and a specific measurement situation.
Currently, measurement refers to the construction of any function that isomorphically maps an empirical structure to a symbolic structure. As noted above, such a structure does not necessarily have to be numerical. This can be any structure with which you can measure the characteristics of objects, replacing them with others that are more convenient to use (including numbers). (2,3).
TYPES OF SCALES
In psychology, various scales are used to study different characteristics of socio-psychological phenomena.
Initially, four types of numerical systems were identified, which respectively defined four levels, or scales of measurement:
) scale of names - nominal;
) order scale - ordinal;
)interval scale - interval;
) ratio scale is proportional.
The first two scales are called non-metric, the second two are called metric. In accordance with this, in psychology they talk about two approaches to psychological measurements: metric (more strict) and non-metric (less strict).
A number of experts also distinguish the absolute scale and the difference scale.
Let's look at the features of each type of scale.
2.1 Name scale
The naming scale or nominal scale is used only to indicate that an object belongs to one of several non-overlapping classes. The symbols assigned to objects, which can be numbers, letters, words, or some special characters, represent only the labels of the corresponding classes. A characteristic feature of the nominal scale is the fundamental impossibility of ordering classes according to the attribute being measured - judgments such as “more - less”, “better - worse”, etc. cannot be applied to them. Examples of nominal scales are: gender and nationality, specialty in education, brand of cigarettes, preferred color. The only relation defined on the naming scale is the relation of identity: objects belonging to the same class are considered identical, objects belonging to different classes are considered different. A special case of a naming scale is a dichotomous scale, which is used to record whether an object has a certain quality or its compliance with a certain requirement.
In this scale, the numbers assigned to objects only indicate that these objects are different. Essentially, this is a classification scale. So, for example, a researcher can assign a zero to women and a one to men, or vice versa, and this will only indicate that these are two different classes of objects. There can be as many numbers in the naming scale as there are classes of objects to be measured, but neither the sum of these numbers, nor their difference, nor the product will have any meaning, because Not a single arithmetic operation is feasible in the naming scale. The numbers in the naming scale can be any number, although, as a rule, negative numbers are not used. Most often in psychological research, a dichotomous naming scale is used, which is specified by two numbers - zero and one. The most common examples of such scales in psychology are: gender (male - female), success in completing a task (coped - failed), compliance with the norm (norm - pathology), psychological type (extrovert - introvert).
The naming scale is obtained by assigning “names” to objects. In this case, it is necessary to divide a set of objects into disjoint subsets.
In other words, objects are compared with each other, and their equivalence or non-equivalence is determined. As a result of the procedure, a set of equivalence classes is formed. Objects belonging to the same class are equivalent to each other and different from objects belonging to other classes. Equivalent objects are given the same names.
The comparison operation is primary for constructing any scale. To construct such a scale, it is necessary that the object be equal or similar to itself (x=x for all values of x), i.e. the reflexivity relation must be implemented on a set of objects. For psychological objects, for example, subjects or mental images, this relation is realizable if we abstract from time. But since the operations of pairwise (in particular) comparison of a set of all objects are not empirically implemented simultaneously, then during the empirical measurement even this simplest condition is not met.
It should be remembered: any scale is an idealization, a model of reality, even such a simple one as a naming scale.
The objects must implement the relation of symmetry (R (X=Y) -> R (Y=X)) and transitivity R (X=Y, Y=Z) -> R (X=Z). But in many psychological experiments these conditions may be violated.
In addition, repeated repetition of the experiment (accumulation of statistics) leads to “mixing” of the composition of classes: at best, we can obtain an estimate indicating the probability of an object belonging to a class.
Thus, there is no reason to talk about the naming scale (nominative scale or strict classification scale) as the simplest scale, the initial level of measurement in psychology.
There are more “primitive” (from an empirical, but not from a mathematical point of view) types of scales: scales based on tolerance relations; “fuzzy” classification scales, etc.
We can talk about a naming scale in the case when empirical objects are simply “marked” with a number.
So, if objects are equivalent in some respect, then we have the right to classify them as one class. The main thing, as Stevens said, is not to assign the same symbol to different classes or different symbols to the same class.
Despite the tendency to “overestimate” the power of the scale, psychologists very often use the naming scale in research. “Objective” measurement procedures in diagnosing personality lead to typology: the assignment of a specific personality to one type or another. An example of such a typology is the classical temperaments: choleric, sanguine, melancholic and phlegmatic. (2, 3).
The simplest nominative scale is called dichotomous. When measuring on a dichotomous scale, the characteristics being measured can be coded by two symbols or numbers, for example 0 and 1, or 2 and 6, or the letters A and B, as well as any two symbols that differ from each other. A trait measured on a dichotomous scale is called an alternative trait. In a dichotomous scale, all objects, signs or properties being studied are divided into two non-overlapping classes, and the researcher raises the question of whether the trait of interest “appeared” in the subject or not.
A researcher using a naming scale can use the following invariant statistics: relative frequencies, mode, correlations of random events, criterion.
2 Order scale
Order scales allow not only dividing objects into classes, but also ordering classes in ascending (descending) order of the characteristic being studied: it is known about objects assigned to one of the classes, but only that they are identical to each other, but also that they have a measurable property to a greater or lesser extent than objects from other classes. But at the same time, ordinal scales cannot answer the question of how much (how many times) this property is expressed more strongly in objects from one class than in objects from another class. Examples of order scales include level of education, military and academic ranks, type of settlement (large - medium - small city - village), some natural scientific scales (hardness of minerals, strength of a storm). Thus, we can say that a 6-point storm is certainly stronger than a 4-point storm, but it is impossible to determine how much stronger it is; a university graduate has a higher educational level than a high school graduate, but the difference in level of education cannot be directly measured. Ordered classes are often numbered in ascending (descending) order of the characteristic being measured. However, due to the fact that differences in the value of a feature cannot be accurately measured, arithmetic is not applied to order scales, as well as to nominal scales. The exception is rating scales, when using which the object receives (or gives) ratings based on a certain number of points. Such scales include, for example, school grades, for which it is considered quite acceptable to calculate, for example, the average grade on the matriculation certificate. Strictly speaking, such scales are a special case of an order scale, since it is impossible to determine how much more the knowledge of an “excellent” student is than the knowledge of a “C” student, but due to some theoretical considerations they are often treated as scales of a higher rank - interval scales . Another special case of the order scale is the rank scale, usually used in cases where a characteristic is obviously not amenable to objective measurement (for example, beauty or the degree of hostility), or when the order of objects is more important than the exact magnitude of the differences between them (places occupied in sports competitions). In such cases, the expert is sometimes asked to rank a certain list of objects, qualities, motives, etc., according to a certain criterion.
The numbers assigned to objects on this scale will indicate the degree of expression of the measured property in these objects, but, at the same time, equal differences in numbers will not mean equal differences in the quantities of measured properties. Depending on the desire of the researcher, a larger number can mean a greater degree of expression of the property being measured (as in a scale of mineral hardness) or less (as in a table of results of sports competitions), but in any case, the order relationship remains between the numbers and the objects corresponding to them. The order scale is defined by positive numbers, and there can be as many numbers in this scale as there are measured objects. Examples of order scales in psychology: rating of subjects on some basis, results of expert assessment of subjects, etc.
If it is possible to establish the order of psychological objects in accordance with the severity of some property, then an ordinal scale is used.
An ordinal scale is formed if one binary relation is implemented on a set - order (the relations “more” and “less”). Constructing an order scale is a more complex procedure than creating a naming scale. It allows you to record the rank, or place, of each value of a variable in relation to other values. This rank can be the result of establishing an order between some stimuli or their attributes by the subject himself (the primary indicator of ranking methods, or rating procedures), but it can also be established by the experimenter as a secondary indicator (for example, when ranking the frequencies of positive responses of subjects to questions related to to different topics).
Equivalence classes, identified using a naming scale, can be ordered according to some basis. There is a scale of strict order (strict order) and a scale of weak order (weak order). In the first case, the relations “more than” and “less than” are implemented on the elements of the set, and in the second case, “not more than or equal to” and “less than or equal to.”
Values can be replaced by squares, logarithms, normalized, etc. With such transformations of the values of quantities determined on the order scale, the place of objects on the scale does not change, i.e. no inversions occur.
Stevens also expressed the view that the results of most psychological measurements, at best, correspond only to order scales.
Order scales are widely used in the psychology of cognitive processes, experimental psychosemantics, and social psychology: ranking, evaluation, including pedagogical ones, provide ordinal scales. A classic example of the use of ordinal scales is in testing personality traits as well as abilities. Most experts in the field of intelligence testing believe that the procedure for measuring this property allows the use of an interval scale and even a ratio scale.
Be that as it may, this scale allows you to introduce a linear ordering of objects on a certain axis of the attribute. This introduces the most important concept - a measurable property, or a linear property, while the naming scale uses a “degenerate” version of the interpretation of the concept “property”: a “point” property (there is a property - there is no property).
The ordinal (rank) scale must contain at least three classes (groups): for example, answers to a questionnaire: “yes”, “I don’t know”, “no”; or - low, medium, high; etc., so that the measured characteristics can be arranged in order. That is why this scale is called an ordinal, or rank, scale.
It’s easy to move from classes to numbers, if we assume that the lowest class receives a rank (code or number) 1, the middle - 2, the highest - 3 (or vice versa). The greater the number of classes of partitions of the entire experimental set, the wider the possibilities for statistical processing of the obtained data and testing statistical hypotheses.
When encoding ordinal variables, any numbers (codes) can be assigned to them, but the order must be preserved in these codes (digits), or, in other words, each subsequent digit must be greater (or less) than the previous one.
A wider range of statistical measures (in addition to those that are valid for a naming scale) can be used to interpret data obtained through an ordinal scale.
The median can be used as a characteristic of central tendency, and percentiles can be used as a characteristic of dispersion. To establish a relationship between two measurements, ordinal correlation (Kandell's t- and Spearman's p-correlation) is acceptable.
Numerical values on an ordinal scale cannot be added, subtracted, divided, or multiplied. (2, 3).
3 Interval scale
Unlike the two previous scales, in the interval scale there is a unit of measurement, either real (physical) or conventional, with the help of which it is possible to establish quantitative differences between objects in relation to the property being measured. Equal differences in numbers on this scale will mean equal differences in the amounts of the property being measured in different objects, or in the same object at different points in time. However, the fact that one number turns out to be several times larger than another does not necessarily indicate the same relationships in the quantities of measured properties. In an interval scale, the entire numerical axis can be used, but zero does not indicate the absence of the property being measured, because the zero point is often arbitrary (for example, as in the Celsius temperature scale), or absent altogether, as in some psychological test scales. Thanks to these properties, the interval scale has become widespread in psychology; most psychodiagnostic scales are based on it: intelligence, self-esteem, etc.
Examples of interval scales are calendar time, Celsius and Fahrenheit temperature scales. A rating scale with a given number of points is often considered to be intervallic, under the assumption that the minimum and maximum positions on the scale correspond to some extreme ratings or positions, and the intervals between scale points are of the same length. Ratio scales include the vast majority of measurement scales used in science, technology and everyday life: height and weight, age, distance, current strength, time (the duration of the interval between two events), Kelvin temperature (absolute zero).
The interval scale is the first metric scale. Actually, starting with it, it makes sense to talk about measurements in the narrow sense of the word - about the introduction of a measure on a set of objects. The interval scale determines the magnitude of differences between objects in the manifestation of a property. An interval scale can be used to compare two objects. At the same time, they find out how much more or less pronounced a certain property is in one object than in another.
The interval scale allows you to use almost all parametric statistics to analyze data obtained with its help. In addition to the median and mode, the arithmetic mean is used to characterize the central tendency, and dispersion is used to assess the spread. You can calculate skewness and kurtosis coefficients and other distribution parameters. To assess the magnitude of the statistical relationship between variables, Pearson's linear correlation coefficient, etc. is used.
Most psychological measurement theorists believe that tests measure mental properties using an interval scale. First of all, this concerns intelligence and achievement tests. Numerical values from one test can be converted to numerical values from another test using a linear transformation: x" = ax + b.
A number of authors believe that there is no reason to classify intelligence tests as interval scales. Firstly, each test has a “zero” - any individual can receive the minimum score if he does not solve a single problem in the allotted time. Secondly, the test has a maximum scale - the score that the test taker can receive by solving all the problems in the minimum time. Third, the difference between individual scale values is not the same. At the very least, there is no theoretical or empirical basis for asserting that scores of 100 and 120 on an IQ scale are as different as scores of 80 and 100.
Most likely, the scale of any intelligence test is a combined scale, with a natural minimum and/or maximum, but ordinal. However, these considerations do not prevent testologists from considering the IQ scale as an interval one, converting “raw” values into scale values using the well-known procedure of “normalizing” the scale
4 Relationship scale
The ratio scale is the only scale on which the ratio ratio is defined, that is, the arithmetic operations of multiplication and division are allowed and, therefore, the answer to the question of how many times one value is greater or less than another is possible.
In a ratio scale there is also a unit of measurement with which objects can be ordered in relation to the property being measured and quantitative differences between them can be established. A feature of the ratio scale is that all mathematical operations are applicable to the numbers on this scale, which means that the relationships between numbers correspond, or are proportional to the relationships between the quantities of measured properties in different objects. This scale necessarily, at least theoretically, contains a zero, which indicates the absolute absence of the property being measured. Most of the existing physical scales (length, mass, time, Kelvin temperature, etc.) are clear examples of ratio scales. In psychology, the most commonly used relationship scales are the probability scale and the scale of “raw” points (the number of solved tasks, the number of errors, the number of positive answers, etc.).
The relationship scale is also called the equal relationship scale. A feature of this scale is the presence of a firmly fixed zero, which means the complete absence of any property or characteristic. The ratio jackal is the most informative scale, allowing any mathematical operations and the use of a variety of statistical methods.
The ratio scale, in fact, is very close to the interval scale, since if you strictly fix the starting point, then any interval scale turns into a ratio scale.
The ratio scale shows data on the expression of the properties of objects, when you can say how many times one object is larger or smaller than another.
This is possible only when, in addition to the definition of equality, rank order, and equality of intervals, the equality of relations is known. The ratio scale differs from the interval scale in that the position of the “natural” zero is determined on it. A classic example is the Kelvin temperature scale.
It is on the ratio scale that precise and ultra-precise measurements are made in sciences such as physics, chemistry, microbiology, etc. Measurements on the ratio scale are also made in sciences close to psychology, such as psychophysics, psychophysiology, psychogenetics.
Measurements of mass, reaction time and test performance are areas of application of the ratio scale.
The difference between this scale and the absolute scale is the absence of a “natural” scale unit.
2.5 Other scales
Dichotomous classification is often considered as a variant of the naming scale. This is true, with the exception of one case when we are measuring a property that has only two levels of expression: “yes - no”, the so-called “point” property. There are many examples of such properties: the presence or absence of any hereditary disease in the subject (color blindness, Down's disease, hemophilia, etc.), absolute hearing, etc. In this case, the researcher has the right to “digitize” the data, assigning a number to each type “ 1" or "O", and work with them as with interval scale values.
The difference scale, unlike the ratio scale, does not have a natural zero, but does have a natural scale unit. It corresponds to the additive group of real numbers. A classic example of this scale is historical chronology. It is similar to the interval scale. The only difference is that the values of this scale cannot be multiplied (divided) by a constant. Therefore, it is believed that the difference scale is the only one accurate to a shift. In psychology, the difference scale is used in paired comparison techniques.
The absolute scale is a development of the ratio scale and differs from it in that it has a natural unit of measurement. This is its similarity to the difference scale. The number of solved problems ("raw" score), if the problems are equivalent, is one of the manifestations of the absolute scale.
Absolute scales are not used in psychology. Data obtained using an absolute scale is not transformed; the scale is identical to itself. Any statistical measure is acceptable.
In the literature devoted to the problems of psychological measurements, other types of scales are also mentioned: ordinal (ordinal) with a natural beginning, log-interval, ordered metric, etc.
Everything written above applies to one-dimensional scales. Scales can also be multidimensional: the sign being scaled in this case has non-zero projections onto two (or more) corresponding parameters. Vector properties, unlike scalar ones, are multidimensional.
2.6 Relationship between different schools
There are also order relationships between the scales themselves. Each of the listed scales is a scale of a higher order in relation to the previous scale. So, for example, measurements made on a ratio scale can be transferred to an interval scale, from an interval scale to an order scale, etc., but the reverse procedure will be impossible, because when moving to scales of a lower order, some information (about units of measurement, quantities of properties) is lost.
However, this does not always mean that higher order scales are preferable to lower order scales, and in some cases, even vice versa. For example, it is much more advantageous to represent the number of correctly completed tasks in an intelligence test (ratio scale) in a standardized IQ scale (interval scale), and a variety of different behavioral reactions in the form of a personality type (naming scale). Finally, there are characteristics of objects that can be measured on any scale, such as age, and those that can only be measured on one scale, such as gender. The choice of a measurement scale, therefore, can be influenced by many factors, both the merits of the scale itself and the specifics of the measurement object itself.
· Measuring tools
To carry out measurements in the natural and exact sciences, and in everyday life, special measuring instruments are used, which in many cases are quite complex devices. The quality of the measurement is determined by the accuracy, sensitivity and reliability of the instrument. The accuracy of an instrument is its compliance with the standard (standard) existing in the field. The sensitivity of the instrument is determined by the size of the unit of measurement, for example, depending on the nature of the object, the distance can be measured in microns, centimeters or kilometers. Reliability is the ability of an instrument to reproduce measurement results within the sensitivity of the scale. In the humanities and social sciences (with the exception of economics and demography), most indicators cannot be directly measured using traditional technical means. Instead, all kinds of questionnaires, tests, standardized interviews, etc. are used, collectively called measurement tools. In addition to the obvious problems of accuracy, sensitivity and reliability, for humanitarian instruments there is also a rather acute problem of validity - the ability to measure exactly the personality trait that is assumed by its author.
· Qualitative and quantitative scales
Due to the fact that the symbols assigned to objects in accordance with ordinal and nominal scales do not have numerical properties, even if written using numbers, these two types of scales are collectively called qualitative, in contrast to quantitative scales of intervals and ratios. Interval and ratio scales have a common property that distinguishes them from qualitative scales: they assume not only a certain order between objects or their classes, but also the presence of some unit of measurement that allows one to determine how much the attribute value of one object is greater or less than that of another. In other words, on both quantitative scales, in addition to the relations of identity and order, the relation of difference is defined; the arithmetic operations of addition and subtraction can be applied to them. Naturally, the symbols assigned to objects in accordance with quantitative measurement scales can only be numbers.
· Interval scale and ratio scale
The main difference between the interval and ratio scales is that the ratio scale has an absolute zero, which does not depend on the arbitrariness of the observer and corresponds to the complete absence of the measured characteristic, and on the interval scale, zero is set arbitrarily or in accordance with some conventional agreements.
· Discrete and continuous scales
Quantitative scales are divided into: discrete and continuous. Discrete indicators are measured as a result of counting: the number of children in the family, the number of solved problems, etc. Continuous scales assume that the property being measured changes continuously and, given the availability of appropriate instruments and means, could be measured with any required degree of accuracy. The results of measuring continuous indicators are quite often expressed in whole numbers (for example, the IQ scale for measuring intelligence), but this is not due to the nature of the indicators themselves, but to the nature of the measurement procedures. There are primary and secondary measurements. The primary ones are obtained as a result of direct measurement: the length and width of the rectangle, the number of births and deaths in a year, the answer to a test question, the score on the exam. The latter are the result of some manipulations with primary measurements, usually with the help of certain logical-mathematical constructions: the area of a rectangle, demographic rates of mortality, fertility and natural increase, test results, enrollment or non-enrollment in an institute based on the results of entrance exams.
CONCLUSION
measuring scale psychological discrete
Thus, measurement scales are usually classified according to the types of measured data, which determine the mathematical transformations acceptable for a given scale, as well as the types of relationships displayed by the corresponding scale. The modern classification of scales was proposed in 1946 by Stanley Smith Stevens.
· Scale of names (nominal, classification)
Used to measure the values of quality attributes. The value of such a feature is the name of the equivalence class to which the object in question belongs. Examples of the meanings of qualitative characteristics are names of states, colors, car brands, etc. Such characteristics satisfy the identity axioms:
Either A = B or A? IN;
If A = B, then B = A;
If A = B and B = C, then A = C.
For a large number of classes, hierarchical naming scales are used. The best known examples of such scales are those used to classify animals and plants.
With values measured in the scale of names, you can perform only one operation - checking their coincidence or non-coincidence. Based on the results of such a check, it is possible to additionally calculate filling frequencies (probabilities) for various classes, which can be used to apply various methods of statistical analysis - the Chi-square goodness-of-fit test, the Cramer test to test the hypothesis about the relationship of qualitative characteristics, etc.
· Ordinal scale (or rank scale)
It is built on the relationship of identity and order. Subjects in this scale are ranked. But not all objects can be subject to the relation of order. For example, it cannot be said that a circle or a triangle is larger, but one can identify a common property in these objects - area, and thus it becomes easier to establish ordinal relationships. For this scale, a monotonic transformation is acceptable. Such a scale is crude because it does not take into account the differences between the subjects of the scale. An example of such a scale: academic performance scores (unsatisfactory, satisfactory, good, excellent), Mohs scale.
· Interval scale (aka Difference scale)
Here there is a comparison with the standard. The construction of such a scale allows us to attribute most of the properties of existing numerical systems to numbers obtained on the basis of subjective assessments. For example, constructing an interval scale for reactions. For this scale, linear transformation is acceptable. This allows you to reduce test results to common scales and thus compare indicators. Example: Celsius scale.
The starting point is arbitrary, the unit of measurement is specified. Acceptable transformations are shifts. Example: measuring time.
· Absolute scale (aka Ratio scale)
This is an interval scale in which there is an additional property - the natural and unambiguous presence of a zero point. Example: number of people in the audience. In the ratio scale, the relation “so many times more” applies. This is the only one of the four scales that has an absolute zero. The zero point characterizes the absence of the measured quality. This scale allows similarity transformation (multiplication by a constant). Determining the zero point is a difficult task for psychological research, imposing restrictions on the use of this scale. Using such scales, mass, length, strength, and value (price) can be measured. Example: Kelvin scale (temperatures measured from absolute zero, with the unit of measurement chosen by agreement of experts - Kelvin).
Of the scales considered, the first two are not metric, and the rest are metric.
The issue of the type of scale is directly related to the problem of the adequacy of methods for mathematical processing of measurement results. In general, adequate statistics are those that are invariant with respect to admissible transformations of the measurement scale used.
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Name scaleused to describe the belonging of objects to certain classes. This is the weakest quality scale. All objects of the same class are assigned the same number, and objects of different classes are assigned different numbers. In this regard, the naming scale is often called classification scale . It preserves equivalence relations and differences between objects and is used for indexing product ranges (product specifications), documents and types of information in automated control systems, numbering departments in an organization, etc. There are a large number of options for assigning numbers to classes of equivalent objects. Consequently, the concept of uniqueness of a mapping f consists for the scale of names in interambiguity valid transformation. This means that if there are two options for assigning numerical values to classes, then they must be related to each other one-to-one, which makes it possible to establish a connection between the numerical options for describing equivalence classes. Thus, the naming scale is unique up to one-to-one conversion. This means that in this scale there are no concepts of scale and origin.
The name “nominal” is explained by the fact that such a sign gives only unrelated names to objects. These values are either the same or different for different objects; no more subtle relationships between values are recorded. Nominal type scales allow only the distinction of objects based on checking the fulfillment of the equality relation on the set of these elements.
The nominal type of scales corresponds to the simplest type of measurements, in which scale values are used only as names of objects, therefore nominal type scales are often also called naming scales.
Examples of measurements in the nominal type of scales include car numbers, telephone numbers, city codes, persons, objects, etc. The only purpose of such measurements is to identify differences between objects of different classes. If each class consists of one object, a naming scale is used to distinguish objects.
Figure 3.5 shows the measurement on a nominal scale of objects representing three sets of elements A, B, C.
Fig.3.5. Measuring objects on a nominal scale
Here the empirical system is represented by four elements: a A, b B, (c, d) C, belonging to the corresponding sets. The sign system is represented by a digital scale of names, including elements 1,2,...,n and preserving the relation of equality. A homomorphic mapping associates each element from the empirical system with a specific element of the sign system. Two features of nominal scales should be noted.
Firstly, elements cud the same value of the measurement scale is assigned (see Fig. 3.5). This means that these elements do not differ when measured.
Secondly, when measured in the name scale, symbols 1,2,3,...,n , used as scale values are not numbers, but numbers that serve only to designate and differentiate objects. So, the number 2 is not twice or one more than the number 1, unlike the numbers 2 and 1.
Any processing of measurement results on a nominal scale must take these features into account. Otherwise, erroneous conclusions may be made regarding the assessment of systems that do not correspond to reality.
Order scale
The scale is called rank (scale of order), if the set of admissible transformations consists of all monotonically increasing admissible transformations of scale values. Consequently, the order scale is unique up to a monotonic transformation.
A transformation that satisfies the condition: if , then and 
for any scale values from the domain of definition. The ordinal type of scales allows not only the distinction of objects, like the nominal type, but is also used to order objects according to measured properties. The numbers on the scale determine the order in which objects appear and do not make it possible to say by how much or how many times one object is preferable to another. This scale also lacks the concepts of scale and origin.
Order scale measurement can be used, for example, in the following situations:
· it is necessary to arrange objects in time or space. This is a situation when one is not interested in comparing the degree of expression of any of their qualities, but only in the relative spatial or temporal arrangement of these objects;
· you need to arrange objects according to some quality, but it does not require accurate measurement;
· any quality is measurable in principle, but cannot currently be measured for practical or theoretical reasons.
An example of an order scale would be a scale of mineral hardness proposed in 1811 by the German scientist F. Mohs and still common in geological field work. Other examples of order scales include scales of wind strength, earthquake strength, grades of goods in trade, various sociological scales, etc.
Any scale obtained from an order scale by an arbitrary monotonically increasing transformation of scale values will also be an exact order scale for the original empirical system with relations.
Somewhat more “strong” than ordinal scales are hyperorder scales. Acceptable for these scales are hypermonotonic transformations, i.e. transformations such that for any 
:
only when belong to the domain of definition and 
.
Thus, when measuring on hyperorder scales, the ordering of the differences in numerical estimates is preserved.
Interval scale
Interval scale used to display the magnitude of the difference between the properties of objects. An example of the use of this scale is to measure temperature in degrees Fahrenheit or Celsius. In expert evaluation, an interval scale is used to assess the usefulness of objects. The main property of the interval scale is the equality of intervals. An interval scale can have arbitrary reference points and scale. Consequently, the interval scale is unique up to a linear transformation. In this scale, the ratio of the difference between numbers in two number systems is determined by the scale of measurement.
One of the most important types of scales is interval type. The type of interval scales contains scales that are unique up to a set of positive linear admissible transformations of the form
,
wherea>0; b – any value. The main property of these scales is that the ratios of intervals in equivalent scales remain unchanged:
This is where the name of this type of scale comes from. An example of interval scales is temperature scales. In this case, the function of the permissible conversion of degrees Celsius to degrees Fahrenheit has the form
,
conversely, the permissible conversion function from degrees Fahrenheit to degrees Celsius is:
.
Another example of a measurement on an interval scale can be the “date of event” attribute, since to measure time on a specific scale it is necessary to fix the scale and origin. The Gregorian and Muslim calendars are two specifications of interval scales.
Thus, when moving to equivalent scales using linear transformations in interval scales, a change occurs in both the origin (parameter b ), and the measurement scale (parameter a ).
Interval scales, like nominal and ordinal scales, preserve the distinction and ordering of the objects being measured. However, in addition to this, they also preserve the relation of distances between pairs of objects. Record
means that the distance between and in TO times greater than the distance between x 3 and x 4 and in any equivalent scale this value (the ratio of the differences in numerical estimates) will be preserved. In this case, the relations between the estimates themselves are not preserved.
In sociological research Interval scales usually measure the temporal and spatial characteristics of objects. For example, dates of events, length of service, age, time for completing tasks, differences in marks on a graphic scale, etc. However, directly identifying the measured variables with the property being studied is not so simple.
As another example, consider a mental ability test that measures the time it takes to solve a problem. Although physical time is measured on an interval scale, time used as a measure of mental ability belongs to an order scale. In order to construct a more advanced scale, it is necessary to explore the richer structure of this property.
Typical error: properties measured on an interval scale are taken as indicators of other properties that are monotonically related to the data. When used to measure related properties, the original interval scales become merely order scales. Ignoring this fact often leads to incorrect results.
The following two types of interval scales are most widely used when conducting sociological measurements.
Based Likert scales the degree of agreement or disagreement of respondents with certain statements is studied. This scale is symmetrical in nature and measures the intensity of the respondents' feelings. For example, it contains the following gradations: completely agree (1); somewhat agree (2); I am neutral (3); somewhat disagree (4); completely disagree (5). The points assigned to the answers to the questionnaire questions contained in certain gradations are indicated in brackets.
Using a Likert scale, the opinion (attitude) of employees of an organization can be studied towards various management aspects: the work motivation system, the psychological climate in the team, the policy of innovation, etc.
There are various options for modifying the Likert scale, for example, introducing a different number of gradations (5-9).
Semantic differential scale(semantic differentiation) contains a series of bipolar definitions that characterize various properties of the object being studied. This scale was developed by the American scientist Charles Osgood to measure the meaning of concepts and words, and primarily to differentiate the emotional side of the object of measurement when studying social attitudes. In this way, a person’s reaction in relation to the object being studied was determined.
For example, when assessing the moral climate in a team, when developing a questionnaire, indicators characterizing it are first selected (relationships between employees, relationships between managers, relationships between managers and subordinates, etc.). Then, for each indicator (questionnaire question), a scale is compiled, which is a continuum formed by a pair of antonymous adjectives. The continuum contains seven gradations of relationship intensity. For example, on a question characterizing relationships between employees, the scale has the following gradations:
Very good (+3);
Good (+2);
Rather good (+1);
Neither good nor bad (0)
Rather bad (-1);
Bad (-2);
Very bad (-3).
Each respondent expresses his attitude to the problem under study using the entire set of scales. This type of scale is also often used to determine the image of a brand, store, etc.
Relationship scale
Relationship scale (similarity) is called a scale if the set of admissible transformations consists of similarity transformations
wherea>0 are real numbers. It is easy to verify that in ratio scales the ratios of numerical estimates of objects remain unchanged. Indeed, let objects in one scale correspond to scale values and , and in the other and . Then we have:
This relationship explains the name of the ratio scales. Examples of measurements in ratio scales are measurements of the mass and length of objects. It is known that a wide variety of numerical estimates are used to establish mass. So, when measuring in kilograms, we get one numerical value, when measuring in pounds - another, etc. However, it can be noted that no matter what system of units the mass is measured in, the ratio of the masses of any objects is the same and does not change when moving from one numerical system to another, equivalent one. Measuring distances and lengths of objects has the same property.
As can be seen from the examples considered, relationship scales reflect the relationships between the properties of objects, i.e. how many times a property of one object exceeds the same property of another object.
Ratio scales form a subset of interval scales by fixing the zero value of the parameter b: b = 0. Such fixation means setting the zero point of reference for scale values for all ratio scales. The transition from one scale of relations to another scale equivalent to it is carried out using similarity (stretching) transformations, i.e. changing the measurement scale. Ratio scales, being a special case of interval scales, when choosing a zero reference point, preserve not only the relations of the properties of objects, but also the relations of distances between pairs of objects.
Difference scale
Difference scales are defined as scales that are unique up to shift transformations
b – real numbers. This means that when moving from one number system to another, only the origin changes. Difference scales are used in cases where it is necessary to measure how much one object is superior to another object in a certain property. In difference scales, the differences in numerical estimates of properties remain unchanged. Indeed, if -
assessments of objects and on the same scale, and 
And 
-
on another scale, we have:
Examples of measurements on difference scales include measurements of the increase in enterprise production (in absolute units) in the current year compared to the previous year, an increase in the number of institutions, the amount of equipment purchased per year, etc.
Another example of a measurement on a difference scale is chronology (in years). The transition from one chronology to another is carried out by changing the starting point.
Like ratio scales, difference scales are a special case of interval scales obtained by fixing a parameter a (a= 1), i.e. choosing a measurement scale unit. The starting point in difference scales can be arbitrary. Difference scales, like interval scales, preserve the relations of intervals between assessments of pairs of objects, but, unlike the ratio scale, they do not preserve the relations of assessments of the properties of objects.
Absolute scale
Absolute scale –in which the only valid transformations are identity transformations: . It means that there is only one mapping of empirical objects into a numerical system. Hence the name of the scale, since for it the uniqueness of measurement is understood in a literal absolute sense.
Absolute scales are used, for example, to measure the number of objects, objects, events, decisions, etc. Natural numbers are used as scale values when measuring the number of objects when objects are represented by whole units, and real numbers if, in addition to whole units, parts of objects are also present.
Absolute scales are a special case of all previously considered types of scales, therefore they preserve any relationship between the numbers of estimates of the measured properties of objects: difference, order, ratio of intervals, ratio and difference of values, etc.
In addition to these, there are intermediate types of scales, such as, for example power scale() and its variety logarithmic scale ().
Figure 3.6 shows the relationship between the main types of scales in the form of a hierarchical structure of the main scales.
Fig.3.6. Hierarchical structure of the main scales
Here the arrows indicate the inclusion of sets of admissible transformations of more “strong” to less “strong” types of scales. Moreover, the scale is “stronger” the less freedom in choice . Some scales are isomorphic, i.e. equivalent. For example, the interval scale and the power scale are equivalent. The logarithmic scale is equivalent to the difference scale and the ratio scale.
Naming and order scales are quality scales. The scale of names describes the difference or equivalence of objects, and the scale of order describes the qualitative superiority, difference of objects. In these scales there is no concept of origin and scale of measurement.
Interval, ratio, difference and absolute scales are quantitative scales. In these scales there are concepts of origin and scale, which are chosen arbitrarily. Quantitative scales allow you to measure how much (interval and difference scales) or how many times (ratio and absolute scales) one object differs from another according to a selected indicator.
The choice of a particular scale for measurement is determined by the nature of the relationships between the objects of the empirical system, the availability of information about these relationships and the goals of decision-making. The use of quantitative scales requires significantly more complete information about objects compared to the use of qualitative scales.
Attention should be paid to the correct alignment of the selected measurement scale with the goals of the solution. For example, if the goal of the decision is to organize objects, then there is no need to measure the quantitative characteristics of objects; it is enough to determine only the qualitative characteristics. A typical example of such a solution is the determination of the best enterprises. To solve this problem, as a rule, it is not necessary to determine how much or how many times one object is better than another, i.e. There is no need to use quantitative scales for this measurement.
Let us consider the main types of measurement scales and the corresponding groups of permissible transformations.
All scales are divided into two groups - scales of qualitative characteristics and scales of quantitative characteristics.
Qualitative scales include nominal and ordinal scales.
Name scale (nominal scale). The measurements on this scale are designed to distinguish objects. That is, only two relations are fixed: “equal” and “not equal”. The only permissible operation with measurements on a nominal scale is counting. This is how characteristics such as people’s proper names, nationality, and names of settlements are recorded. Mathematical operations such as addition or multiplication are not allowed with such measurements. It makes no sense to add up, for example, phone numbers.
Ordinal scale is a ranking scale in which numbers are assigned to objects to reflect the relative strength of certain characteristics in certain objects. The simplest example is student assessments. In this scale you can set your professional status. The data table contains information on only three empirical relationships: ”<, >, =”. Valid transformations for this type of scales are all monotonic transformations, i.e. those that do not violate the order of the values of the measured quantities. Such data does not contain information on how different one rank is from another.
As numerous experiments have shown, a person answers questions of a qualitative, for example, comparative, nature more correctly (and with less difficulty) than quantitative ones. Thus, it is easier for him to say which of two weights is heavier than to indicate their approximate weight in grams.
Quantitative scales include: “interval scale”, “ratio scale”, “absolute scale”.
Interval scale This is a numerical scale in which quantitatively equal intervals are displayed. An interval scale contains not only all the information contained in an ordinal scale, but allows you to compare the differences between them. The difference between two adjacent scale values is identical to the difference between any two other adjacent interval scale values. There is a constant or equal interval between the values on an interval scale. The interval scale is used, for example, when measuring temperature.
In an interval scale, the location of the reference point is not fixed. The reference point and units of measurement are chosen arbitrarily. Any linear transformation preserves the properties of the scale. Here x– initial scale value, y– converted scale value, b is a positive constant.
On the relationship scale Compared to the interval scale, the starting point is also determined. Well-known examples of measurements on this scale are height, weight, and amount of money. Relative scales only allow conversion. The following values have the same empirical meaning: 12 kg, 12,000 g, 0.012 t.
Absolute scale admits transformation only in the form of identity. This type of scale is convenient for recording the number of elements in some finite set. If, after counting the number of apples, one researcher writes the value 6 into the data table, and another VI, then it is enough to know that 6 means the same thing as VI, that is, 6 = VI.
The relative information content of measurements in different scales increases in the order in which the scales are considered. Different scales require the development of their own methods of analysis. When considering characteristics measured on different scales together, methods for converting measurement scales are used. Converting data from one scale to another is possible only by reducing the power of the scale.
Types of scales
Measurement scales are usually classified according to the types of measured data, which determine the mathematical transformations acceptable for a given scale, as well as the types of relationships displayed by the corresponding scale. The modern classification of scales was proposed in 1946 by Stanley Smith Stevens.
Name scale (nominal, classification) Used to measure the values of qualitative characteristics. The value of such a feature is the name of the equivalence class to which the object in question belongs. Examples of the meanings of qualitative characteristics are names of states, colors, car brands, etc. Such characteristics satisfy the identity axioms:
- Either A = B, or A ≠ B;
- If A = B, then B = A;
- If A = B and B = C, then A = C.
Of the scales considered, the first two are non-metric, and the rest are metric.
The issue of the type of scale is directly related to the problem of the adequacy of methods for mathematical processing of measurement results. In general, adequate statistics are those that are invariant with respect to admissible transformations of the measurement scale used.
Use in psychometrics
Using different scales, different psychological measurements can be made. The earliest methods of psychological measurement were developed in psychophysics. The main task of psychophysicists was how to determine the relationship between the physical parameters of stimulation and the corresponding subjective assessments of sensations. Knowing this connection, you can understand what sensation corresponds to this or that sign. The psychophysical function establishes a relationship between the numerical value of the physical measurement scale of a stimulus and the numerical value of the psychological or subjective response to that stimulus.
Some common scales
- Temperature scales of different countries and times (Celsius, Fahrenheit, Kelvin, etc.)
see also
Notes
Wikimedia Foundation. 2010.
Synonyms:- Schroeder, Gerhard
- Heresy
See what “Scale” is in other dictionaries:
scale- (lat. scala ladder) a tool for measuring the continuous properties of an object; is a numerical system in which the relationships between various properties of objects are expressed by the properties of a number series. In psychology and sociology, various Sh.... ...
SCALE- SCALE, scales, women. (Latin scala ladder). 1. Ruler with divisions in various measuring instruments. Thermometer scale. 2. A series of quantities, numbers in ascending or descending order (special). Patient temperature scale. Disease scale. Scale... ... Ushakov's Explanatory Dictionary
SCALE- see ROCK. Dictionary of foreign words included in the Russian language. Pavlenkov F., 1907. SCALE, or ROCK i.e. a ruler with divisions on a thermometer, barometer and other physical instruments; also used in a broader sense to mean... Dictionary of foreign words of the Russian language
scale- s; pl. scales; and. [from lat. scala ladder] 1. Marks (dashes) and numbers on the reading device of a measuring device (serve to determine which values); ruler or dial with divisions in various instruments. Sh. thermometer. Sh... ... encyclopedic Dictionary
Scale I - E- Scale I E (from the English internal external internal external) psychodiagnostic questionnaire, author J. Rotter. Scale for identifying locus of control. Initially it contained 29 items, each of which was represented by two opposite... ... Psychological Dictionary
SCALE- SCALE, s, plural. scales, scales, scales, women. 1. A ruler or table with marks and numbers on the reading device of the measuring device. Receiver sh. 2. A series of quantities, numbers in ascending or descending order (special). Tariff highway | adj. scale, oh... Ozhegov's Explanatory Dictionary
Scale- a set of different interest rates on certificates of deposit. In English: Scale See also: Certificates of Deposit Financial Dictionary Finam... Financial Dictionary
scale- scale; microscale, grid, vernier, limb, vernier, sensitogram Dictionary of Russian synonyms. scale noun, number of synonyms: 9 vernier (4) ... Synonym dictionary
SCALE F- English scale, F; German F Skala. Sweat. Adorno's scale of authoritarian attitudes, allowing one to compare authoritarianism with anti-Semitism. see AUTHORITARIAN PERSONALITY. Antinazi. Encyclopedia of Sociology, 2009 ... Encyclopedia of Sociology
I-E scale- Etymology. Comes from English. internal external internal external. Author. J. Rotter. Category. Psychodiagnostic questionnaire. Specificity. Scale for identifying locus of control. Initially it contained 29 items, each of which was... ... Great psychological encyclopedia
Measuring scales(from Lat. scala - “ladder”) - a form of fixing a set of features of the object being studied with ordering them into a certain numerical system. Measuring scales are metric systems that model the phenomenon under study by replacing direct designations of the objects under study with numerical values and displaying the proportions of the continuum composition of the elements of the object in the corresponding numbers. Each element of the set of manifestations of the properties of the object under study corresponds to a certain score or scale index, which quantitatively establishes the position of the observed unit on a scale that covers the entire set or part of it, significant from the point of view of the research objectives. The operation of arranging initial empirical data into scale data is called scaling. Measuring scales are the main means of collecting and analyzing statistical material in both applied and theoretical research. They differ depending on the nature of the function underlying their construction. Such a function can serve as: comparison based on decreasing or increasing, ranking, assessment of the intensity of a feature, or assessment of proportional relationships between features. The most general classification of measuring scales has been proposed S. Stevenson . It is based on the sign of metric determinacy. According to this feature, the scales are divided into metric(interval and ratio scales) and non-metric(nominative, order scales).
1. Nominative scales
Nominative scales (name scales) establish the correspondence of a characteristic to a particular class. Objects are grouped into classes based on some common property (equivalence classes) or symbol (notation). It is not necessary that there be an internal relationship between the identified classes. The very name “name scale” indicates that the values on the scale play the role only of class names. One of the common types of nominative scale is the classification of objects into two groups according to the principle “A - non-A” (alternative features in a dichotomous scale of names). Specific examples of the use of such a scale are the assessment of a subject’s response to a questionnaire item in the form of an affirmation or negation, the correspondence or non-compliance of the received type of answer with the key (code) of the property being measured (see personality questionnaires).
An example of assessment on a nominative scale can be the classification of solutions to a test problem or a questionnaire item with a closed-type problem.
Of the named cities, the city located to the north is…
2) Nizhny Novgorod;
3) Volgograd;
4) Novosibirsk;
5) Krasnoyarsk.
The opposite of generous is...
1) wasteful;
2) stubborn;
3) cowardly;
4) stingy;
5) generous.
Another simplest type of nominative scale is a list or set of any characteristics that are grouped when collecting information or processing it.
Do you prefer to spend your leisure time...
1) with comrades and friends;
2) in the lap of nature;
3) in sports;
4) with family, etc.
The distribution of features in the classes of the naming scale can be characterized by determining the absolute and relative frequencies of occurrence; it is also possible to determine the modal and central values in the classes. Assessing the statistical relationship between groups of characteristics is possible using correlation analysis (see correlation of qualitative characteristics).
If one of the series of variables is presented on a dichotomous scale of names, and the other on any other scale (internal, relational or ordinal), then biserial correlation coefficients are applied. Variables on a dichotomous scale can be distributed normally or otherwise, depending on this, the method for calculating correlation coefficients is chosen.
In a strict sense, a nominative scale is not a measurement scale. It allows only the operation of equality and inequality and a more or less differentiated classification of characteristics. At the same time, in psychological research and psychological diagnostics, this type of measurement scale is quite important, especially when recording qualitative information (for example, data from projective techniques when collecting a psychological history, etc.).
2. Ordinal scales
Ordinal scales (ordinal) are designed to divide a set of characteristics into elements connected by the “more-less” relationship and allow variables to be assigned to groups ordered (ranked) relative to each other and representing a certain systemic unity. Ordinal scales make it possible to assess the degree of severity of a trait. They contain at least three classes with a fixed sequence that does not allow permutation. Thus, between two indicators of objects A and B, which have attribute X, three types of relationships are possible: X A = X B; X A ‹ X B ; X A › X B . If there are three objects A, B, C and the relations X A ‹ X B, X B ‹ X C are established between them, it follows that X A ‹ X C. In this case, the values of the differences between the characteristics are not established (the scale is non-metric, there are no units of measurement). The ordering of features in an ordinal scale can be unipolar (when determining classes, they are based on the degree of expression of the property being measured) and bipolar (the division is based on the rank of the degree of approximation to one of the opposite poles of the property).
As an example of unipolar ordering, a scale for assessing the qualities of attention can be given: “very stable / stable / labile / scattered.” An example of assessment using the bipolar principle is the identification of the severity of properties between the polar antonymic characteristics of the properties of personal manifestations:
1) balanced...unstable;
2) sociable... reserved;
3) mobile... slow.
Ordinal scales are among the most common in psychological diagnostics. One of the practical methods for assessing a subject’s results on an ordinal scale is a modification of the Raven’s Progressive Matrices test, in which each answer includes three options that successively approach the correct one. An option for using an ordinal scale could be a closed differentiated response to a questionnaire item:
It happens that I just can’t make a final decision and miss the opportunity to do something in a timely manner.
1. I completely agree.
2. I guess I can agree.
3. Not sure.
4. Rather disagree.
5. I completely disagree.
The ordinal scale allows operations of equality/inequality and comparison by intensity. Compared to the naming scale, it is possible to define median of the distribution, usage rank correlation coefficients And conjugacy(see correlation of qualitative characteristics).
3. Metric scales
The interval scale refers to metric scales in which elements are ordered not only according to the principle of the severity of the characteristic being measured, but also on the basis of ranking the characteristics by size, which is expressed by the intervals between the numbers assigned to the degree of expression of the measured characteristic.
In an interval scale, the zero reference point can be set arbitrarily, and the values of the units and the reference direction can be determined by selectable constants.
The category of interval scale includes scales of standard IQ indicator, T-scores, percentiles and others (see standardization, scale assessments). Interval scale scaling forms the basis of psychometric measurements.
In ratio (proportional) scales, numerical values are assigned to objects in such a way that proportionality is maintained between numbers and objects. The starting point in such a scale is fixed. The scale provides the operations of equality/inequality, greater than/less than, equality of intervals and equality of ratios.
An example of the use of such a scale in psychological measurements is the scale of absolute sensitivity thresholds of the analyzer.
Along with the division of scales into metric and non-metric, there is a classification based on the form of recording empirical data, namely: verbal scales, numerical scales and graphic scales.
In psychological diagnostics, an important practical issue is the assessment of the reliability, unidimensionality and validity of measurement scales. The reliability of the scale is determined based on repeated measures robustness analysis.
Validity is understood as the substantiation of the hypothesis about the suitability of a given scale for measuring criterion quality, the completeness of its reflection and the technical compliance of the scaling procedure itself. By one-dimensionality or proportionality of a scale we mean the comparability of the scaled parameters, the absence of their shifts or proportionality between the positive and negative poles of the scale, the equality of scale intervals or the symmetry of various positions.